COGNITIVE PROCESSES OF LETTER AND DIGIT
IDENTIFICATION
by
Teresa Marie Schubert
A dissertation submitted to Johns Hopkins University in conformity with the
requirements for the degree of Doctor of Philosophy
Baltimore, Maryland
January, 2015
© Teresa Marie Schubert 2015
All Rights Reserved
ABSTRACT
Letter identification, the process of determining letter identities and their positions
from a visual stimulus, has a long research history. Debate remains concerning the levels
of representation involved, as well as the manner in which letter position is coded: letters
must be specified at particular positions. Digit identification, a cognitive process with
arguably parallel goals to letter identification, has been less studied. A central question
concerns overlap between letter and digit identification processes: Given the similarities
between digits and letters as visual symbols, do they share a single identification process
or does processing differ based on stimulus category? This thesis combines two
investigations, concerning the letter position code employed in identification, and the
extent of overlap of digit and letter processing, including variables determining letter and
digit identification speed, accuracy, and error patterns. To address the first topic, I elicit
letter perseveration errors in a character identification task, seeking evidence for the type
of position code which can successfully predict both letter position specificity and
flexibility in word recognition. Consistent with prior results from other paradigms,
conclusions from this study suggest a key role for representing letters based on their
distance from both the beginning and end of the word. Addressing the second topic, I
explore the ability of character frequency, visual similarity, and visual complexity of
letters and digits to predict a categorical distinction in identification performance. In
behavioral experiments with unimpaired readers, I elicit identification errors for mixed
letter and digit strings and same/different judgment response times to pairs of characters,
providing a rich empirical dataset on which to further test the influence of these variables.
The results have implications for our knowledge of letter and digit processing, and are
ii
consistent with a shared identification system in which both character types are
identified. Together these investigations inform cognitive processes of letter and digit
identification, which is the first stage in the reading process. Reading is a skill which is
remarkably automatic, yet not innate, and the study of reading introduces broad questions
about the nature of cognitive and neural processes that evolved to solve other problems in
visual cognition.
Thesis Committee
Michael McCloskey (primary advisor), Cognitive Science
Brenda Rapp, Cognitive Science
Colin Wilson, Cognitive Science
Howard Egeth, Psychological and Brain Sciences
Marina Bedny, Psychological and Brain Sciences
iii
ACKNOWLEDGMENTS
The completion of this dissertation would not have been possible without the
support of numerous people; I mention only the most salient here.
I would like to thank Mike and Brenda, who never stopped asking hard questions
and pointing out the ugly facts to ruin my beautiful theories. I could not have asked for
better mentors. Thanks also to my other committee members, Colin, Marina, and
Howard, for insightful questions about my research and productive discussions of big
picture issues.
Thanks to my parents, Margaret and Peter, and my sister, Christina, for always
believing in me (and teaching me how to make chocolate cake along the way).
Thanks to Darko, Laura, and Megan for beautiful friendships near and far.
Thanks to my officemates, past and present (but especially past, but especially present),
for keeping me sane with coffee, chocolate, and snowflake breaks. All remaining stupid
questions will be sent via email. Thanks to Bob, Dan, and Chris for always being on-call
to play board games, often with very little notice.
And lastly, thank you to my husband, Carter, for his unwavering faith in me
through everything.
I would like to dedicate this dissertation to my brother Joe, whose life inspired me in
countless ways.
iv
TABLE OF CONTENTS
ABSTRACT ....................................................................................................................... ii
ACKNOWLEDGMENTS .............................................................................................. .iv
TABLE OF CONTENTS ................................................................................................. v
LIST OF TABLES ............................................................................................................ x
LIST OF FIGURES ......................................................................................................... xi
CHAPTER 1: INTRODUCTION .................................................................................... 1
Overview of the dissertation ........................................................................................ 3
CHAPTER 2: LETTER IDENTIFICATION ................................................................ 5
Goals of letter identification ........................................................................................ 7
Invariance over visual forms ................................................................................ 8
Representing position ......................................................................................... 10
Invariance over position ..................................................................................... 10
Theories of letter identification ................................................................................. 12
Bigram-Based Theories of Letter Identification ................................................. 13
Letter-Based Theories of Letter Identification ................................................... 17
Evidence for stored letter-form representations ........................................................ 21
Evidence from unimpaired participants.............................................................. 23
Evidence from neuropsychological studies ........................................................ 26
Evidence from LHD ........................................................................................... 27
Computational modeling .................................................................................... 33
Revised Caramazza & Hillis theory of letter identification ....................................... 35
v
Position representation in letter identification ........................................................... 36
Letter string similarity ........................................................................................ 37
Empirical evidence for flexible position coding ................................................ 39
Reconciling graded both-edges position coding with previous results ..................... 50
Summary: Letter identification theory under consideration ...................................... 52
CHAPTER 3: DIGIT IDENTIFICATION AND RELATIONSHIP TO LETTER
IDENTIFICATION ........................................................................................................ 54
Digit identification ..................................................................................................... 54
Theories of digit identification .................................................................................. 54
Shared letter and digit identification .................................................................. 57
Separate letter and digit identification ................................................................ 59
Shared identification systems .................................................................................... 64
McCloskey and Schubert (2014) ........................................................................ 65
Review of evidence for shared system ............................................................... 68
Reconciling differential digit and letter accuracy with shared identification ............ 77
Digits comprise a smaller set .............................................................................. 78
Differential role of semantics and/or the right hemisphere ................................ 79
Within-set visual similarity ................................................................................ 80
Character frequency differences ......................................................................... 82
Summary of hypotheses ..................................................................................... 84
Overview of Studies 1-3 ..................................................................................... 84
vi
CHAPTER 4: EXPLORING HYPOTHESES FOR LETTER AND DIGIT
ACCURACY DISCREPANCY (STUDY 1) ................................................................. 86
Methods ..................................................................................................................... 88
Frequency ........................................................................................................... 88
Visual similarity ................................................................................................. 89
Visual complexity............................................................................................... 92
Discriminability .................................................................................................. 92
Results........................................................................................................................ 93
Frequency ........................................................................................................... 93
Visual similarity ................................................................................................. 94
Discriminability .................................................................................................. 96
Visual complexity............................................................................................... 97
Discussion ................................................................................................................ 100
Frequency ......................................................................................................... 100
Visual similarity ............................................................................................... 100
Discriminability ................................................................................................ 102
Visual complexity............................................................................................. 103
Moving beyond set-wise analyses .................................................................... 104
CHAPTER 5: LETTER AND DIGIT IDENTIFICATION STUDIES .................... 106
Letter identification: Confusions and response time ............................................... 106
Inter-letter similarity ......................................................................................... 107
Visual complexity............................................................................................. 108
Letter frequency................................................................................................ 109
vii
Letter and Digit Identification Accuracy (Study 2) ................................................. 112
Methods ............................................................................................................ 113
Long Duration Experiment Results .................................................................. 118
Main Experiment Results ................................................................................. 118
Discussion......................................................................................................... 125
Response Times in Letter and Digit Same/Different Judgments (Study 3)............. 130
Methods ............................................................................................................ 131
Results .............................................................................................................. 134
Discussion......................................................................................................... 143
General Discussion .................................................................................................. 150
Differences between Study 2 and Study 3 ........................................................ 151
Shared identification systems ........................................................................... 152
CHAPTER 6: POSITION IN LETTER IDENTIFICATION (STUDY 4) .............. 154
Methods ................................................................................................................... 156
Long Duration Experiment ............................................................................... 157
Accuracy and Perseveration Analyses .............................................................. 158
Perseveration Position Analyses ....................................................................... 159
Long Duration Experiment Results ......................................................................... 163
Main Experiment Results ........................................................................................ 164
Perseveration and position analyses ................................................................. 165
Syllable-based schemes .................................................................................... 172
Discussion ................................................................................................................ 174
Conclusions about the level of position representation .................................... 178
viii
CHAPTER 7: GENERAL DISCUSSION .................................................................. 181
Summary of experiments ......................................................................................... 181
Study 1 .............................................................................................................. 181
Study 2 .............................................................................................................. 182
Study 3 .............................................................................................................. 183
Study 4 .............................................................................................................. 184
Conclusions.............................................................................................................. 186
Future directions ...................................................................................................... 187
APPENDIX A: CHARACTER FEATURE SET ....................................................... 192
APPENDIX B: CHARACTER CONFUSION MATRIX ......................................... 198
APPENDIX C: SAME/DIFFERENT RESPONSE TIMES ...................................... 201
BIBLIOGRAPHY ......................................................................................................... 205
VITA............................................................................................................................... 218
ix
LIST OF TABLES
Table 2.1: LHD‘s performance on Same/Different tasks ................................................. 33
Table 4.1: Perimetric complexity comparisons.......... ...................................................... 98
Table 4.2: Number of pixels comparisons ........................................................................ 99
Table 5.1: Predictor variables for by-character error rate and Same trials ..................... 115
Table 5.2: Predictor variables for substitution errors and Different trial.........................117
Table 5.3: By-character dependent measures..................................................................120
Table 5.4: Significant predictor variables in regressions of substitution data ................ 124
Table 5.5: Significant predictor variables in regressions of Different pair RT data ....... 140
Table 6.1: Results of non-syllabic position schemes ...................................................... 166
Table 6.2: Results of adding schemes to Narrowly-graded Both-edges scheme ............ 169
Table 6.3: Results of adding Narrowly-graded Both-Edges scheme to other schemes...171
Table 6.4: Results of syllabic scheme analyses...............................................................173
Table A1: Features for uppercase letters and digits........................................................193
Table A2: Rules for computing feature overlap ............................................................. 195
Table A3: Feature overlap matrix ................................................................................... 196
Table B1: Behavioral confusion matrix from Study 2 .................................................... 199
Table C1: SameAll and Different response times from Study 3 .................................... 202
Table C2: SameFirst RT from Study 3 ........................................................................... 204
x
LIST OF FIGURES
Figure 2.1: Simplified schematic of letter identification and reading processes ................ 6
Figure 2.2: Abstract letter identities as a common code ..................................................... 7
Figure 2.3: Revised theory of letter identification ............................................................ 35
Figure 3.1: Shared theory of letter and digit identification ............................................... 58
Figure 3.2: Separate systems theory of letter and digit identification .............................. 62
Figure 4.1: The four fonts used in Study 1 ....................................................................... 90
Figure 5.1: RT dendrogram computed from Different trials .......................................... 136
xi
CHAPTER 1: INTRODUCTION
Though reading is a skill which has to be explicitly taught, literate adults are
astonishingly fast, needing as little as 50 milliseconds of exposure to accurately read a
word in a normal sentence context (Rayner, Inhoff, Morrison, Slowiaczek, & Bertera,
1981). In addition to this extreme speed, readers can also recognize 26 Latin letters
(most with a distinct upper- and lowercase form) across a wide variety of visual inputs,
including countless typewritten fonts, handwriting styles, and variation in size, position,
and color. Even novel forms of letters, such as those written in unusual fonts or a
stranger‘s handwriting, are recognized with relatively little difficulty. The input to
reading begins at the retina, and the first step of reading is letter identification. This
process culminates with activation of a single letter identity. Letter identities are abstract
entities, corresponding not to a physical stimulus but to a concept of identity which is
shared across many stimuli: ‗A‘, ‗A‘, ‗A‘, ‗a‘, and ‗a‘ are all instances of the [A] identity.
Research on letter identification explores the representations and processes which
allow identities to be selected. In particular, what are the intermediate representations
which allow identification to occur? Multiple letters (forming a word or string) are often
identified in parallel, adding a need to represent not only the identity but also the position
of each element. The ability to accurately represent position allows the words CAT and
ACT to be distinct lexical items, though they are distinguished only by the relative
positions of their constituent letter identities. Therefore, in considering the computation
of a letter identity one must also consider the manner in which position is coded to
maintain the order of identities in the input.
1
Like letters, digits also occur as elements of combinatorial strings, and the digits
must be identified before further processing of the strings can occur. Again, the position
of digits is vital, distinguishing 84 from 48. Given these basic similarities between letters
and digits—and others to be explored in later sections—an interesting question concerns
the extent to which letter and digit identification processes are overlapping or identical.
Conceptual processing of digits differs from letters in that individual digits have meaning
while letters1 do not; at present it is unclear whether this high-level difference influences
the character identification processes. Much prior work has focused on letter
identification, leaving open a number of parallel questions about the identification of
digits.
In this dissertation I examine both letter and digit identification. I consider
identification processes that begin with visual input of an alphanumeric stimulus, and
conclude with specification of the identities of the letters and/or digits present in the
stimulus along with their positions. In addition to exploring the representations and
processes involved in these computations, I evaluate the extent to which they can be
considered as a single shared identification system.
As an example of more general object identification processes, the study of letter
and digit identification has the advantages of a relatively circumscribed set of twodimensional stimuli and a small set of identities: 26 Latin letters and 10 Arabic numerals.
Though the processing of letter and digit stimuli is strongly tied to language processing
and is often thought to be distinct from identification of non-symbolic visual objects,
principles uncovered in letter and digit identification may apply more broadly. The
ultimate goal of the study of letter identification and reading is a theory that is capable of
1
With the possible exception of the one-letter words ―I‖ and ―a.‖
2
accounting for the success readers achieve across such a wide variety of inputs. Such a
theory would suggest precise diagnoses and treatments for acquired dyslexias in letter
identification (‗peripheral dyslexias‘), and combined with an account of how the
identification system is acquired in children it would provide the same for developmental
dyslexias. Additionally, a complete theory of the process could be formalized into a
computer model which would be capable of human-like identification performance, and
would have utility in industry and clinical contexts.
Overview of the dissertation
The work in this dissertation involves data from an individual with acquired
dyslexia and unimpaired adult participants; the latter experiments serve as follow-up
studies to extend and confirm the neuropsychological findings. First I review relevant
research on letter and digit identification, respectively, and their overlap. Chapter 2
addresses letter identification, reviewing the literature of letter identification theories and
computational models as well as work published in Schubert and McCloskey (2013)
leading to a revised theory of letter identification which will be the basis for the
remainder of work in the dissertation. In Chapter 3 I review the small literature
addressing digit identification, and consider two proposals for letter and digit
identification: separate identification systems, and a single shared system. In favor of the
latter view I review recent evidence published by McCloskey and Schubert (2014) as
well as the broader literature. Chapter 4 contains analyses of the properties (e.g., visual
similarity) of letter and digit stimuli, considering the two categories as sets (Study 1).
Chapter 5 describes two studies conducted with unimpaired participants exploring the
dynamics of the shared systems hypothesis of letter and digit identification (Studies 2 and
3
3) through a delayed typing character identification task and a same/different judgment
task on pairs of characters. Chapter 6 returns to letter identification specifically to
consider the nature of position representation with a study of perseveration errors elicited
from unimpaired participants (Study 4). Chapter 7 concludes the dissertation with a
general discussion, conclusions, and directions for future research.
4
CHAPTER 2: LETTER IDENTIFICATION
Letter identification operates over visual information and produces as an output
one or more letter identities corresponding to the input. Though some disagreement
exists on this issue, a majority of researchers agree that (for alphabetic writing systems)
letters are a vital unit of abstract orthographic structure for word recognition and reading
(see Frost, 2012, and commentary; also Grainger, 2008, for review).When multiple letters
are processed simultaneously, the position as well as the identity of incoming stimuli
needs to be represented. Once identified, the representations of the letters and their
positions serve as input to central reading processes which accomplish access to semantic
and/or phonological information about the string. Figure 2.1 presents a simplified
schematic of the components of the letter identification and reading systems; this
schematic will be enriched and revised throughout the dissertation in line with both past
research and new findings.
5
Figure 2.1: Simplified schematic of letter identification and reading processes.
After letter identification, the central reading processes consist of lexical and sublexical processes, which deal with whole words and sub-word parts, respectively. These
will not be considered here aside from the orthographic lexicon, which is the first
processing stage on the lexical route (left side of Figure 2.1) and the long term memory
store of orthographic words. The orthographic lexicon contains information about which
letters, and in what order, comprise the words that an individual knows. The combined
processes of letter identification and accessing the orthographic lexicon are sometimes
referred to as ‗word recognition‘ rather than reading; the latter entails access to semantics
and/or phonology.
Abstract letter identities may also be mapped to their corresponding letter name
(e.g., /bi/ for [B]), one of many possible written forms (e.g., lowercase handwritten b ), or
another form of output such typing. These mappings are depicted in Figure 2.2. The
6
assumption is that abstract letter identities serve as a common code for converting
between different types of information, including visual (as letter identification) and
motor information (as writing or speaking letter names; Besner, Coltheart, & Davelaar,
1984; Brunsdon, Coltheart, & Nickels, 2006; Hillis & Caramazza, 1995; Margolin &
Goodman-Schulman, 1984; Rothlein & Rapp, 2014; Tainturier & Rapp, 2003). This
view is not universal; some researchers assume that the abstract orthographic units which
are the end product of letter identification are reading-specific (e.g., Behrmann, Plaut, &
Nelson, 1998; Dehaene, 2009). Though letter identification is the focus of this
dissertation, the path to various modes of output is relevant for interpreting results of
varying orthographic tasks (letter naming, copying, spelling, etc.).
Figure 2.2: Depiction of abstract letter identities as a common code for multiple types of
representations for output and further processing.
Goals of letter identification
There are a number of goals that letter identification needs to accomplish. Three
major ones will be discussed here: identity invariance over visual forms, encoding of
7
letter identity position, and identity invariance over positions. These describe the qualities
of a sufficient letter identification process.
Invariance over visual forms
Identity invariance over visual forms refers to the need to recognize stimuli
referring to the same letter identity (e.g., [A]) when they appears in different visual
forms. A letter can appear in a number of different ways by varying the case (a, A), style
(a, a), and even material (e.g., A in pebbles on a beach). Despite the varying visual
appearance of these stimuli, they all correspond to a single identity; the identification
process must be able to handle this variation in input and still activate an invariant
identity.
Unusual visual forms
Different proposals exist for how very unusual letter forms are recognized. One
approach, as suggested by Hofstadter, is that the representations of letter shapes used in
identification may be quite abstract (Hofstadter & McGraw, 1995). For example,
describing lowercase q as a vertical line and a truncated ellipse could obscure the fact that
q and q also correspond to forms of q. Rather, a more abstract description such as a
‗stick‘ (term intended to give more leeway: straight or curved, vertical or slanted) on a
‗loop‘ (i.e., closed region) would capture these more unusual examples.
Though it is true that the perceptual system will identify these unusual letter
exemplars, it is not clear that the same identification computations occur for unusual
forms as for the more standard forms with which we have extensive daily experience. A
number of results have indicated that letter identification is slowed by novel and/or mixed
8
fonts and speeded by experience with a previously-unfamiliar font and the use of
consistent fonts (Gauthier, Wong, Hayward, & Cheung, 2006; Sanocki, 1987, 1988;
Sanocki & Dyson, 2012; Walker, 2008). Sanocki suggested that assistance in identifying
the letters of an unusual font comes from seeing multiple letters in the font, allowing the
perceptual system to ‗tune‘ to the systematic alterations present in the font (1987). This
suggestion is well taken if you consider this unusual letter in isolation: q versus in a
same-font context: queen, where its identity is obvious (font: Ergonome ghijklmnopqrst). By
hypothesis, a basic letter form and the transformations applied to it to derive the surface
forms of the letters are both used by the identification system to recover the basic shape
of each letter. Further, this procedure takes advantage of the systematicities of shape
within a font, and the same procedure is used for each letter within a given font. This
approach assumes that basic letter shapes are represented, perhaps as a collection of
(somewhat-abstract) letter features, and provides an account for how variability in visual
appearance is handled to extract the basic shape, from which the identity is then derived.
Though the question of how unusual letter stimuli are identified is fascinating, the
bulk of reading and word recognition research has focused on letter identification of
fairly standard characters with a few basic shapes (i.e., script/print forms, and
upper/lowercase). These are the forms which provide the bulk of our daily experience
with letters. The suggestion by Sanocki that font-tuning adds on to standard character
recognition processes highlights the need to first understand and detail these underlying
standard processes, and then consider what additions or alterations allow them to contend
with the full range of letters experience in the wild.
9
Representing position
Encoding of letter position becomes relevant when more than one letter is present
in the stimulus, such as in a letter string or word. Various schemes have been proposed
for representing letter positions. These include a left- or beginning-based scheme—often
the default position scheme intended by authors when a specific one is not noted—in
which letter positions are considered based on their position from the leftmost/initial
letter. Under this scheme, CAT would contain a [C] in position 1, [A] in position 2, and
[T] in position 3. Conversely, a right- or end-based scheme counts positions from the
rightmost/final letter, with [C] in position 3, [A] in position 2, and [T] in position 1.
Midpoint schemes consider positions from the center of the letter string (e.g., [C] in
position -1). By contrast to these schemes, which have extrinsic anchor points, other
position schemes assign letter positions based on the context of letter identities in the
stimulus. These include bigram and trigram schemes, which will be described in some
detail when considering existing proposals for letter identification systems. The method
of representing position will determine how positions align in different strings. The
position assigned to a particular letter may vary based on string length, syllable structure
(for words, pseudowords), and the context of surrounding letters.
Invariance over position
Identity invariance over positions must also be accomplished by the letter
identification system. This fact is particularly transparent given the fact that letters in the
Latin alphabet (c.f., Arabic alphabet) appear in the same visual form regardless of their
position in the stimulus. (The exceptions are capitalization of the initial letter in proper
10
names and in sentence-initial position. However, the majority of our experience with
words is with all letters in lowercase.). A g at position 1 refers to the same abstract
identity as a g at position 3; both should map onto the same identity and have the same
letter name. Likewise, a G at position 1 refers to the same identity as a g at position 3
(position invariance combined with visual form invariance).
Davis and Bowers (2006) refer to two problems in letter identification which are
both subsumed by this concept of identity invariance over position. The first is the
‗alignment problem,‘ which is demonstrated with compound words (Davis & Bowers,
2006, p. 549). For example, to know that CAT is contained in TOMCAT the letter
sequence CAT must be represented in a similar fashion despite the differing position of
the letters within the word (though whether and how the positions differ depends on the
manner of representing letter position). The second problem is the ‗dispersion problem,‘
referring to the fact that the reading system seems to extract generalizations about single
letters (e.g., their corresponding phoneme(s)); Davis and Bowers argue that some of this
information does not depend on the position of the letter within a string (2006, p. 550). A
clear example of this type of information seems to be the letter name, which is clearly
invariant across letter positions. Correspondences between letters and phonemes are
another example, though these are often position- or context-specific (e.g., C  /s/ before
I, but C  /k/ before A).
These three basic goals define the desired end-state of letter identification: a string
of abstract letter identities and corresponding positions. This outlines the computational
problem of letter identification: to compute from visual input an abstract letter identity,
11
along with its position.2 Any sufficient theory of letter identification must include
mechanisms that produce this output, given the known variation in letter stimuli. For the
purposes of this dissertation, I will use the phrase ―letter identification‖ to include these
three goals. That is, identification must additionally compute position in order to be a
successful and complete identification process.
Theories of letter identification
Various competing accounts attempt to describe the mental process of letter
identification (e.g., Brunsdon, Coltheart, & Nickels, 2006; Caramazza & Hillis, 1990a;
Davis & Bowers, 2006; Davis, 2010; Dehaene, Cohen, Sigman, & Vinckier, 2005;
Gomez, Ratcliff, & Perea, 2008; Grainger & Van Heuven, 2003; Norris & Kinoshita,
2012; Whitney, Bertrand, & Grainger, 2011). Theories3 of letter identification generally
consider as input the small line segments and curves (i.e., features) which form visual
letter stimuli, and describe the computations which produce orthographic representations
for input to word and nonword reading processes (i.e., orthographic lexicon). Many
theories are built from the foundation of the McClelland & Rumelhart (1981) Interaction
Activation Model (IAM), which accomplishes letter identification in the narrow sense of
2
In addition to letter identities and positions, in certain contexts letter case must be represented, for
example to distinguish between the acronym ‗PET‘ and the noun ‗pet.‘ The case of the letters needs to be
represented up to the level of orthographic entries, so that these word forms can map onto distinct semantic
entries. Therefore, a truly complete theory of letter identification must include representations of letter
case. Further discussion on this point and a proposals for letter case representation can be found in
Peressotti, Cubelli, and Job (2003) and Schubert & McCloskey (2013).
3
Some authors use the terms ‗theory‘ and ‗model‘ interchangeably, though a distinction can be drawn
between a theory, a set of verbal assumptions about representations and processes, and a model, a computer
program which attempts to implement this processing. I will use the term used by a given author to refer to
his/her own work, regardless of whether the theory is instantiated as a computational model. Implemented
computational models will be explicitly noted as such or as a ‗simulation‘. In practice, predictions are
drawn both from formalized simulation work and from the stated commitments of a non- or less-formal
theory. However, in the case of simulations, some aspects of the simulation may not be intended as
theoretical commitments but rather were required implementational details.
12
activating letter identities, but does not deal with the issue of position representation.
Two broad classes of theory can be distinguished: bigram-based, and letter-based. This
classification rests on the most abstract orthographic representation of letters described
by the theory, which is generally the unit which accesses the orthographic lexicon for
word recognition.
Bigram-Based Theories of Letter Identification
A bigram representation combines information about letter identity and letter
position (Dehaene et al., 2005; Grainger & Van Heuven, 2003b; Whitney, 2001a).
Bigrams represent two letters: For example, the bigram [CA] indicates the presence of a
[C] identity, [A] identity, and their relative position: [C] precedes [A]. So-called closed
bigrams represent only adjacent letter positions while open bigrams represent nonadjacent positions, preserving relative ordering. For example, the closed bigram [CA] is
found in the stimulus CAT, and the open bigram [C*A] (and closed bigram [CR]) is
found in the stimulus CRATE. Theorists who posit open-bigram representations
generally indicate a maximum number of intervening characters (or character spaces)
which can separate the two elements of an open bigram. This limits the number of
representations necessary to specify a stimulus, and open-bigram representations also
include closed bigrams which are effectively open bigrams with zero intervening
elements (e.g., when limited to two intervening elements CRATE is represented by [CR]
[C*A] and [C*T] but not [C*E]).
There are three influential bigram-based theories of letter identification: the Bimodal Interactive Activation Model (BIAM, Grainger, Granier, Farioli, Van Assche, &
van Heuven, 2006; Grainger & Holcomb, 2009a; Grainger & Van Heuven, 2003; Madec,
13
Rey, Dufau, Klein, & Grainger, 2011), Local Combination Detector model (LCD,
Dehaene et al., 2005; Dehaene, 2009; Vinckier et al., 2007) and SERIalization Of Letters
model (SERIOL2, Whitney & Marton, 2013). Of these, the first and third have been
implemented in whole or part as computational models.
The BIAM consists of two routes of orthographic coding, one of which contains
bigram representations (Grainger & Holcomb, 2009; Grainger & Van Heuven, 2003b;
Grainger, Granier, et al., 2006; Holcomb & Grainger, 2006; Madec et al., 2011;
Schoonbaert & Grainger, 2004). The bigram route has received the most work and
scrutiny within the theory. It includes three levels of representation: features, letters, and
open bigrams. Features and letters are represented in retinotopic space. Letter detectors
in the ―alphabetic array‖ are duplicated horizontally across near-fixation positions and
identify abstract letters across a small range of sizes, all fonts and both cases (Grainger,
2008; Grainger & Van Heuven, 2003b). A store of open bigrams receives input from the
alphabetic array, representing letter identities and their relative positions. Independently,
the alphabetic array also provides input to a sequential representation of graphemes, for
activation of their corresponding phonemes (on the other processing route). Grainger and
Van Heuven (2003b) implemented the alphabetic array, open bigrams, and orthographic
word units in a computational model; they successfully simulated the results of published
priming studies to support the feasibility of open-bigram representations in word
recognition.
The bulk of work on this model has focused on the level of open bigram
representations. The earliest descriptions of the theory did not include any principled
limit on the number of letters allowed to intervene between the two letters of a bigram
14
(though it was limited to 2 for the purposes of simulation); this was later modified to
specify that two or fewer letters can intervene (Schoonbaert & Grainger, 2004). This
specification allows the model to generate predictions about similarity of letter strings,
which will vary depending on the length of the string.
In recent papers Grainger and colleagues refer to simply the ‗open bigram‘ model
or ‗overlap open bigram‘ model (Grainger, 2008; Grainger, Granier, et al., 2006). The
latter refers specifically to a version of the model in which the alphabetic array is
redefined from a strict slot-based mechanism that receives input from only one position
in the visual field to instead receive input from and represent letters present across a
small number of nearby positions. The strength of a letter in each slot of the array
depends on its distance from the center of that slot‘s receptive field. With multiple letters
active in each slot, the bigram units at the next level will end up representing not only
closed bigrams but also open bigrams with a small number of intervening letters. For
example, if C and A are both active in slot1 and C, A, and T active in slot2, the resulting
activate bigrams will be CC, CA, AC, AA, AT, (ordered combinations of slot1 and slot2
letters); note that this includes some bigrams not actually present in the stimulus,
allowing this theory to predict transposition priming (to be discussed later). The graded
slot-based alphabetic array results in a slightly more principled way to limit open bigrams
to two intervening letters: the cut-off results from the assumed width of the receptive
fields of the alphabetic array.
The Local Component Detector (LCD) theory of visual word recognition, though
similar in some respects to the BIAM, is characterized by strong ties to the
neurophysiology of the ventral visual stream (Dehaene, 2009; Dehaene et al., 2005;
15
Vinckier et al., 2007). This theory proposes a hierarchy of neuronal responses building
up to the abstract representation of words in the Visual Word Form Area (VWFA) in the
left fusiform gyrus (Dehaene, 2009). The representations at each level, or the ‗coded
units,‘ correspond to the size and properties of receptive fields, a construct that carries
through the model even to the level of small words and morphemes (Dehaene et al.,
2005). The earliest stages detect simple visual features, such as oriented line segments.
The next stage of the model represents the shapes of letters as combinations of line
segments, and contains separate sets of neurons coding for the lower and uppercase forms
of letters. To achieve case invariance, units at the following level receive input from the
neurons coding for the lower and uppercase form of a single letter, thereby computing
and representing abstract letter identity. The abstract letter detectors are repeated across
the visual field; though these units achieve identity invariance across visual forms they do
not achieve invariance across position (Dehaene et al., 2005). This bank of detectors is
very similar to the alphabetic array of the BIAM in that retinal position is encoded and
letters are identified in parallel at multiple positions. The next level of representation is
open bigrams, which are also duplicated across the visual field. Bigrams represent
abstract (case- and style-free) letter identities, along with information of which letter of
the bigram is to the left of (preceding) the other, within a given region of the visual field.
By contrast to the open bigrams in the BIAM, these representations are not location
invariant.
The third bigram model: SERIalization Of Letters (SERIOL2), is an alteration of
a previous model, Sequential Encoding Regulated by Inputs to Oscillations within Letter
units, or SERIOL (Whitney, 2001a, 2001b; Whitney & Berndt, 1999; Whitney & Marton,
16
2013). Both models rely heavily on principles of neural computation, modeling letter
recognition in a neurally-plausible manner. The lowest level of representation in
SERIOL2 consists of visual features. These provide input into abstract letter detectors
which correspond to particular retinal positions. The subsequent level represents letters
in a location invariant manner, with input from the position-specific abstract letter
detectors. Finally, open bigrams represent letters and their relative positions, including
representation of word-edges in open bigrams bordering a word boundary. These
representations are quite similar to those posited by Grainger and colleagues, making
largely overlapping though non-identical predictions of orthographic similarity (Lupker,
Zhang, Perry, & Davis, 2014; Whitney et al., 2012).
Letter-Based Theories of Letter Identification
Letter-based theories of letter identification include the Spatial Coding Model
(SCM, Davis & Bowers, 2006; Davis, 2010), Overlap model (Gomez et al., 2008), Noisy
Channel model (Norris & Kinoshita, 2012; Norris, Kinoshita, & van Casteren, 2010), and
two unnamed theories developed by Brunsdon and colleagues (2006), and Caramazza and
Hillis (1990a, 1990b).
The first three of these are computational models of letter identification, and
differ in the manner in which they solve the problem of position representation in
identification. The latter two contain a more enriched description of the levels of
representations involved in letter identification, but do not consistently specify the types
of position representation used.
The Overlap model (Gomez et al., 2008) deals exclusively with position coding
and includes only a single level of letter representations. The model includes uncertainty
17
about letter identity as well as letter position: The elements of a stimulus initially have
imprecise coding along both dimensions but the precision improves with the exposure
duration of the stimulus. In the limit, with unlimited viewing time, the Overlap model
posits that letters have fully specified positions, with no overlap into adjacent positions.
In order to deal with strings of different lengths, each string is aligned by its two ends and
scaled to a set width, resulting in a type of position coding which encodes distance from
the ends as well as the midpoint of the string (Gomez et al., 2008).
The Spatial Coding Model (Davis, 2010; Davis & Bowers, 2006) encodes letter
identities and positions, as well as implementing an orthographic lexicon and the process
of word recognition. Processing begins with letter features, which map onto letter units
and then onto orthographic word units. The spatial coding aspect is the position
representation: Each letter identity has a corresponding position gradient which defines a
distribution over ordinal positions. The distributed nature of the representation implies a
noisy or uncertain coding of letter position; the relative pattern of position across the
letters encodes their relative ordering. More uncertainty (a wider distribution of position
values) is used for longer words, and additional units mark the beginning and end letters
of the string.
The Noisy Channel model of Norris and Kinoshita (2012; 2010) builds from the
premise that the same computations are used in letter identification as in visual object
perception more generally. The basic units of computation are features, letters, and then
words. Norris and Kinoshita conceive of visual perception as a process of recovering
distal stimulus information passed through the ―noisy channel‖ of the visual system. To
this end, letter identification processes attempt to account for the types of degradation the
18
visual system can produce, including perturbations of evidence for the presence of letters,
as well as their identities and positions. Over time the model collects additional evidence
from the stimulus, refining the representations for the letters present. Like the Overlap
Model, the Noisy Channel model achieves a precise coding of letter identity and position
given sufficient presentation time/evidence.
The two remaining theories of letter identification include commitments to three
levels of representation, including one level intervening between visual features and letter
identities. Brunsdon, Coltheart, & Nickels (2006) detail a theory of reading and spelling
as suggested and supported by extensive study of a child with developmental dyslexia.
They posit that letter features map onto a font-free letter representation. The font-free
representations are stored representations, and do not encode the visual features that
e
differentiate different forms of a letter of the same case (e.g., e and ), but do encode case
differences (i.e., e is represented separately from E). This is followed by a case-free
letter representation, or abstract letter identity. One caveat of the font-free
representations posited is that support for these representations came directly from the
observed patterns of impaired and spared performance in a developmental dyslexic
individual, without independent support from cases of acquired dyslexia or normal
readers. As study of a developmental dyslexic individual may not reveal a damaged adult
reading system but rather an abnormally-developed system, this claim would benefit from
additional converging evidence.
In several papers, Caramazza and Hillis (1990a, 1990b) describe a three-stage
reading theory: visual features, letter shapes, and abstract letter identities. The
intermediate level represents the shapes of the letters in the stimulus. The term ‗character
19
shape‘ adopted by Schubert & McCloskey (2013), is a more neutral term for this level
which captures the fact that any visual stimulus consisting of letter-like features will have
a representation at this level, including pseudoletters. The features of the previous level
have been combined into units corresponding to the letters (presumably on the basis of
visual characteristics of the stimulus such as proximity). The character shape is a
constructed representation: character shapes are stored as a collection of activated
abstract orthographic features for a given stimulus. These features are more abstract than
those represented at the visual feature level, with some increased tolerance for changes in
size and position of the feature. This level can be considered to contain a case-specific
and font-specific representation of the letters in the stimulus, without knowledge of letter
identities. Abstract letter identities are represented at the third and highest level of the
theory.
Caramazza, Hillis, and colleagues (Caramazza & Hillis, 1990a, 1990b; Hillis &
Caramazza, 1995; Hillis, Rapp, Benzing, & Caramazza, 1998; Rapp & Caramazza, 1991)
specify that at each level of their theory, the position of elements is represented according
to a particular frame of reference. The levels progress from stimulus-driven to abstract,
with each progressive level sensitive to fewer differences in the visual stimulus. Visual
features are represented relative to the observer in a viewer-based frame of reference. As
a consequence, the contents of this level are updated often, with each change in fixation
or head position. Position at the character shape level is represented by reference to the
stimulus itself, which is considered to have a right and left side and a top and bottom
side. These spatial properties of the stimulus are preserved in the position representation.
However, representations at this level are invariant to the stimulus‘ location relative to
20
the viewer. At the abstract letter level, the position of letter identities is represented
according to their canonical ordering, rather than any relation derived from the visual
stimulus itself. Caramazza and Hillis (1990a, 1990b) further specified that letters occupy
positions with respect to the midpoint of the word. At this level all aspects of the form of
the stimulus have been discarded: The same word presented in different locations, case,
font, or orientation has identical representations.
This theory has been extended and found extensive support in neuropsychological
case studies (e.g., Hillis & Caramazza, 1995; Hillis, Rapp, Benzing, & Caramazza, 1998;
Rapp & Caramazza, 1991; Subbiah & Caramazza, 2000). Patients have been reported
with deficits to each of the three hypothesized levels, with viewer-based, stimulus-based,
and word-based deficits respectively. Schubert and McCloskey (2013) proposed a
number of additions and modifications to the Hillis and Caramazza theory, adding an
intermediate allograph level between the character shape and identity levels, an explicit
representation of letter case, and exploring the properties of allograph representations. In
the following section I review evidence for stored letter representations preceding
abstract letter identities in the literature, as well as other evidence leading to the revised
theoretical account.
Evidence for stored letter-form representations
As discussed above, the letter identification process solves the difficult problem
of identifying a small set of letters from a wide variety of inputs. A literate adult can
recognize letters across numerous printed fonts and across changes in size, color,
orientation, and more. At its core, this process is one of categorization: Inputs are sorted
into one of 26 categories of letter. In addition to varying in visual properties such as size
21
and orientation, which are transformations of a basic letter shape, letters also vary in case
and style. These variations are often arbitrarily related to each other. For example, g and
G are not highly visually similar, yet they represent the same letter identity. Other letter
shapes which are visually related, such as C and G, do not correspond to the same
identity. Mapping directly from the various letter inputs (more accurately, from
representations of their character shapes as visual features) to letter identities is a hard
computational problem due to these considerations (e.g., Finkbeiner & Coltheart, 2009).
This difficult categorization process can be simplified through the use of subcategories: allographs. An allograph is a stored representation of a letter: a particular
letter shape defined by a case (i.e., upper/lower) and a style (i.e., print/script), such as a,
a, and A. Allographs represent the limited set of basic shapes of letters, and abstract over
other visual properties of the stimulus. Thus, the visually distinct forms g and G map onto
separate allographs; however, stimuli varying only in font but depicting the same letter
shape/style (e.g., g and g), will activate the same allograph. Font differences are those
which are systematically related to the letter shape (e.g., to create the font Courier New,
serifs are added to the letters in predictable locations; to create bold type the line weights
are increased), while style differences such as a and a reflect a difference in visual shape
that is to some degree arbitrary.
In the following sections I present empirical evidence in support of allograph
representations in letter identification. As noted previously, most explicit
theories/models of letter identity reviewed here do not include a level of letter
representation intervening between features and letter representations. However, many
researchers—sometimes implicitly—consider letter identification to include a structural
22
description of the stimulus as a precursor to activation of letter identities, analogous to
structural descriptions in general object recognition. However, the term and concept of
‗structural description‘ does not specify whether the representations are stored or
computed for the stimulus, so it is unclear to what extent these representations are
intended to have the same properties as allographs: stored representations of letter shape.
Evidence from unimpaired participants
Few studies have explicitly explored stored font-free/style-specific case-specific
letter representations. Behavioral priming experiments have been one important source
of evidence. In their 1995 paper, Arguin and Bub found that in a letter decision task on
single character targets, only identical primes (e.g., prime - target: A - A) and not crosscase primes (e.g., a – A) had a facilitatory effect on response time. By contrast, when
the task was to name a single letter target, they found robust cross-case priming effects.
They took these results to imply the presence of two types of stored letter representations:
case-specific letter codes, which support letter decision responses; and abstract codes
divorced from letter shape, which support letter naming. This distinction parallels the
distinction between allographs and abstract letter identities, though it does not specify
style-specific allograph forms (only case-specific). Petit and Grainger (2002) reported
very similar results: In a masked priming letter decision task they found that same-case
primes provide more facilitation than cross-case primes, while no such difference was
found in a masked priming letter naming task. Similar conclusions were drawn by Norris
and Kinoshita (2008) from a cross-case same-different matching task with single letters.
On each trial a probe was presented (e.g., a), followed by a masked prime (e.g., A), and a
target letter (e.g., A). The task was to determine whether the target and probe were the
23
same or different. In Experiment 3 of their paper, they manipulated the task so that the
decision was based either on identity matching (e.g., a is the same as a and A) or casespecific form matching (e.g., a is the same as a but different from A), as well as
manipulating the visual similarity between prime and target (e.g., a and A are dissimilar,
c and C are similar). Results indicated that visual similarity only affected response times
in the case-specific matching condition; this task was sensitive to visual similarity at a
case-specific letter level, suggesting that it depended on case-specific letter
representations.
Case-specific letter frequency effects
Further behavioral evidence from unimpaired subjects comes from a letterdecision study by New and Grainger (2011). Participants distinguished between letters
and pseudoletters (re-combinations of letter parts). New and Grainger correlated reaction
time in the letter decision task on a by-letter basis with the written frequency of that letter
(in French). Frequency correlated with RT both in a single-character letter decision task
and a character-in-string (e.g., XXCXX for C) letter decision task. Highest correlations
were found using frequency counts for case-specific forms in initial word position, and
token frequency (letter frequencies weighted by the frequency of the containing words)
rather than type frequency. These frequency-dependent results suggest that the letter
identification system stores case-specific letter representations and tracks their frequency.
The authors noted that prior studies of letter frequency effects have had variable
outcomes; New and Grainger‘s use of a letter-decision task (which can easily be
performed on the basis of activation at the level of stored visual forms, see discussion in
24
‗Evidence from neuropsychological studies‘ section) may have boosted their ability to
find case-specific letter frequency effects.
Jones and Mewhort (2004) compiled case-specific letter frequency counts (token
frequency) for English letters, digits, and typographical symbols from a large corpus (~14
million words) of New York Times articles. In a speeded single letter naming
experiment with uppercase stimuli they found adjusted naming time to correlate with
uppercase letter frequency but not lowercase frequency. The adjustment was subtracting
out the time taken in cued naming of each letter (after a long visual presentation); this
presumably results in values which reflect the visual letter identification processes rather
than letter name production (output) processes, and it is therefore sensible that this
measure is sensitive to case-specific letter frequency.
These studies provide evidence for the use of case-specific letter representations,
though they do not speak to the existence of stored representations of forms within a case
(e.g., a and a). Walker and Hinkley (2003) reported behavioral evidence from normal
subjects in a conjunction memory study indicating that font-free, case-specific visual
letter representations can be used to bind color to shape. They found that accuracy did
not diminish between study and test for within-case but cross-font variations in letter
shape (e.g., b vs. b, [not actual stimuli]). However, when there was a case change
between study and test (within font, e.g., b vs. B), accuracy diminished. They took these
results to indicate that the color is bound to a font-free letter shape representation which
is case-specific. Whether these representations are also style-specific (rather than font)
within a case was unexamined (13 of the 14 fonts they used were print fonts, and results
were not analyzed by font).
25
Turning to neuroimaging and neurorecording methods, Petit, Midgley, Holcomb,
and Grainger (2006) found event-related potentials for letter stimuli consistent with the
computation of case-specific representations; however they did not manipulate font in
their study. Another ERP study from the same group found an early time window in
which signals for the same word written in different fonts diverged; these results accord
with a style-specific representation early in processing (Chauncey, Holcomb, & Grainger,
2008). With fMRI, Gauthier and colleagues (2000) found evidence for sensitivity to font
differences among single letters in a right fusiform region. These results are consistent
with representations of case- and style-specific letter forms in letter identification, with
some indication (from ERP time courses) that these are computed early in processing.
Evidence from neuropsychological studies
Some acquired dyslexic individuals exhibit a preserved ability to distinguish
upright letters from among rotated or reflected letters or to distinguish letters of the Latin
alphabet from letters of other alphabets and pseudoletters, despite an impaired ability to
access abstract letter identities (e.g., Brunsdon et al., 2006; Chanoine, Teixeira Ferreira,
Demonet, Nespoulous, & Poncet, 1998; Dalmás & Dansilio, 2000; Miozzo & Caramazza,
1998; Mycroft, Behrmann, & Kay, 2009; Rapp & Caramazza, 1989; Schubert &
McCloskey, 2013; Volpato, Bencini, Meneghello, Piron, & Semenza, 2012). In the intact
reading system, without assuming allograph representations, the ability to recognize
letters from non-letter or transformed-letter distractors could be accomplished by
accessing abstract letter identities: Letters will activate their associated identity, while
non-letters will not activate any single identity. In acquired dyslexia this may not be
possible if abstract letter identity representations have been lost or are not fully
26
accessible. Patients who are unable to access abstract letter identities but show a
preserved ability to recognize letters from non-letter distractors could be activating stored
visual forms of letters (i.e., allographs) in order to distinguish real letters (have stored
forms) from non-letters (no stored form). Following this logic, the existence of
individuals who have an impaired ability to activate abstract letter identities but an intact
ability to recognize letter forms as known or unknown provide support for a level of
stored allograph representations used in identification. A specific case of this pattern of
impaired and spared performance was found in individual LHD, with acquired dyslexia.
Evidence from LHD
Despite the preceding empirical observations, to my knowledge no researchers
have explicitly integrated both a constructed level of character shape and a stored level
allograph representations into a theory of letter identification. We tested an individual
with acquired dyslexia, LHD, on a number of tasks to provide further evidence for
allographs and investigate their properties (these results and others are reported in
Schubert & McCloskey, 2013). LHD displayed the characteristic described above:
limited ability to activate abstract letter identities, but intact ability to distinguish between
letters and non-letter forms. Through this study we expanded the theory of Caramazza
and Hillis, making explicit the delineation between constructed and stored letter
representations by including both character shape and allograph representations.
LHD, a right-handed woman, was 69 years old when the study began in 2010.
She holds a Master‘s degree and was an avid reader prior to her neurological damage: a
ruptured posterior cerebral artery aneurysm in February 2007. Hemorrhage and surgery
resulted in a large medial and ventral left hemisphere lesion. Brain imaging revealed
27
extensive damage stretching from the occipital pole to the temporal pole, following the
medial portion of the hemisphere, and affecting striate and ventral extrastriate cortex,
with involvement of the hippocampal region, parahippocampal gyrus, lingual gyrus, and
fusiform gyrus.
Letter Identification Deficit
Evaluating LHD‘s performance with respect to the Caramazza and Hillis letter
identification theory revealed that she is able to activate character shapes but unable to
accurately activate abstract letter identities. Testing with naming from oral spelling
revealed that central reading processes are wholly intact (Schubert & McCloskey,
submitted). Once abstract letter identities are activated LHD processes them normally,
including the abilities to produce their corresponding letter names and written forms.
LHD is impaired on tasks which require access to abstract letter identities from
visual input, including letter naming, copy transcoding, cross-case same/different
decisions, and auditory word generation from written letter cues (see Figure 2.2).
Pseudoletter copying confirmed that she correctly represents character shapes (and can
reproduce them accurately). Given the location of this deficit in the cognitive
architecture of letter identification, it provided an opportunity to investigate letter
representations preceding letter identities. A series of letter decision experiments
provided evidence in favor of allographs mediating letter identification.
Letter Decision Experiments
Two sets of pseudoletters were utilized across three letter decision experiments.
The pseudoletters were constructed from letters, with letter parts altered through deletion,
28
addition, and/or movement, and with the constraint that a pseudoletter could not be a
simple translation, reflection, or rotation of a real letter. The first set contains 13
pseudoletters based on the uppercase letters of Arial font. The second set contains 26
pseudoletters based on the lowercase letters of the Segoe UI font. Both base fonts and
therefore all pseudoletters are sans serif. The experiments were conducted with
4-character strings and required a letter/non-letter decision, either to each character or to
the entire string. The results were extremely consistent: LHD was excellent at
distinguishing letter from pseudoletter stimuli. Across the three experiments, she made
only one error in letter decision, misclassifying a single pseudoletter character as a letter.
The stimuli from one experiment were presented for LHD to name the letters and she was
characteristically impaired on this task, with a statistically significant difference between
her performance on letter naming and letter decision.
The result of the letter decision tasks is quite clear: LHD is perfectly able to
distinguish letters from pseudoletters despite her impairment at naming letters. This
result cannot be explained by the existing theoretical framework of character shape
representations and abstract letter identities: Character shape representations cannot
underlie letter decision because they represent both letters and pseudoletters without
distinction. In the unimpaired system, activation at the level of abstract letter identities
could support letter decision but LHD has a demonstrated inability to activate abstract
letter identities normally. If LHD‘s letter decision were based on the activation at the
abstract letter identity level, we would have expected some errors due to pseudoletters
causing erroneous activation of a letter identity, just as letters cause erroneous activation
of other letter identities (resulting in misidentifications).
29
Consequently, LHD‘s intact performance on letter decision provides additional
evidence for a level of allographs which follow character shape representations and
precede abstract letter identities. Allographs are learned representations of the visual
forms of letters; pseudoletters do not have a representation at this level. Given her
demonstrated ability to activate allographs normally in the service of letter decision, we
concluded that LHD‘s deficit is in activating letter identities from this level. This
updated localization of her deficit allowed us to investigate the properties of allograph
representations, as described in the following section.
Allograph Properties
In a series of experiments with LHD we investigated the properties of allographs.
The locus of LHD‘s deficit provided a unique opportunity to determine what is
represented at the allograph level; the deficit spares this level and affects only the
mapping to the subsequent level. We utilized same/different tasks which required a
decision as to whether two letter strings contained the same letters (see Rapp &
Caramazza, 1989 for similar logic and tasks). The logic in these experiments was as
follows: When the decision for a given set of stimuli only required accessing allographs,
LHD should be accurate. However, if the decision required accessing abstract letter
identities, LHD should be impaired. We determined the properties of allographs by
submitting various stimuli to LHD in this way. Four same/different tasks were
conducted, investigating case, style, size, and font. The basic procedure used for all tasks
was the presentation of a pair of three-letter strings to LHD; the pair could be of two
strings that differed in the property under investigation (e.g., Cross-Case) or two strings
that had the same property value (e.g., Same-Case).
30
Same-Case/Cross-Case Same/Different Task. This task utilized the following
Courier New letters: b, d, f, g, h, j, l, m, n, q, r, t, and y, in upper and lower case. LHD
performed with 100% accuracy on Same-Case pairs (e.g., mfh-mfh) but showed a
statistically significant impairment on Cross-Case pairs (e.g., mfh-MFH). Correct
performance on the Cross-Case trials depends on accessing an abstract (case-free)
representation of letter identity; one must determine that the distinct shapes f and F are
both instances of the same letter identity. The accuracy difference across conditions thus
represents a decrement in performance when judgments must be made on the basis of
abstract letter identity.
Same-Style/Cross-Style Same/Different Task. Courier New was used as the print
style and Vladimir Script as the script (i.e., cursive) style; the letters a, d, e, f, g, h, i, j, k,
l, p, q, r, s, t, x, y, z were used. LHD performed nearly perfectly (106/107 correct) on
Same-Style trials, but was impaired on Cross-Style trials (96/108 correct, 89%). This
result suggests that making a decision about the Cross-Style pairs required access to
abstract letter identities and that at least some of the letter forms used are represented
distinctly at the allograph level.
Same-Size/Cross-Size Same/Different Task. All stimuli in this task were in
Courier New font, size 36 or 52. The letters used were: a, b, d, f, h, k, n, p, q, r, s, u, w, x,
y, and z. LHD‘s accuracy was extremely high in both conditions: Cross-Size accuracy
was 98% and Same-Size accuracy was 99%. This result suggests that the differences
between letters across size did not activate distinct allographs, allowing for LHD to
complete the task without need for activating abstract letter identities.
31
Same-Font/Cross-Font Same/Different Task. The fonts used in this task were
Courier New and Consolas; unlike the fonts selected for the Cross-Style task these were
chosen because they have similar letter forms and differ primarily in serif
presence/absence. The same sixteen letter identities from the size task were used, in
lowercase. LHD‘s performance was perfect in both conditions of the task. As in the
Cross-Size task, this result implies that the two font variations activate the same
allographs rather than distinct ones. This finding is particularly striking when
considering the serifs and visual complexity of Courier New: Fluent readers know that
these are irrelevant visual details yet they are comparable in size to features which
differentiate letter identities (e.g., the horizontal serif at the bottom of r is the same size
as the crossbar distinguishing c from e).
To quantify the observation that the serifs and other visual differences between
the two fonts are quite large, I conducted a post-hoc analysis of the visual stimuli,
computing the pixel overlap between the two fonts. Examining first the Consolas letters,
for 5 of the 16 stimuli the most visually similar stimulus (i.e., with the highest pixel
overlap) among the Courier New stimuli was not the same-identity letter. Rather, the
Consolas a is most similar to Courier s, Consolas b to Courier h, and Consolas p, q, and
r to Courier n. Considering Courier New, there are three stimuli which are not most
similar to their same-identity counterpart in Consolas: Courier s is most similar to
Consolas a, and Courier k and r are most similar to Consolas x. This simple analysis
demonstrates that reliance on low-level visual features representing the stimulus precisely
as it appears on the retina would not support perfect performance on the same/difference
task, suggesting that some visual information has been discarded in the identification
32
process. This result supports the conclusion that allograph representations are somewhat
abstract, as well as the intuition that high similarity among letter stimuli is not always
consistent with matching letter identity.
The results of these four tasks, as summarized in Table 2.1, provided evidence for
the properties of allograph representations. We concluded specifically that allographs
represent the distinct shapes of letters: print and script forms, as well as upper and lower
case. Additionally, the Cross-Font and Cross-Size tasks confirmed that allographs
abstract away from irrelevant visual details and size of the stimulus.
Table 2.1: LHD‘s performance on Same/Different tasks
Within property
Across property
Case
Style
Size
Font
Intact
Intact
Intact
Intact
Intact
Intact
Impaired Impaired
Computational modeling
Future studies should seek additional evidence for the role of allograph
representations in letter identification. One source of evidence for the existence of this
level could be computational modeling, providing a formalized version of the
categorization problem of letter identification. With such a model one could seek
evidence for intermediate representations which abstract over certain visual differences in
the input. However, it may be difficult to fully simulate even the somewhat limited
variability of letter stimuli readers commonly encounter, a vital aspect of the
computational problem. Though previous computational models of letter identification
33
have been successful without an allograph level, such models rarely provide letter inputs
which vary in case or style (Chang, Furber, & Welbourne, 2012; Finkbeiner & Coltheart,
2009). One step towards modeling the full range of case and font differences was taken
by Chang et al., (2012): the inputs to their simulation are in both cases, multiple fonts,
and multiple sizes. However, the fonts they present (e.g., Arial, Bookman, Courier New,
Times New Roman, Helvetica, 5x7 dot matrix), while common, hardly address the visual
differences present in letter stimuli (e.g., none of the fonts employ the single-story
lowercase a, none are italicized or script/cursive). Furthermore, the generalization
performance of their model to new fonts (90%, Simulation 2, p. 2777) is hardly humanlike.
Turning from the Latin alphabet to other scripts, a recent paper by Lake,
Salakhutdinov, & Tenenbaum, (2013) describes a hierarchical Bayesian model of lettershape in terms of motor strokes. A basic inventory of motor strokes was learned from a
large dataset of movies of letter productions. After the inventory has been learned, the
model can correctly determine from single exemplar of a letter whether a second stimulus
is an exemplar of the same letter or not. This performance suggests that the model is
using visual information which is relevant to letter identity differences and discarding
irrelevant differences between exemplars of the same letter. However, this study did not
attempt to contend with different allographs of the same identity; each letter had only a
single form (with variation on this form introduced by the humans producing in the letter)
to be matched. In summary, no existing simulation can be considered to fully contend
with the computational problem of letter identity invariance across visual forms.
34
Revised Caramazza & Hillis theory of letter identification
The results from letter decision tasks with LHD, combined with evidence from
other neuropsychological studies and unimpaired subjects, strongly suggest the presence
of an allograph level of representation in letter identification. Therefore, in Schubert and
McCloskey (2013), we proposed a revised version of the Caramazza and Hillis theory
which involves an allograph level subsequent to character shape representations. This
revised theory is depicted in Figure 2.3. As described above, allographs represent the
distinct visual forms of letters. Activation at this level can support a decision about
whether a stimulus is a letter or non-letter character, but it does not provide any
information about letter identity.
Figure 2.3: Depiction of the revised theory of letter identification proposed by Schubert &
35
McCloskey (2013).
These assumptions about the representations used in letter identification answer
how letter identification accomplishes goal 1: Identity invariance over visual forms. To
accomplish goals 2 and 3 requires an account of how positions are represented in letter
identification, which is the topic of the following section.
Position representation in letter identification
Just as different levels of representation in identification employ different units
(e.g., allographs, abstract letter identities), these levels may utilize distinct position codes.
The simplest manner of representing letter position at any level is slot-based coding (also
called channel-based), in which each letter occupies one of a number of discrete
positions. For example, the Interactive Activation Model (McClelland & Rumelhart,
1981) contained just four positions (slots), and was only capable of identifying the letters
in four-letter words. This trivially solves the problem of alignment because each letter is
unambiguously positioned into a single slot, and slot-based coding is sufficient for a toy
dataset. Obviously, however, this is not a complete model of the letter identification
system as we are able to identify letters in strings of varying lengths, and the system for
representing letter position must therefore be considerably richer.
In addition to those reviewed above in the context of letter identification theories,
a number of coding schemes have been used for representing the positions of letters
during identification. A complete list includes position schemes based on the letter
identities present in a string, ‗letter context‘ schemes, and schemes which do not refer to
the identities of other letters in the string (‗extrinsic anchor‘ schemes, terminology from
36
Fischer-Baum, McCloskey, & Rapp, 2010). Letter context schemes include open-bigram
schemes (Dehaene et al., 2005; Grainger & Van Heuven, 2003a; Whitney, 2001a;
Whitney & Marton, 2013) and trigram schemes (Plaut, McClelland, Seidenberg, &
Patterson, 1996; Seidenberg & McClelland, 1989). Extrinsic anchor schemes include
those representing position with reference to the midpoint of the letter string (e.g.,
Caramazza & Hillis, 1990a, 1990b; Gomez, Ratcliff, & Perea, 2008), the first/leftmost
letter (Coltheart, Rastle, Perry, Langdon, & Ziegler, 2001; Davis, 2010; Plaut, 1999), the
last/rightmost letter (Friedmann, Kerbel, & Shvimer, 2010), the closer edge of the string
(first or last, Jacobs, Ziegler, Rey, & Grainger, 1998), and both edges of the string
(Fischer-Baum, Charny, & McCloskey, 2011; McCloskey, Fischer-Baum, & Schubert,
2013). Position schemes based on orthographic syllables (which have some dependence
on the letter identities present) have been used by Zorzi, Houghton, & Butterworth,
(1998), Harm et al., (1999) and Perry, Ziegler, & Zorzi, (2010). These authors have
employed them as the structuring principle of inputs to computational models of reading:
the letters/graphemes are assigned to a specific role (i.e., onset, nucleus/vowel, coda)
within a syllable. These schemes differ in why they have been proposed (e.g., coding
inputs in a neural network, as a suggestion of the code used in human cognition); what
they have in common is that all have been used or proposed for the purpose of
representing letter position.
Letter string similarity
In addition to providing a full description of the representations in the
identification process, the position codes in letter identification also determine the
similarity between letter strings. The slot-based coding of IAM creates a situation in
37
which strings are similar to each other if they activate the same letters in the same slots
(e.g., SNOT and SPOT are similar because they contain the same letters in 3 of 4 slots).
Metrics of orthographic similarity attempt to describe how letter strings are
related and provide a basis for exploring effects of orthographic similarity. One such
metric is Coltheart‘s N (Coltheart, Davelaar, Jonasson, & Besner, 1977), which is an
index of the number of orthographic neighbors (i.e., similar lexical entries) of a word.
This metric only considers two strings as neighbors if they are related by a single letter
substitution; all neighbors are the same length. Furthermore, Coltheart‘s N is binary in
that two words either are or are not neighbors; the N-value for a given word is the
number of other words which are its neighbors. While this metric has had a great deal of
success in accounting for experimental findings thought to be tied to orthographic
similarity, like the IAM it limits similarity to items of the same length. A more recent
metric of orthographic similarity, OLD20, begins to capture both the intuition that the
two strings CAT and CART are highly similar, and empirical data suggesting that these
strings are confusable (Yarkoni, Balota, & Yap, 2008). This metric considers all strings
to have some similarity to all other strings, with similarity determined by the Levenshtein
distance from one string to another, allowing for letter deletions and additions as well as
substitutions (based on the edit-distance metric originally proposed in Levenshtein,
1966). OLD20 can be used to determine orthographic similarity for experimental
purposes, and out-performs Coltheart‘s N in accounting for empirical effects thought to
be due to orthographic similarity (Yarkoni et al., 2008). The gold standard of an
orthographic similarity metric will be derived directly from knowledge of letter position
coding in word recognition, describing the similarity of strings based on their cognitive
38
similarity. That OLD20 provides an improvement over Coltheart‘s N in accounting for
behavioral word recognition data suggests that the true similarity between letter strings is
non-zero for strings of different length, further suggesting that strict slot-based coding is
not a sufficient model of letter position coding.
Empirical evidence for flexible position coding
Peressotti and Grainger (1995) investigated letter position coding with consonant
string stimuli. Use of consonant strings rather than words was an attempt to parse out
bottom-up position coding, involved in identifying any letter stimulus regardless of its
lexicality, from the combined effects of bottom-up and top-down position coding which
may occur with word stimuli (top-down effects in the form of feedback from lexical
processing). Using a primed letter decision task with 3-letter strings (task: determine
whether the target contains either all letters or letters and a typographical symbol), they
found evidence for both position-specific and position-independent letter priming, with
earlier effects of position-specific priming. Given the short length in letters of their
stimuli and the corresponding fact that the positional displacement of letter identities was
small, they suggest that the findings can be accounted for by position-specific letter
detectors with some ‗cross-talk‘ between nearby positions, with greater cross-talk
between adjacent than non-adjacent positions (Peressotti & Grainger, 1995). They do not
specify how position should be considered (e.g., from the left, from the midpoint of the
string); it is irrelevant to their particular results as all of the strings were the same length.
They further suggest that leaky position-specific letter detectors feed activation to
position-independent letter detectors. This approach would later be abandoned by
Grainger and colleagues in favor of an open-bigram position scheme, but it provides a
39
sufficient model of the position effects obtained with 3-letter strings. In addition to the
conclusions of this study, a growing literature of masked priming studies has provided
evidence that letter identification cannot employ strict slot-based position coding.
Masked priming with lexical decision
A large number of priming studies has addressed the issue of position
representation in letter identification. The core paradigm involves a masked prime
stimulus followed by a target stimulus requiring a lexical decision. Researchers compare
reaction time to the target when it is preceded by an experimental prime, with some
hypothesized orthographic similarity to the target, to when it is preceded by a baseline
prime, with less or no similarity to the target. Generally, primes and targets are presented
in different cases to avoid low-level visual overlap (pixels/features) between primes and
targets as a possible source of any facilitation. Three main prime-types are commonly
used: transposed letter (TL), subset, and superset. The latter two are also known as
relative-position priming, as letters of the target are present in the primes in different
absolute positions but the same relative positions4.
Transposition priming has been the most popular paradigm for investigating
position representations in letter identification. TL priming refers to a facilitatory effect
on lexical decision times when primes consist of the target word with two central letters
transposed, (e.g., prime: talbe target: TABLE) (e.g., Forster, Davis, Schoknecht, & Carter,
1987; Perea & Lupker, 2003, 2004; Schoonbaert & Grainger, 2004). There is
disagreement in the literature whether these effects should be compared to the effect of
4
Naturally, the definition of ‗same position‘ depends on the positional scheme that is considered.
When unspecified, researchers may be referring to a left/beginning-based scheme.
40
baseline primes consisting of unrelated letters (e.g., prime: hofhi target: TABLE) or to
primes that contain replaced letters in the TL positions (e.g., prime: tafhe target: TABLE).
The use of the latter, so-called orthographic control primes, is a more stringent and
perhaps appropriate control, as it accounts for the effect of other overlapping letters in the
prime, leaving only any facilitation caused by the two transposed letters themselves
(Lupker, Perea, & Davis, 2008; Perea & Lupker, 2003). Regardless, consensus has been
reached that primes involving transpositions of interior letters of the target lead to
facilitation relative to both completely unrelated and replaced-letter primes. The effect of
transpositions involving the initial and final letters of the target rather than interior letters
are equivocal, and may depend on target word length (Guerrera & Forster, 2008; Perea &
Lupker, 2003; Schoonbaert & Grainger, 2004).
In subset priming, again with masked lexical decision, primes contain a subset of
the letters of the target. For example, the target APRICOT may be preceded by the prime
apct; this experimental condition is compared to an unrelated condition in which
APRICOT is preceded by a prime such as egrl, which does not have any letters in
common with the target. Results with this prime-type reveal that it facilitates reaction
times to the target word relative to unrelated primes (e.g., Grainger, Granier, et al., 2006;
Humphreys, Evett, & Quinlan, 1990; Peressotti & Grainger, 1999; Schoonbaert &
Grainger, 2004; Stinchcombe, Lupker, & Davis, 2012; Van Assche & Grainger, 2006).
The presence of hyphens that shift the subset letters into the same ‗absolute position‘
(e.g., ap--c-t) do not alter the priming effect (Grainger, Granier, et al., 2006; Peressotti &
Grainger, 1999).
41
Superset priming refers to facilitation of processing of a target word with a prime
which consists of all letters of the target plus additions. For example, jusmtice primes the
target JUSTICE, relative to a completely unrelated prime, and the size of the priming
effect decreases with additional letters added (Van Assche & Grainger, 2006; Welvaert,
Farioli, & Grainger, 2008). Recent results have suggested that though superset priming is
more effective than unrelated baseline primes, it is less effective than TL priming, which
is not predicted by open bigram theories (Lupker et al., 2014).
The major conclusion from these masked priming studies can be summarized as
follows: Letter position coding is not strictly slot-based, rather some level of flexibility is
present. Strict slot-based position coding does not predict any transposition priming, as
the transposed letter prime is no more similar to the target than a replaced-letter prime;
any change from the target will produce a non-match in that position. Consider the
example of tafhe: In a slot-based representation the t, a, and e overlap with the
representation of TABLE, and this is the same amount (and locations) of overlap for talbe.
Many researchers conclude in favor of open bigram-based models of letter identification
on the basis of these priming data. Transposed and relative-position priming argue
against closed-bigram schemes, which would code a subset/superset prime and the target
with fairly dissimilar representations (e.g., grdn [GR], [RD], [DN] and GARDEN [GA]
[AR] [RD] [DE] [EN] share only one bigram), and therefore do not predict a large
facilitatory priming effect. However, the transposition and relative priming effects do not
solely support open-bigram representations; the evidence is also consistent with other
types of non-strict-slot position coding. One example is the graded both-edges coding
scheme, which will be described in detail in a subsequent section.
42
These findings inform position representations but do not specify the level at
which these position representations apply. Given the evidence presented for an
allograph level in addition to character shape and abstract letter identity levels, and the
likelihood that these levels could represent the position of their elements in different
ways, it becomes obvious that determining the position representation(s) in letter
identification needs to be specific for a particular level(s) of representation. The question
of what levels give rise to the masked priming effects will be considered next.
Level of priming effects. These masked priming studies—which form the bulk of
the evidence on letter position—have been conducted with unimpaired subjects, so it is
more difficult to know at what particular level of representation the effects arise.
Processing of the stimuli is occurring at all levels of the identification system, though the
experimental conditions may target or manipulate a particular level or levels. The
implications of priming results on letter string similarity depend on the level at which the
effects arise.
The TL and relative priming effects are often thought to arise at a level which
encodes the position of abstract letter identities; prime and target stimuli are generally
presented in different cases to rule out featural or letter shape priming. Transposition and
relative position priming thereby constrain theories about position coding of abstract
letter identities: Position must be represented in a manner consistent with similar
representations for transposed and subset primes compared to intact target words. Lupker
and colleagues (2008) found that letter frequency affects transposition priming, which
suggests that the effect arises at least in part at a stored letter level of representation, such
as the allograph or abstract letter identity levels. However, while the use of cross-case
43
stimuli rules out a locus of effect prior to abstract letter identities, additional influence
may be derived from later levels such as lexical entries.
Many researchers assume that masked priming with a lexical decision task
reflects similarity between the prime string and the word target, involving pre-activation
or partial activation of the lexical entry for the target. This is consistent with a general
failure to find a significant priming effect on nonword targets, as nonwords cannot
benefit from pre-activation in the lexicon. Despite parallel manipulations on the nonword
targets as the word targets and an equal number of trials (due to the lexical decision task),
very few studies have reported priming for nonwords. Some results of nonword target
priming are found in Perea and Carreiras (2008), Perea and Lupker (2003), and
Schoonbaert and Grainger (2004), however the majority of masked priming studies report
no significant effects for nonword targets. Kinoshita and Norris (2009) suggested that
rather than arising at a single level of representation, the priming manipulations may
reflect processing of multiple levels. In this case, some priming at a prelexical level (e.g.,
abstract letter identities) would result in slight facilitation of word and nonword targets.
Priming in lexical access would result in additional priming for word targets, resulting in
stronger and more robust facilitation for words than nonwords.
Several authors have addressed the question of whether these orthographic
priming effects could be instead explained by phonological similarity between primes
and targets. Researchers have determined that transposition and relative position priming
effects do not seem to mirror phonological similarity (Grainger, Kiyonaga, & Holcomb,
2006; Perea & Carreiras, 2006, 2008), suggesting that they arise at a purely orthographic
44
level. However, this does not differentiate between a locus in letter identification and one
in orthographic lexical access.
Same/different matching
Garcia-Orza and colleagues (2010) also reported transposition priming in a samedifferent task (same case) for pseudowords and consonant strings, suggesting that flexible
coding is at play for letters in non-word contexts. Norris and colleagues have recently
applied a similar same-different paradigm with cross-case pairs (Kinoshita & Norris,
2009; Norris & Kinoshita, 2008; Norris et al., 2010). In this task participants are first
presented with a probe item (e.g., TABLE) followed by a masked prime (e.g., talbe) and a
target item (e.g., table). The task is to determine whether the probe and target are the
same word; these two stimuli are always in different cases. In this example, the prime
has a transposed letter manipulation relative to the target. In their 2009 paper, Kinoshita
and Norris report manipulations pointing to the level of abstract letter identities as
responsible for the priming effects in the cross-case same-different matching task. This
conclusion is supported by equivalent priming for word and nonword targets, a lack of
word frequency effect, a lack of letter visual similarity effect, and a lack of effect of
pseudohomophone primes: these results point to a prelexical, abstract orthographic locus
(Kinoshita & Norris, 2009). These are null effects (lack of difference between two
conditions), which weakens the claim somewhat. Research by Fischer-Baum and
colleagues has provided some converging evidence to back up the conclusion that the
position representation of abstract letter identities treats adjacent letter positions as
similar.
45
Illusory word paradigm
Fischer-Baum, Charny, and McCloskey (2011) conducted a study with
unimpaired individuals providing further evidence about position representations in
reading. They used the illusory word paradigm (Davis & Bowers, 2004), in which two
items (words or pseudowords) are simultaneously presented and the participant is
subsequently cued to recall one of the items. Participants often err by reporting some
combination of the cued item and its distractor, such as reporting ―TUNE‖ when cued to
recall TUBE in the presence of TANK. This is a migration error of the N in TANK into
TUBE. Previous research indicated that letters migrate into the same or adjacent position
in the cued item as they occupied in the distractor (Davis & Bowers, 2004). In order to
distinguish between various position representations, which make differing predictions
about what positions are considered the same and adjacent, Fischer-Baum and colleagues
manipulated the distractor item, varying the position of a letter to-be-migrated. For
example, in TANGLE the N is in the third position from the beginning of the word, while
in THRONE the N is in the second position from the end of the word. These were both be
used as distractors for TUBE. They recorded how often a critical migration error (e.g.,
intruding the N from the distractor) occurred in the presence of beginning-based
distractors, end-based distractors, and midpoint-based distractors (e.g., TRANCE). Note
that the distractor items were of a different length than the cued items, allowing for
different position schemes to make differing predictions.
The results of two experiments—one with typed responses and one with spoken
responses—converged to reveal that migration errors most often occurred in the presence
of beginning-based and end-based distractors. In Fischer-Baum et al.‘s results,
46
migrations occurred not only from exact positions but also adjacent positions, suggesting
a ‗graded both-edges‘ coding of letter position. Some terminology will aid in discussing
the results of this and future studies: beginning-based positions are denoted by B+X (e.g.,
B+1 ‗beginning plus one‘), while end-based positions are denoted by E-X (e.g., E-2 ‗end
minus two‘). For example, the response TUNE occurred in the presence of TANGLE (an
exact B+3 match) and also, less often, TRANCE (B+4 is adjacent to B+3). In other
words, immediately-adjacent positions are more similar to each other than positions at a
greater distance, therefore producing some migration errors of letters into adjacent
positions. The authors took these results as evidence for graded both-edges coding of
letter position in reading. However, as with the priming studies described above, the
paradigm and use of unimpaired participants does not allow a particular level of
representation to be delineated. Their evidence for the existence of a both-edges graded
representation of letter position must apply to some representations in word recognition,
yet the particular level or levels are not evident from these results.
Dyslexia
Friedmann, Kerbel, and Shvimer (2010) reported data from developmental
dyslexic individuals who made transposition errors between words when reading word
pairs. They found that in cases when the two words of the pair have different lengths
(and therefore different position schemes make differing predictions), their errors
maintain relative position counting from the final (in Hebrew, i.e., leftmost) letter. They
suggest that these errors arise at the level of abstract letter identities but do not rule out
prior levels (e.g., allographs) as sources.
47
McCloskey, Fischer-Baum, and Schubert (2013) analyzed a large corpus of
reading data from the acquired dyslexic individual LHD (described previously) to draw
conclusions about position representation in letter identification. Because LHD has a
deficit localized to a particular level of letter identification—the mapping between
allographs and abstract letter identities—her errors reflect the position representation of
these levels. Therefore, the conclusions McCloskey and colleagues drew about position
representations on the basis of these errors are specific to the allograph and ALI levels
(for further discussion of this point refer to McCloskey et al., 2013).
LHD‘s primary error type in reading is letter substitution. Of these errors,
perseveration errors—a letter from a previous response occurring as an error in the
current response—form a high proportion. Analyses determined that such errors occur
more often than expected by chance, and are therefore thought to be causally related to
their presence in a previous response (the ‗source‘). Given this relationship, the authors
examined the position of the intrusion and source letter, asking whether the source and
intrusion are in the same position in their respective responses. This requires defining
position, which was done according to a large number of position schemes in order to
contrast their predictions. The schemes tested include those based on a letter‘s distance
from the beginning, end, and/or midpoint of the word; orthographic syllable structure;
and open bigrams within the response. Overwhelmingly, the position scheme
considering distance from the beginning and end of the word was most successful in
accounting for the position of the source and intrusion; when a letter perseverated from
one response to another, it maintained its both-edges position within the response.
Alternative position representations, including open-bigram, syllable-based, midpoint-
48
based, and beginning- or end-based representations alone were less successful in
accounting for the positions of the perseverations errors. Adding the immediately
adjacent positions (‗narrowly-graded‘ both-edges scheme) improved the ability of the
scheme to account for the perseverations, and including second-adjacent positions
(‗broadly-graded‘) improved it further.
McCloskey et al. (2013) concluded that the positions of allographs and ALIs are
represented with respect to the beginning and end of the string, and that the position
representation is graded such that adjacent positions are more similar than distant ones.
Specifically, it was determined that immediately-adjacent positions are highly similar,
and second-adjacent positions are less similar. This similarity is the result of letters being
represented not only at the correct, precise position within the string (e.g., T in CATCH in
the B+3/E-3 positions), but also represented less strongly at immediately-adjacent
positions (e.g., T weakly in B+2/E-4 and B+4/E-2) and to an even lesser degree at
second-adjacent positions (e.g., T more weakly still in B+1/E-5 and B+5/E-1). This type
of position coding can be considered a leaky or ‗sloppy‘ slot-coding scheme: Letters are
represented most strongly at a single position but there is some spillover of activation into
nearby positions.
Another aspect of some letter position theories is the assumption that letter
position is initially coded coarsely (i.e., graded across positions), and longer duration
stimulus presentations improve and fine-tune the representation into a precise position
code. The Overlap model and Noisy Channel Model both include such assumptions. The
data from LHD involves unlimited stimulus duration; under these conditions by
hypothesis a normal reader would come to represent the stimulus letter positions
49
precisely. It is unclear at this point how Gomez, Norris, and Kinoshita would account for
LHD‘s data: Is the result of a deficit in activating abstract letter identities a position code
which cannot be fine-tuned, thereby explaining the success of the both-edges graded
scheme under conditions of unlimited stimulus duration?
The conclusions of McCloskey and colleagues are similar to those found by
Fischer-Baum et al. (2011), but additionally specify the levels of representation at which
graded both-edges coding is used: the allograph and abstract letter identity levels.
Position of allographs and abstract letter identities is coded by approximate distance in
letters from the beginning and end of the word (as canonically-represented, see
Caramazza & Hillis, 1990a, 1990b; Schubert & McCloskey, 2013). Furthermore,
McCloskey et al. reported evidence in favor of broad grading of both-edges position,
while Fischer-Baum and colleagues only tested a narrowly graded version.
Reconciling graded both-edges position coding with previous results
How do the results of McCloskey and colleagues (2013) compare to results from
other studies suggesting that letter position coding is flexible? Studies which found
evidence against strict slot-based coding and instead in favor of similar representations of
adjacent letter positions are consistent with the graded quality of the graded both-edges
position representation. The core finding of many studies—similar representations for
adjacent letter positions—is consistent with any slot-based scheme which includes some
grading or sloppiness in the position representation. However, the broadly-graded both
edges scheme has some particular advantages in accounting for existing data beyond this
basic finding.
50
Here I consider the three main results of masked priming lexical decision studies:
transposition priming, subset priming, and superset priming; and the results of cross-case
same-different matching: transposition priming for words and nonwords. All of these
effects are cross-case (prime in one case, target in the other), suggesting that they must
take place at the ALI level or beyond. Assuming for now that the priming effects arise at
the abstract letter identity level, graded both-edges coding could account for the results.
Transposition priming with adjacent transpositions is easily accounted for by the
narrowly-graded scheme, which states that adjacent positions are highly similar to each
other. Non-adjacent priming is less often found and produces weaker results, consistent
with the suggestion in the broadly-graded scheme that second-adjacent positions, though
similar, are less similar than immediately-adjacent positions.
Subset primes which involve omission of one intervening letter (e.g., grdn for
GARDEN) can likewise be accounted for with the broadly-graded scheme. Subsets with
two omitted letters between letters present in the prime could potentially be explained by
an even more broadly-graded scheme. Superset priming can also be accounted for by the
graded both-edges position scheme: supersets formed by adding one or two letters
between adjacent letters are consistent with the broadly-graded scheme. The finding by
Welvaert and colleagues (2008, see also Van Assche & Grainger, 2006) that superset
priming effects are graded based on the number of added letters accords, as previously,
with the suggestion that immediately-adjacent positions are highly similar, and secondadjacent positions are less similar. The similarity of the string ABCXD to its base string
ABCD is greater than ABCXXD to the base string. In beginning-based position, the
ABC elements are in the same position in all three strings, while in end-based position
51
the C in ABCXD is one position away from the C in the base string, and the C in
ABCXXD is two positions away from the C in ABCD, with the result that ABCXXD is
less similar than ABCXD.
Another empirical finding which is easily accounted for by the graded both-edges
position scheme is that longer word targets generally show greater transposition priming
than short word targets (Forster et al., 1987; Perea & Carreiras, 2008; Perea & Lupker,
2003). This result has often been interpreted as resulting from stricter position coding for
short words than long, with varying numbers of post hoc assumptions to derive that
prediction. In McCloskey et al. (2013) the authors concluded that the graded both-edges
scheme codes letter positions with differential strength according to their position relative
to the anchor point (beginning/end of the word). Specifically, the beginning-based
coding was found to be stronger for letters in the first half of the word, and the end-based
coding stronger for letters in the latter half of the word, with a gradient of strength from
the anchor towards the midpoint. Therefore longer words will have weaker position
coding for the central letters (which are the letters generally manipulated in transposition
priming) than short words, by virtue of the increased distance of central letters from the
word-ends. This entails that short letter strings differing by a single central letter will be
more similar to each other than long letter strings differing by a single central letter, as
the representation of the central letter is weaker and contributes less to the similarity in
the long strings.
Summary: Letter identification theory under consideration
The experiments in this dissertation build from the revised Caramazza and Hillis
letter identification theory (Figure 2.3). This theory posits four levels of processing in
52
letter identification: visual features, character shapes, allographs, and abstract letter
identities. Visual features are represented retinotopically, and consist of oriented edges
and other similar elements of the stimulus. From the active features, character shapes are
computed to represent each letter in the stimulus as a group of more abstract features,
represented with respect to their relative position in the stimulus. Subsequently these
representations activate allographs, which are stored representations corresponding to the
learned basic shapes of letters. Evidence has suggested that allographs are represented
according to the canonical beginning and end of the presented word/string (see Schubert
& McCloskey, 2013) using graded both-edges position coding. Allographs activate
corresponding abstract letter identities at the next level, which are representations of
letter identities divorced from any visual properties. Abstract letter identities are also
represented with respect to the beginning and end of the word/string in a graded bothedges manner. These theoretical commitments will be utilized throughout the remainder
of the dissertation in considering digit identification as well as forming the basis for the
experiments conducted.
53
CHAPTER 3: DIGIT IDENTIFICATION AND RELATIONSHIP TO
LETTER IDENTIFICATION
Digit identification
The goals of digit identification largely parallel those of letter identification.
Identity invariance over visual forms, though it may be less pervasive in digits than in
letters (e.g., digits do not have upper and lowercase forms), is still present in a small
number of distinct shapes (e.g., 4, 4 ) for some digits, in addition to ubiquitous visual
differences across font and handwriting styles (e.g., 4, 4). Encoding of digit position is
vital to digit reading. Unlike in word-reading contexts, when an ordering error may be
recognized if it leads to a nonword, an ordering error in digit reading may not be
immediately obvious, and is therefore potentially more costly. Digit identity invariance
over position is equivalent to that in letter identification. Though the semantic
interpretation of a digit depends on its position (e.g., compare the meaning of the 5 in 529
and 15), the digit identities (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) are represented identically
regardless of position in a string. In summary, the goals and challenges of digit
identification are very similar to those of letter identification, though differences arise in
conceptual/semantic processing of numbers (numerical processing). Analogously to
letter identification, digit identification is the process of determining the digit identities
and positions in a stimulus.
Theories of digit identification
By contrast to the large field of work in letter identification, little work has
focused on digit identification. A few authors have proposed specific theories of digit
identification, while a handful of others have simply noted some key considerations for
the process. First I consider whether the letter identification theories described in
54
previous sections have relevance to digit identification. Of these theories, Gomez‘s
overlap Model, the Spatial Coding Model, and the Local Combination Detectors model
are all specific to letter processing. By contrast, SERIOL2, the theory of Brunsdon et al.,
and the Hillis and Caramazza theory include lower levels (i.e., feature representations,
also font-free representations for Brunsdon) which represent both letter and digit shapes
(Brunsdon et al., 2006; Caramazza & Hillis, 1990a; Whitney & Marton, 2013). On the
other end of the spectrum from the letter-only theories, the Noisy Channel model posits
identification processes for both letters and digits (as instances of general object
recognition; Norris & Kinoshita, 2012).
In a recent adaptation of the open bigram model, Grainger and Hannagan (2014)
revised the conception of the alphabetic detectors to ‗character detectors‘ which index the
presence of a particular character identity (letter or digit) at a particular location in the
visual field. However, they continue to posit that only letter identities participate in
bigram representations at the following level, while digit identities are coded in a more
strict manner without positional uncertainty or flexibility (Grainger & Hannagan, 2014).
This places the open bigram model in the same class as SERIOL2 and the other models
which posit some low-level overlap of letter and digit representations but later divergence
of processing.
In their 1998 paper describing a case of acquired dyslexia, Miozzo and
Caramazza propose a theory of letter and digit identification. Their identification theory
is somewhat similar to that of Caramazza & Hillis (1990a), though without character
shape representations. They posit that digit stimuli activate stored structural descriptions
(i.e., allographs), in parallel with letters. Subsequently, digits directly access semantics,
55
bypassing abstract identity representations and therefore diverging from letter
identification processes.
Cohen and Dehaene (1991) describe a theory of digit processing, focusing on the
later semantic aspects. This theory involves representation of a constructed visual
number form, by analogy to the stimulus-based character shape level of Caramazza and
Hillis. Cohen and Dehaene posit that this representation provides access to semantics for
calculation and comparison tasks and to digit names, but do not address any overlap with
letter identification processes (Cohen & Dehaene, 1991).
In a number of papers, Polk and Farah (1994, 1995, 1998) suggest that due to
differences in experience with letter and digit stimuli, letter and digit identification
processes are likely to exist in distinct neural substrates. They suggest that letters and
digits rarely co-occur in experience while members of the same category often co-occur,
and these two factors combine to pressure the neural system to develop distinct neural
representations. This conclusion was supported by simulation work: Distinct units
developed for digits and letters when the inputs consisted of pure digit and pure letter
stimuli (Polk & Farah, 1995). However, a cognitive account of letter and digit processing
has not been described by these authors.
One important consideration for a digit identification system is the extent to
which it overlaps with (shares levels of representation and computations) or is separate
from, the letter identification system. Of the systems already described, some include
fully separate letter and digit processing (e.g., Overlap model, LCD model), some posit
early overlap of letter and digit processing and later divergence into separate systems
(e.g., Caramazza & Hillis, open bigram model, SERIOL2), while Kinoshita and Norris
56
posit a completely shared system. In a system with purely separate processes for letter
and digit identification, activation and representations in one system would not affect
activation or representations in the other system. Here I describe the assumptions and
commitments of separate and shared letter and digit identification systems. To make the
exercise more concrete I use the revised Caramazza and Hillis letter identification system
described in Chapter 2 (and Schubert & McCloskey, 2013), considering what separate
and shared versions of this system would entail.
Shared letter and digit identification
The primary characteristic of a fully shared (or ‗overlapping‘) identification
system is that there is no distinction between the processing of letter and digit stimuli.
Information about digit/letter category would have no impact on the identification
process, and representations of both types of characters would undergo the same
computations5. The four levels of representation discussed for letters would also be used
for digits. At the first two levels, visual feature and character shape representations for
letters and digits would share overlapping representations. Allograph and abstract letter
identity representations are specific to a given character form or identity, entailing that
letters and digits would activate distinct representations at these levels, but connections
from the character shape level would be present to both letter and digit allographs based
on visual similarity. For example, activation of the feature ―curve opened left‖ (e.g., as
part of the representation for a 3) at the character shape level would activate both the 3
5
To account for the fact that readers can report the category (letter or digit) of a given stimulus,
we could posit a representation of stimulus category which receives input from one of the identification
levels, similar to the suggestion that one output from the allograph level is an explicit representation of
letter case.
57
allograph and also the 5, B, P, and R allographs. Explicit or implicit knowledge about the
category of a given character would not alter processing within the system. A schematic
of this system is shown in Figure 3.1. This type of system is akin to the Noisy Channel
model: an identification system which does not distinguish at any stage between the two
character types.
Figure 3.1: Shared theory of letter and digit identification. Adapted from McCloskey and
Schubert (2014).
The ramifications of a shared identification system are fairly straightforward: The
dynamics of the system would not differ for letters and digits and therefore the other
active representations (and any errors) would not be restricted by category. Errors and
slowed response times in identification would result from strong competitors from either
58
character set. To the extent that visual similarity, frequency, and other variables have
been shown to influence the letter identification system they would also influence digit
identification. Initial support for a shared system of the type just described would be
evidence for digit allographs and abstract digit identities, in parallel with evidence for
these representations for letters. Results that identification errors were independent of the
category of the target stimulus would provide further support; effects of variables such as
visual overlap would be found independently of categorical differences.
Separate letter and digit identification
By contrast to the shared systems hypothesis—predicated on character
identification without regard to character category—the separate systems hypothesis is
built on the premise that letter and digit identification processes differ. Multiple versions
of separate systems hypotheses can be developed which follow this principle. For
example, one might posit different levels of representation involved in letter and digit
identification (e.g., abstract letter identities but no abstract digit identities, as suggested
by Miozzo & Caramazza, 1998, or no digit allographs due to the lack of upper- and
lower-case forms). Separate systems hypotheses of this type would be support by
evidence for the various posited levels of representation specific to each character set.
Another possible meaning of separate letter and digit identification systems could be that
while the computations used for both character types could be the same, they could take
place in different neural substrates. Some authors suggest that distinct neural substrates
would naturally arise due to differing demands and contexts of letter and digit
identification (e.g., Polk & Farah, 1998). The question of neural underpinnings of the
cognitive identification system(s) is not the topic of this particular investigation.
59
A more subtle version of the separate systems hypotheses is one in which the
same levels of representation are employed for both characters but processing differs by
character type (e.g., processing within each level). To explore this type of hypothesis I
will again use the letter identification theory discussed by Schubert and McCloskey
(2013) with the assumption that letters and digits are involved in the same
representational levels.
This theory states that the visual features used for letters also represent other
similar visual objects and therefore can be assumed to represent visual features of digits.
To the extent that letters and digits both contain abstract visual features of the type
represented at the character shape level, processing for letters and digits would continue
to be shared at the character shape level. However, visual differences between the stimuli
(e.g., if a particular visual feature only occurs in digits, never in letters) could lead to nonoverlapping featural representations6. In this instance, stimuli with digit-features would
activate these within the character shape level, while stimuli with letter-features would
activate these within the character shape level, resulting in distinct representations of the
two character types at this level. Regardless of the separation of character shape
representations, representations of letter shapes would map onto letter allographs,
followed by abstract letter identities. Similarly, digit shapes would activate digit
allographs and abstract digit identities, but these representations (recall that both are
stored in long term memory) would be separate from the letter representations.
Activation of an allograph (letter or digit) would inform the identification system of the
6
The feature set used in letter identification is a topic of current research and it is unclear whether
letters and digits consist of distinct or overlapping sets of features. To a reasonable approximation they
appear to involve the same basic inventory of abstract feature (e.g., slanted and orthogonal lines, curves),
but this remains an open question.
60
category of the stimulus (and may also underlie the reader‘s ability to report the same).
Furthermore, and integral to the separate systems, processing at this point diverges
dependent on the stimulus category.
In one version of such a system, an inhibitory mechanism might be in place once
an allograph is fully active which would reduce activation of any allographs of the other
category. (Similar effects would result if any mechanism were in place to restrict the
output to the selected category, or if the cross-category inhibition described here began
before any allograph was fully active.) Consequently, an identification error arising after
the category determination has been made would result in activation of a same-category
competitor. A separate systems account of this type is presented in Figure 3.2.
61
Figure 3.2. Separate systems theory of letter and digit identification. Both types of characters
undergo the same computational steps but once the category of a stimulus has been determined
(at the allograph level) representations corresponding to the other category are inhibited, limiting
processing to a single category.
Without a mechanism restricting output to a single category, potential
competitors (and therefore error responses) could come from either category. A subset of
digit and letter identities would have some activation (particular identities dependent on
the stimulus as well as other factors such as residual activation from the past and resting
activation levels), and in the event that the target is not selected, the strongest competitor
from either category might be selected. However, a system that operates in this way does
62
not follow the separate systems principle of processing determined by the character
category: No differences in the identification processes result from presentation of a letter
versus digit stimulus. This system is not an alternative to the shared system, it is rather a
version of a shared system, following the principle that character category does not
impact the identification process.
The hypothesis described previously—with only one identification system active
at a time—involves processing dependent upon character category and entails separate
systems. Assuming that the correct system is activated, an error (due to the target
identity not being the most active identity) would take the form of another identity of the
same category, and cross-category errors (e.g., miss-identifying 8 as B) would never
occur. The resulting identity will reflect high similarity (e.g., visual feature overlap) or a
robust competitor (e.g., higher frequency) to the target. It is possible that representations
in the other system had activation prior to being inhibited, but these would not be
selected. For example, if abstract letter identities had some residual activation from
previous trials but the current stimulus activated a digit allograph, the letter system would
be inhibited and the residual letter activation would not impact processing. If an error
were to arise earlier in processing such that the incorrect identification system were
activated and the target identification system inhibited, the resulting identity would be
from the incorrect category. By hypothesis a cross-category error would reflect similarity
(e.g., visual feature overlap) between the target and a representation in the other system
which resulted in the wrong system becoming active, and the resulting error would
therefore be similar to the target in this way. Due to the presence of within-category
errors arising from when the correct system (but not the correct target identity) is
63
selected, similarity computed without regard to category would not perfectly predict the
errors produced by these separate systems. Similarity within a category, (e.g., digits with
other digits) will closely parallel the within-category errors, while similarity across
categories will be less successful. Furthermore, perseveration errors (in which a
representation with residual activation from a previous identification is erroneously
selected again) arising due to residual activation at a level after the systems separate
would not be cross-category if the correct category is selected on the current trial; if a
letter identity maintains activation but the letter system is inhibited this activation will not
be revealed as a perseveration error.
These observations suggest sources of evidence which would distinguish separate
systems from a shared system. Another consequence of separate processing systems is
that acquired disorders of letter and digit identification would not be expected to
associate. Deficits in letter and digit identification would occur independently and only
overlap when the deficit is localized at the shared visual feature level.
The two hypotheses of shared and separate identification systems represent
endpoints on a continuum of possibilities for interactions between letter and digit
identification within the letter theory under consideration. Research reviewed in the
following sections is generally consistent with the shared identification system described
here.
Shared identification systems
In their 2014 paper, McCloskey and Schubert proposed the theory of shared digit
and letter identification described above. The evidence leading to the theory‘s
64
development will be described in some detail in this section, followed by a review of
evidence from other authors, largely consistent with the shared system architecture.
McCloskey and Schubert (2014)
Evidence was collected from LHD (see case history details in Chapter 2:
Evidence for stored letter-form representations) which favors the shared systems
hypothesis. In addition to a letter identification deficit, LHD also has a digit
identification deficit which results in digit substitution errors (e.g., 148459 → 148479).
Three main results supported the proposal of a shared identification system. First, we
found evidence for digit allographs, similar to letter allographs. Second, error patterns by
position (i.e., serial position functions) in letter and digit strings were very similar,
substitutions were the predominant error type, and perseveration errors were present for
both character types. Third, in mixed letter/digit strings, identification errors were not
constrained by stimulus type: Letters and digits freely substituted for each other.
Digit allographs
By analogy to the letter decision tasks described in Chapter 2, we also
administered digit decision tasks to LHD. Ten pseudodigit characters were created from
the digits 0-9 (Segoe UI font, sans-serif). Six-character strings consisting of a mix of
digits and these pseudodigits were presented to LHD and she made a digit/non-digit
decision on each character. Her accuracy was 100% in this task; these results led us to
conclude that her ability to distinguish digit from non-digit characters is intact.
By analogy to the letter decision task summarized above, the conclusion from
LHD‘s excellent performance on this task is that digit allographs underlie her ability to
65
make pseudodigit/digit decisions. Further, we concluded that LHD‘s digit identification
impairment arises in the mapping from digit allographs to abstract (digit) identities,
thereby accounting for her ability to make digit decisions but her impairment in
identifying digits. As these conclusions closely mirror our conclusions about both the
letter identification system (presence of allographs) and LHD‘s letter identification deficit
(mapping from allographs to ALIs), the most parsimonious conclusion is that letters and
digits are identified in a single shared system affected by a single deficit.
Similarity of error patterns for letters and digits
In digit-string identification tasks LHD‘s errors closely resembled those she made
in letter-string identification tasks. Three aspects of her errors contribute: error types,
particular error-prone positions, and presence of perseverations. LHD‘s errors in digit
string identification were almost exclusively substitutions, just as her errors in letter
string identification were almost exclusively substitutions. The serial position functions
for digit and letter strings both showed a pattern of highest accuracy at the initial position
and lowest accuracy at the final position, with intermediate accuracy for intermediate
positions in both types of strings. LHD also displayed an overall effect of character type
(digit accuracy higher than letter accuracy); this result is commonly reported and will be
discussed in the following section. The final aspect of LHD‘s digit identification
performance which paralleled her letter identification performance was the presence of
perseveration errors in both. At rates exceeding chance levels, errors in digit
identification contained digits which were also present in prior responses at levels higher
than chance. This was true also in letter identification, providing further evidence that
the identification errors for both types of stimuli arise from a single deficit.
66
Cross-category substitutions
The third major source of evidence suggesting shared digit and letter
identification systems comes from character naming with mixed letter and digit strings
(e.g., G4MH32). LHD was to name each character in the strings and she often misnamed
digits as letters and vice-versa. In fact, the category of her errors was independent of the
category of the stimuli and therefore these errors suggest that her responses come from a
system where letters and digits are both represented7. This is perhaps the strongest
positive evidence that LHD‘s errors arise from a common process in which both letters
and digits are represented without distinction. Interestingly, LHD was able to accurately
categorize characters as letters or digits, even in the same contexts in which she made
cross-category errors. This result is in line with the suggestion made earlier that
knowledge of letter/digit category must be made available in a shared identification
system. Based on the locus of LHD‘s identification deficit, we suggest that explicit
category information is made available at the allograph level, but that this knowledge
does not affect processing of character identity: Letter and digit stimuli are identified
without regard to their category.
Conclusions
On the basis of these four results, McCloskey and Schubert (2014) concluded that
letters and digits are identified by a single process, without regard to character category.
Versions of separate identification systems which do not posit digit allographs and
7
We are quite confident that the errors were introduced in the identification process rather than in
later stages of processing (e.g., retrieving the phonological forms of letter/digit names) based on evidence
from oral spelling (production of letter names) and a dice-face naming task (production of digit names).
See McCloskey & Schubert (2014) for more details.
67
abstract digit identities would be unable to explain the results presented. Versions of the
separate system account which posit digit allographs and digit identities would perform
better, but would need to account for the total lack of category-preservation in LHD‘s
errors.
Accordingly, McCloskey and Schubert (2014) expanded the letter identification
theory of Schubert and McCloskey (2013) to include digit representations. The first two
levels of letter identification, visual feature and character shape processing, were already
assumed to represent digit stimuli in addition to letters, just as these levels represent
pseudoletters and other related shapes. We concluded that there are digit allographs and
that selection of letter and digit identities are not separate processes; therefore we
proposed a combined level of digit and letter allographs followed by a combined level of
digit and letter abstract identities. In the following sections I review evidence from
unimpaired individuals as well as further cognitive neuropsychological evidence, largely
consistent with shared letter and digit identification processes.
Review of evidence for shared system
Behavioral evidence from unimpaired participants
Numerous authors have demonstrated parallels between letter and digit
identification, often by contrast to identification processes of non-alphanumeric shapes
(e.g., pseudoletters, symbols). Serial position functions for response times to letter and
digit strings parallel each other and pattern differently from functions for symbols not
generally seen in text contexts (e.g., ,; Hammond & Green, 1982). More recently,
García-Orza, Perea, and Muñoz (2010) investigated masked transposition priming in a
same/different task with pseudowords, consonant strings, digit strings, typographical
68
symbol strings (e.g., &%$!), and pseudoletter strings. They found evidence for
transposed character priming in the pseudoword, consonant string, digit string, and
symbol string conditions, but not the novel pseudoletters. They concluded that the
position of known characters is encoded in a relative rather than strict manner, and that
this similarity suggests use of the same mechanism to represent position, consistent with
a shared identification system. Strings of pseudoletters seemed to be represented in a
stricter manner which is distinct from that used for known characters. Using an unmasked
same/different task on consonant, digit, and typographical symbol (e.g., %, £) strings,
Duñabeitia and colleagues (2012) revealed a facilitation of reaction times when one string
had two characters transposed (e.g., NDTF – NTDF), relative to when the string had two
characters replaced (NDTF – NSBF), regardless of string type, though some early
differences in concurrent ERP recordings suggested differences between letter strings and
other string types.
In some contexts letters and digits may be processed distinctly from both familiar
symbols and unfamiliar characters. Tydgat and Grainger (2009) compared the serial
position effects in the identification of strings of letters, digits, and typographical
symbols. They found a W-shaped accuracy function for letter and digit strings, but an
inverted U for symbols. Results for symbol strings differed from letter and digit strings
in both a two-alternative forced-choice task and a partial report task, suggesting that the
result is robust to task and may reflect the underlying identification processes for these
stimuli. With lateralized string presentation, Chanceaux and Grainger (2012) found an
accuracy advantage when presenting letters and digits in the leftmost position in the left
visual field, but no such advantage for symbols or Greek letters. One exception to the
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common finding of analogous patterns for letter and digit processing is a study by Mason
(1982) which found different serial position functions for letter and digit RT in a
character detection task with 5-character strings. It is unclear why these results differ
from those revealed by Hammond and Green (1982) in a similar task, but the majority of
research of this type suggests that letter and digit strings are processed in a similar
manner.
Results which suggest that known stimuli (digits, letters, typographical symbols)
are identified distinctly from novel stimuli (Greek letters) can be accounted for within the
shared identification theory. Novel stimuli would activate visual features common to
known stimuli, but processing would diverge at or prior to the allograph level (by
definition, novel stimuli will not have stored forms), with the potential to lead to different
serial position functions. Moreover, the consistency of letter and digit serial position
functions is consistent with a unified identification system for these characters.
A few recent studies have demonstrated that replacing letters with visually-similar
digits (e.g., 4 for A) is nearly as effective as an identity prime in facilitating the
identification of word and pseudoword targets, but that the reverse substitution (i.e.,
letters for digits, S for 5) creates an ineffective prime for digit strings (Perea, Dun, &
Carreiras, 2008; Perea, Duñabeitia, Pollatsek, & Carreiras, 2009). Though Perea and
colleagues interpreted these results as due to a letter-specific feedback mechanisms which
regularize the shape of the digit stimuli, recent evidence from Kinoshita and Lagoutaris
(2010) suggests that feedback may be not involved. Rather, Kinoshita and Lagoutaris‘
experiments with pseudowords, digit strings, and letter strings favor an interpretation in
which letter and digit stimuli activate visually similar items both within and across
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categories. They demonstrated that the difference between priming in digit string and
pseudoword contexts depends on working memory capacity (i.e., pseudowords are easier
to maintain than digit strings), and found comparable priming results when using more
closely-matched target stimuli: digit strings and letter strings. These results are highly
consistent with a unified letter and digit processing stream, in which letter and digit
stimuli are able to activate both letter and digit identities, and do so according to visual
similarity.
Kinoshita and colleagues (2013) conducted a further study of masked priming
with letters of the prime replaced by letters and digits. They manipulated the visual
similarity of the substituting characters, with visually similar letters and digits and
visually dissimilar letters and digits (e.g., substituting for A, similar: H, dissimilar: D,
similar: 4, dissimilar: 6; similarity determined by experimenters; parity of similarity
levels across category verified by 2AFC identification accuracy). They found strong
priming when letters were replaced by a visually similar digit or visually similar letter,
though the letter priming effect was weaker and did not differ from the priming found
with visually dissimilar letters. The ability of digits to prime letters which they resemble
suggests that letters and digits are processed in a shared identification system. The
authors suggest that differences between the facilitation produced by the letter and digit
prime conditions may be due to the use of the lexical decision task, which biases
processing towards letter interpretations of the stimuli. Digit stimuli which are visuallysimilar to letters are assumed to activate those letters, while letter stimuli are assumed to
activate (or equivalently, provide evidence for) only their corresponding letter identities,
not those for other letters; resulting in no difference between visually-similar and
71
visually-dissimilar letter primes because neither activate the target letter. Given their
explanation of this finding as resulting from the task used, it would be informative to
consider a similar manipulation with a different task, such as the masked cross-case
same/different task, which does not require lexical activation. This would serve to test
whether there is an asymmetry in the effects of visually similarity on letter and digit
processing in a shared system, as Kinoshita et al.‘s results suggest.
The preceding results all refer to character strings; single character identification
has been studied more rarely. Single letter and digit identification was studied by
Starrfelt and Behrmann (2011) in a single character identification task. Participants were
asked to name a single briefly-presented masked character drawn from the digits 0-9 and
letters A-J (uppercase only). At all durations which did not result in performance at
ceiling, average digit accuracy was superior to average letter accuracy (Starrfelt &
Behrmann, 2011). While these results suggest that digits are identified more quickly, it
does not bear on whether the identification processes are shared with letters. The
implications of the reported difference in identification accuracy will be considered in
more detail in subsequent sections.
Neural evidence from unimpaired participants
Evidence for or against the shared systems hypothesis is lacking in the
neuroimaging and neurorecording literatures. Relatively few studies have presented both
letter and digit stimuli, and evidence for preferential digit or letter responses is extremely
mixed. fMRI studies have often found no neural preference for digit over letter stimuli
in ventral regions at the group level, consistent with a lack of neural specificity for digit
versus letter recognition (James, James, Jobard, Wong, & Gauthier, 2005; Polk & Farah,
72
1998; Polk et al., 2002; Price & Ansari, 2011; Reinke, Fernandes, Schwindt, O‘Craven,
& Grady, 2008). However, as Shum et al. (2013) noted, ventral temporal cortex is prone
to susceptibility artifacts in fMRI; it is unclear whether null fMRI effects in these regions
reflect a lack of power due to low signal or a lack of preference for digit stimuli. Despite
this, some researchers have reported regions of the right ventral visual stream which
show a preferential response to digit strings relative to letter strings (Carreiras, Quiñones,
Hernández-Cabrera, & Duñabeitia, 2014; Park, Chiang, Brannon, & Woldorff, 2014;
Park, Hebrank, Polk, & Park, 2011; Polk et al., 2002; relative to words: Reinke et al.,
2008), and the complementary pattern of preference for letters over digits has been found
in the left hemisphere (single characters: Cantlon, Pinel, Dehaene, & Pelphrey, 2011;
single characters and strings: James et al., 2005; strings: Carreiras et al., 2014; Park, Park,
& Polk, 2012; Polk et al., 2002). These results suggest that digit processing may be
predominate or stronger in the right hemisphere, relative to letter processing in the left
hemisphere.
Evidence from electrophysiology fails to clarify the status of digit and letter
neurotopography. Studies have reported preferential digit responses at both left and right
inferior temporal electrode sites; nearby sites have been found to respond similarly to
digits and letters (Allison et al., 2004; Roux et al., 2008). Recently, Shum and colleagues
(2013) reported detailed results with single digit as well as letter, pseudo-letter, pseudodigit, and word stimuli. They discovered seven electrode sites (in 4 subjects, of 7 total
studied) which showed a preference for digits over all other stimuli. These sites were in
the inferior temporal gyrus or fusiform gyrus; five of the seven were in the right
hemisphere (3 subjects), the final two (1 subject) were in the left. Additional sites which
73
responded to digits greater than other characters (letters and pseudo-characters) or digits
greater than words (including number words) were found in the inferior
temporal/fusiform region of both hemispheres. Though suggestive of preferential digit
processing at some sites, these results also imply variability in location and preferentiality
of putative digit-selective regions across subjects, which may also contribute to the
difficulty of identifying such areas in fMRI group studies. Recently, using ERP,
Duñabeitia et al. (2012) found differential effects of transposed characters in letter strings
as compared to symbol strings, with some suggestion of a letter-like pattern for digit
strings. Park and colleagues (2014) reported early (~175ms) differences in waveforms
for letter and digit strings. Over left hemisphere sites, letters showed higher signal than
digits and the pattern was reversed in the right hemisphere, and data from single letters
and single digits revealed the same pattern. These results are consistent with the fMRI
findings of a reversed effect for letters relative to digits in the right and left hemispheres.
In summary, studies have reported preferential digit processing in both the right
and left hemispheres (and sometimes bilaterally in the same participant), as well as null
results. Importantly, the neural evidence reviewed demonstrates voxel or electrode-site
preferences for particular stimuli rather than exclusivity of processing in these regions.
Univariate analyses indicate a relative increase in neural activity in one experimental
condition, but generally the conditions activate largely overlapping areas. Additionally,
the evidence does not specify the cognitive processing stage(s) which underlie the neural
responses. In skilled readers such as the adult participants in these studies, digit and
letter recognition as well as subsequent processing of magnitude/semantics is likely
automatic. In the one experiment which might have probed pre-recognition processing
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by presenting digit and letter stimuli extremely briefly (50ms, forward and backward
masked by #) only null effects were reported for the comparison between the character
categories (Price & Ansari, 2011). Thus the extant neural evidence does not adjudicate
between shared and separate letter and digit identification processes, though other types
of neural evidence or more sophisticated analysis techniques (e.g., representational
similarity analysis) may do so in the future.
Evidence from cognitive neuropsychology
Further evidence for the overlap of letter and digit identification processes comes
from the neuropsychological literature. In an identification task (similar to that employed
by Tydgat and Grainger, 2009), Ziegler and colleagues (2010) found that a group of
developmental dyslexic children displayed parallel serial position functions for letter and
digit strings, distinct from the function for symbol strings. Additionally, the
developmental dyslexia case reported by Brunsdon and colleagues (2006) demonstrated
parallel deficits in letter and digit identification. These results suggest that in at least
some cases of developmental dyslexia, letter and digit processing may be jointly
impaired, consistent with shared identification systems.
In cases of acquired dyslexia, letters are generally affected equally or more
severely than digits (e.g., Cohen & Dehaene, 1995; Greenblatt, 1973; Grossi, Fragassi,
Orsini, De Falco, & Sepe, 1984; Ingles & Eskes, 2008; Larsen, Baynes, & Swick, 2004;
McCloskey & Schubert, 2014; Perri, Bartolomeo, & Silveri, 1996). This was the
conclusion of Starrfelt and Behrmann (2011) in a large review of pure alexia (90 cases):
They reported that these individuals generally have an impairment in both single letter
and single digit processing, though letters tend to be more impaired. Holender and
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Peereman (1987) reviewed a selection of cases of individuals with left hemisphere
damage (not limited to pure alexia) and found that many had deficits in single digit
identification in addition to their language deficits. These reviews considered only single
character identification, but it can generally be assumed that a deficit in single character
identification will also impair identification of characters in strings.
Ingles and Eskes (Ingles & Eskes, 2008) compared letter and digit identification
performance of one individual with acquired dyslexia to five control participants with
brain damage not affecting reading. All of these participants completed an attentional
blink task requiring identification of two target letters or digits at varying stimulus onset
asynchronies (SOAs). The control subjects were at ceiling for identifying both letter and
digit targets, except for the second target at the briefest SOAs for which they showed a
digit advantage. The acquired dyslexic individual was at ceiling for identifying digits as
the first target, but had lower accuracy than controls on letters as the first target and both
letters and digits as target two. This study provides additional evidence for impairment
of letter identification over digit identification in acquired disorders as well as further
control data suggesting that digits are identified more rapidly and accurately than letters.
In addition to the general observation that both letter and digit identification are
affected in many individuals, there have been no reported neuropsychological cases of an
identification impairment for digit stimuli that did not also affect letters (McCloskey &
Schubert, 2014; Polk et al., 2002; Starrfelt & Behrmann, 2011). One puzzling exception
is the case reported by Cipolotti, Butterworth, & Denes, (1991) of an individual who,
subsequent to a stroke, was unable to identify any letters, or to perform letter decision
tasks, but was able to identify and perform digit decision exclusively for the digits 1, 2, 3,
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and 4. Numerical processing and calculation skills were extremely impaired, though
some relative sparing was found for the numbers 1-4. The interpretation of this pattern is
unclear; in particular the selective sparing of some digits with complete obliteration of
others may suggest a different mode of processing than the usual digit identification
system. It is quite common for impairments of numerical processing (i.e., of number
semantics, calculation, comparison etc.) to be reported without concomitant difficulty
with letters but these impairments do not reflect a deficit in digit identification.
Three individuals with acquired deficits have displayed an extremely similar
pattern of impairment for letter and digit stimuli (Katz & Sevush, 1989; McCloskey &
Schubert, 2014; Patterson & Wilson, 1990). In all cases the impairment for letters and
digits has been position-specific, affecting the same string positions in letter
strings/words and digit strings. These cases provide strong evidence in favor of
overlapping digit and letter identification processes, with specific and parallel patterns of
impairment for both stimulus classes, as discussed above with respect to LHD.
In summary, though evidence from neuroimaging and neurorecording is
equivocal, the vast majority of behavioral studies with unimpaired and impaired readers
are consistent with the proposal of shared letter and digit identification processes. I will
maintain the theoretical position that these processes are shared and explore the
implications of this assumption in the remainder of this dissertation.
Reconciling differential digit and letter accuracy with shared identification
Though evidence suggests that digit and letter identification processes are shared,
the fact remains that digit identification performance generally exceeds letter
identification. As reviewed above, both unimpaired individuals and individuals with
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acquired deficits tend to show better performance for digit than letter identification. This
pattern might suggest that letters and digits are identified in separate systems which can
be independently damaged (with the letter system more prone to damage than the digit
system). However, the pattern is not inconsistent with a shared identification system if an
explanation can be provided for how the pattern arises within the system. In this section I
consider the general pattern of superior average accuracy (or lower RT) on the set of
digits compared to the set of letters: This is the basic pattern which has been reported,
though accuracy of individual letters may exceed that of some digits (e.g., McCloskey &
Schubert, 2014). Four hypotheses have been proposed in the literature to explain this
core empirical phenomenon.
Digits comprise a smaller set
One explanation for the superiority of digit identification is that there is a smaller
set of digit identities, thereby facilitating the process of activating the target digit. A few
authors have suggested this possibility, though the exact mechanism for the facilitation
has not been described (Cohen & Dehaene, 1995; Ingles & Eskes, 2008; Polk & Farah,
1998; Polk et al., 2002). Starrfelt and Behrmann (2011) made this explanation more
explicit, suggesting that it results simply from the higher chance rate of correctly
guessing one of ten possible digits rather than one of twenty-six possible letters.
However, this hypothesis presupposes that the reader (or her/his identification system)
has knowledge that the target is a digit and accordingly is not considering any letter
identities. This hypothesis is not compatible with evidence suggesting that character
identification is not constrained by knowledge of the category of the stimulus. It may be
true in some particular contexts that readers are only considering letter or digit targets;
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however this situation is not the only situation in which the accuracy discrepancy
between letters and digits is found.8
Differential role of semantics and/or the right hemisphere
Digits and letters differ in their semantic content: Single digits are logographic
symbols which convey a meaning, while letters convey meaning only by virtue of their
combination into larger units9. Some authors have suggested that this difference might
involve a more direct or stronger connection between digit identification and conceptual
processing than between letter identification and conceptual processing (Cohen &
Dehaene, 1995; Ingles & Eskes, 2008; Starrfelt & Behrmann, 2011). This could entail
stronger feedback connections supporting digit identification, leading to more accurate or
faster identification performance. Some authors specifically suggest that digits have
stronger representations in the right hemisphere than letters do and cross-hemispheric
connections therefore preferentially support digit identification (Cohen & Dehaene,
1995). In a review of the neuropsychological literature on letter and digit naming,
Holender and Peereman (1987) suggest that the right hemisphere stores some semantic
representations for digits but not linguistic stimuli such as letters and words. They posit
that the right hemisphere may provide support for digit naming when the left-hemisphere
is damaged. This hypothesis is difficult to test empirically with behavioral data; the role
and strength of feedback from semantics and/or the right hemisphere are currently
unknown.
8
In particular, Starrfelt and Behrmann reported higher accuracy for digits than lowercase letters
from unimpaired readers in a task with digit and letter trials randomly intermixed (Starrfelt & Behrmann,
2011). In this context it is non-obvious that participants would be considering only same-category
competitors.
9
Exceptions are the letters A and I, which can be interpreted as one-letter words depending on
context.
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Within-set visual similarity
Differential degrees of visual similarity among the sets of digits and letters has
been proposed as another explanation for why digit identification is superior to letter
identification. Cohen and Dehaene (1995) first suggested this possibility: If letters are
more visually similar to other letters than digits are to other digits it could be easier to
determine the identity of a digit from its competitors than a letter from its competitors
(see also Polk et al., 2002).
Starrfelt and Behrmann (2011) expanded upon Cohen and Dehaene‘s original
explanation for the digit-letter discrepancy and sought to test it empirically. They first
computed the mean pairwise pixel overlap for lowercase letters and digits in two
common fonts. Using this measure, they computed the number of competitors for letter
and digit stimuli independently, by considering the pairs of same-category stimuli with an
overlap value higher than a set threshold. At all thresholds they considered, digits had
the same number or fewer competitors than letters, therefore digits have higher
discriminability (i.e., lower confusability) than letters. (At the lowest threshold this is
necessarily true because there are fewer digits than letters). This result suggests that
digits are easier to pick out from the set of digits than letters from the set of letters.
However, the explanation also requires the assumption that digit and letter identities are
only being selected from among the set of same-category identities: digits among digits
and letters among letters, which does not accord with the shared systems hypothesis
under consideration. Considered in the shared systems framework, a high degree of
overlap of letters with any other characters (in terms of visual features at the character
shape level) would entail a large number of active character shapes and subsequently
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allographs and abstract letter identities, which could slow the selection of the single target
letter. If there is less overlap between digit features and features of other characters,
fewer other representations will be activated concurrently and competition will be less;
these conclusions would require comparison of visual overlap with the entire set of
characters as competitors.
An open question concerns visual similarity across the combined set of letters and
digits. Under the assumptions of the shared character identification system, letters and
digits compete with all other characters, not just those of the same category.
Additionally, pixel overlap measures of visual similarity have the disadvantage of being
dependent on the font of the stimuli. Pixel overlap computed for different fonts, though
they may show some consistency, also reveals different patterns of visual similarity
(recall the post-hoc analyses of Consolas and Courier New described in Chapter 2). The
sensitivity of this measure to low-level visual attributes (e.g., serifs) may not accurately
reflect the level(s) of representation at which letters and digits are perceptually similar.
Certainly, the digit-letter accuracy difference seems to hold across the (unknown) range
of fonts used in all studies reporting it, leading to the presumption that it may arise from
level of representation(s) which are not sensitive to cross-font visual variations (or that
the variation is font appearances is small). Visual similarity measures which deal instead
with somewhat abstract letter features (e.g., horizontal bar, curve opened left), thought to
be represented at the character shape level, may provide a more motivated basis on which
to visually compare the set of letters and digits.
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Character frequency differences
Ingles and Eskes (Ingles & Eskes, 2008) suggested that differences in written
frequency of occurrence for digits and letters might explain the performance discrepancy.
However, no data was brought to bear on this hypothesis. To provide an explanation for
the superior performance on digits as a set, the average written frequency for digits would
need to differ from that for letters. Presumably identification performance would be
facilitated by a higher frequency of occurrence: if digits were more frequent than letters.
Though letters are overall more frequent than digits in written material, it is possible that
a frequency analysis would reveal higher frequency for some digits than some letters, or
that a comparison of upper case letters and digits would obtain in the required direction.
Assuming that the empirical data to be explained concerns both cases, case-specific
frequency measures should be used. It is unknown whether the neuropsychological
literature surveyed by Starrfelt and Behrmann (2011) and Holender and Peereman (1987)
employed uppercase or lowercase letters; a mix of both is likely.
Effects of character frequency would suggest that the activation of allograph
and/or abstract character identity representations are modulated by character frequency.
Effects of case-specific frequency suggest localization to the case-specific allograph
representations while case-collapsed frequency effects suggest localization to character
identity representations (note that case-specific letter frequency effects have been
reported, see Chapter 2: Evidence for stored letter-form representations). Such an effect
could be produced if frequency were encoded in the resting activation of the
representations, such that more frequent items would have a higher resting activation and
therefore be faster to activate. Another similar alternative would be that more frequent
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items have a lower threshold to be fully activated. This type of explanation is the same as
that used to explain word frequency effects in word recognition and reading, with
differential resting activation or thresholds of lexical entries based on word frequency.
A small number of studies have suggested that digit and letter frequency may be
encoded in the identification system. It has been observed in studies of synesthesia that
the colors reported for letters and digits correlate with character frequency. Specifically,
Beeli, Esslen, and Jäncke (2007) reported significant correlations between the saturation
of synesthetic colors for each character with their respective frequency, and Smilek,
Carriere, Dixon and Merikle (2007) reported significant correlations between luminance
and character frequency. However, both of these studies considered the letter and digit
sets separately; it is not known whether the relationship holds across the combined set of
characters.
Evidence for character-frequency effects across the collapsed letter and digit
character sets would provide evidence for frequency tracking for both types of characters.
To my knowledge no study has considered the effect of frequency on a by-character level
across combined letter and digit stimuli in any context. Such an effect would be
consistent with the shared systems hypothesis as well as providing at least a partial
explanation for accuracy and RT discrepancy between the two character categories:
rather than a categorical effect of letter or digit status, character accuracy/RT would
correlate with character frequency. Two tests of the hypothesis are wanting: an
assessment of set-wise character frequencies (i.e., Are digits more frequent than letters?)
as well as a by-character analysis comparing character identification performance to
character frequency.
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Summary of hypotheses
Four major hypotheses have been proposed to explain the observed discrepancy
between digit and letter identification. However, none of the hypotheses has thus far
provided a satisfactory answer. Some hypotheses require unsupported assumptions, such
as that the category of a character is used to constrain the identification processes. Others
are simply not backed up with sufficient data to explain the phenomenon. In Study 1 I
explore the validity of the visual similarity and character frequency accounts. As
discussed above, the impact of the set of digit stimuli being smaller and possible
differential influence of feedback from semantics are difficult to test and I do not
undertake to do so here.
Critically, these hypotheses were proposed to explain a difference in identification
performance across the entire set of digit and letter characters, what I refer to as
categorical or set-wise versions of the hypotheses. However, considering set-wise
accuracy or RT may obscure differences in accuracy across individual characters. The
phenomenon of higher digit than letter accuracy may only be true for the mean accuracy,
not for all digits compared to all letters; this level of performance detail has not been
reported. In the case of LHD‘s identification performance her average accuracy for digits
exceeded her average accuracy for digits, but there was overlap in the accuracy for
individual digit and letter characters (McCloskey & Schubert, 2014).
Overview of Studies 1-3
I will consider whether the pre-conditions exist for frequency and visual similarity
hypotheses to explain the categorical distinction reported between letters and digits, the
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set wise versions of these hypotheses. These analyses do not require collecting
identification data: The hypotheses require that digits are more frequent than letters and
that digits have lower visual confusability/complexity than letters, which can be tested on
the basis of character frequency metrics and visual properties alone. Of these variables,
frequency and complexity are a measure of a single character‘s properties, while
similarity is defined as a relationship between two or more characters. Any of these
variables could help explain the accuracy/RT discrepancy between the two sets of stimuli
if it is correlated/confounded with the letter-digit categorical distinction. Even if the
effects of the variable arise within a shared systems architecture, an apparent categorical
distinction between the two character types could arise in this way. Revealing such an
effect(s) would reduce tension between the reported performance discrepancy and an
underlying shared identification system. The comparisons of letters and digits on these
three variables will comprise Study 1.
Examining the ability of specific variables to produce differences in the set wise
processing speed/accuracy of characters also introduces a broader question about
character identification. This question concerns the variables which determine accuracy
and speed of character identification more generally. For example, if it is found that A is
identified more rapidly than Z, can this be explained by the higher relative frequency of
A than Z? A second related question concerns the confusions among characters: When a
stimulus character is not correctly identified, why do particular responses occur as errors?
These two questions will be addressed through parallel analyses of Study 2 (accuracy)
and Study 3 (response time) data. I also explore the predictions of shared and separate
identification systems for the results of these studies.
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CHAPTER 4: EXPLORING HYPOTHESES FOR LETTER AND
DIGIT ACCURACY DISCREPANCY (STUDY 1)
Analyses in this study consider whether character frequency and/or visual
similarity are viable hypotheses for explaining the observed categorical difference in
identification performance for letters and digits. The hypotheses involve assumptions
that letters and digits differ in particular ways (e.g., in their frequency), and further that
the differences underlie differences in letter and digit identification performance. The
analyses of this study consider the precondition for the hypotheses: Are there systematic
differences between letters and digits in frequency or visual properties? Support for the
hypothesis that a particular variable (e.g., frequency) is responsible for the accuracy
discrepancy requires not only the precondition to be true (e.g., letters are less frequent
than digits) but also evidence that this difference affects identification performance. The
analyses in this study serve as preliminary analyses to the investigations of by-character
effects in Studies 2 and 3 (in Chapter 5).
Metrics for each character were used to compare the characteristics of the letter
and digit sets, including frequency, visual overlap, discriminability, and visual
complexity. Of these, the first and final are properties of a particular character, which are
computed independently of the remainder of the character set. Visual overlap and
discriminability necessarily refer to the relationship between a given character and a
larger set of characters.
Visual overlap and discriminability differ depending on the set of characters
considered as the comparison set. In this study these measures were computed over two
comparison sets: the entire set of letters and digits (all characters), as well as separately
86
within letters and digits. For letters, this means the measures were computed across all
characters and across the set of letters; for digits they were computed across all characters
and across the set of digits.
In the case of feature overlap, use of these two comparison classes has different
theoretical implications. As indicated in Chapter 3, the shared systems theory of
identification posits that during identification of letters and digits no distinction is drawn
between the two character sets; characters of both types can gain activation and compete
with each other. By contrast, separate systems hypotheses posit that letters and digits are
identified in somewhat independent and distinct processes after the visual feature level
(NB: Not to be confused with the character shape level, where abstract letter/digit
features, such as those in the feature set developed here, are represented) in which they
are only competing with representations of same-set characters. Previous work
comparing visual properties of letters and digits (discriminability based on pixel overlap)
was conducted comparing a given character only to its same-set competitors, an implicit
adoption of an extreme separate systems hypothesis, which assumes that even at the level
of representation of pixels, representations of letter and digits do not compete with each
other. Analyses of both all-character and same-category visual overlap were conducted.
At the level of feature overlap, the distinction between all-character and same-category
competitors follow the assumptions of the two architectures discussed. At the level of
pixel overlap the distinction is much less meaningful, as it is difficult to imagine any
system which could differentiate letter stimuli from digit stimuli based on pixels alone.
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Methods
Throughout this study, comparisons were conducted using nonparametric
statistics (Spearman‘s rank-order correlation and Mann-Whitney U-test) and two-tailed
significance testing. These methods are suited to the unequal variances and small/unequal
sample sizes present in the data. The measures computed here are retained for use in bycharacter analyses in Studies 2 and 3 (Chapter 5).
Frequency
The first analysis compared published metrics of letter and digit frequency,
determining whether the set of digits differ in frequency from the set of letters. Of
existing character frequency metrics (e.g., Benford, 1938; Jones & Mewhort, 2004;
Mayzner & Tresselt, 1965; Solso & King, 1976), Jones and Mewhort‘s is the only to
contain uppercase and lowercase letters as well as digits. These authors computed digit
and case-specific letter frequencies from five corpora: New York Times article archives,
the Brown corpus (source of the Kučera & Francis word frequency counts; 1967), a set of
randomly-selected webpages, an internet discussion forum, and an online encyclopedia.
They concluded that the edited corpora—New York Times and Brown—were most
consistent with commonly-encountered text and recommended use of the former.
The average frequency for letters (each case separately) and digits were compared
using the published New York Times counts. To be consistent with the categorical
version of the character frequency hypothesis, digits would need to be more frequent than
one or both cases of letters.
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Visual similarity
The second analysis compared metrics of visual similarity for the sets of upper
case10 letters and digits. Two measures of visual similarity were used: pixel overlap of
images of letter and digits, and feature overlap. The average visual overlap among the set
of digits was compared to the set of letters, for both visual similarity measures.
Pixel Overlap
The pixel overlap metric was computed in MATLAB2013a (Mathworks) by
computing the overlap of black pixels in images of single letter and digit stimuli.
Characters were in 36pt font and centered (within 300x300pixels of white background)
for maximal overlap. This was conducted for four fonts: Arial, Consolas, Courier New,
and Times New Roman (sans serif, sans serif, serifed, serifed, respectively). Consolas
and Courier New are fixed width fonts, while Times New Roman and Arial are
proportional fonts. Times New Roman is the font used for body text in this dissertation.
Arial is a common fonts for text displayed on a computer screen, including in popular
applications such as Gmail. All four fonts are displayed in Figure 4.1.
10
I considered exclusively uppercase letters in this and subsequent analyses. The reasons are to
limit the characters to present as stimuli in the experiments of Studies 2 and 3, and to give a larger
possibility of finding visual overlap and frequency effects for the letter and digit sets. Upper case letters
occupy the same region of space on a line as digits—unlike lowercase letters which may occupy a smaller
region (e.g., a, x), or extend below the baseline (e.g., j, g)—increasing the measured overlap between letters
and digits centered within the standard character frame.
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Figure 4.1: The four fonts used in this study: Consolas (sans serif, fixed-width), Arial (sans serif,
proportional), Courier New (serifed, fixed-width), Times New Roman (serifed, proportional),
respectively.
Feature Overlap
The feature set developed here was meant to approximate the type of abstract
feature representations hypothesized to be present at the character shape level. These
features include lines and curves, which are assumed to be invariant to character size and
position in the visual field but specific to relative size (i.e., one feature can be larger than
another) and position within a character (e.g., feature ‗horizontal line of length 1 at top of
character‘ is distinguished from ‗horizontal line of length 1 at bottom of character‘). The
feature overlap metric considered an inventory of letter and digit parts, along with their
positions within a letter-based frame. Pelli and colleagues (2006) concluded that
features, smaller than entire letter-shapes, are used in letter identification and further that
features are independently activated and utilized by the identification system.
Specifically, they concluded that the identification of a letter depends on the activation of
each component feature. This result suggests that representation of letter features is
implicated in letter identification. Guidance for the feature set developed here came from
previous proposals (Boles & Clifford, 1989; Briggs & Hocevar, 1975; Changizi &
Shimojo, 2005; Fiset et al., 2008; Pelli et al., 2006; Petit & Grainger, 2002). Features of
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the same type but of different lengths and positions are considered to have some overlap.
This is meant to capture the assumption that there is similarity in the representation of
features that differ only in these parameters.
The variation of letter and digit visual forms complicates describing the forms in a
straightforward manner; a veridical description of one character stimulus may not be
general enough to capture that same character in other fonts or forms. With this visual
feature set I sought to capture the features of the standard fonts of uppercase print letters,
without accounting for the full range of variability. The font used in the behavioral
experiments of Studies 2 and 3 (Consolas) served as a model for the letter and digit
shapes11.
Generally letters have been split into features at points of discontinuity in the
visual stimulus (e.g., Changizi & Shimojo, 2005). In the interest of using a small set of
atomic feature units to describe many letters, some letters were split into smaller
segments in the absence of a discontinuity in the line. For example, U was split into two
straight segments and one curve, whereas Changizi treats it as single stroke. This
division of the character captures that U contains vertical segments which are quite
similar to those in H, D, etc., which would be obscured if U were treated as a single
feature. This decision is also supported by Pelli et al., (2006) who failed to find evidence
for whole-letter templates/features in letter identification. A full listing of the features,
overlap metric, and resulting overlap values for all characters are in Appendix A.
11
The only exception is the zero character, which in Consolas is a crossed-zero (0). This is a
particularly unusual form of this character and therefore the standard form (0) was described in the feature
set.
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Visual complexity
Visual complexity was calculated three ways: First as the number of visual
features and second as the number of black pixels in a given font. In addition, following
the suggestion of Pelli et al., (2006) and Ziegler, Pech-Georgel, Dufau, & Grainger,
(2010), perimetric complexity (defined as the square of the perimeter of the ink area,
divided by total ink area) was computed for each character. Perimetric complexity was
computed over the same image files used for pixel overlap calculations. The method
described in Pelli et al. (2006) was implemented in MATLAB. Complexity as computed
by all three methods was compared for letter and digit sets.
Discriminability
Starrfelt and Behrmann (2011) developed a measure of discriminability for letters
and digits which considers the highest competitors for a given character (i.e., the other
characters with the highest pixel overlap with that character). Here I considered a
simplified notion of discriminability, defined by the overlap value of the highest
competitor for each character. The set of competitors was considered separately as either
all other characters, consistent with the shared identification system, or the other
characters of the same set (as computed by Starrfelt & Behrmann). The pixel and feature
overlap measures were both used. For example, the highest pixel competitor for A
(Consolas) considered out of all the characters is 4, while A‘s highest competitor among
the Consolas letters is R. Considering features, the highest competitor for A is A across
all characters and also within just the letters.
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Results
Frequency
Comparing lowercase letters to digits confirmed that on the whole, lowercase
letters are more frequent than digits (Mann-Whitney U = 41.0, N1 = 10, N2 = 26, p < .01).
The average frequency of lowercase letters (2.37 million) exceeds that of digits (283,418)
by nearly an order of magnitude. The most frequent digit (0) is significantly less frequent
than the most frequent lowercase letter (e; .546 million vs. 7.74 million). These two
comparisons are inconsistent with the hypothesis that better performance for digits than
lowercase letters could arise from digits‘ higher frequency. The very large range of
frequencies across the lowercase letters (54,221 to 7.74 million, q to e) suggests that it is
important to consider the frequency of the particular subset of letter stimuli when the full
alphabet is not used. Considering the relative ranking of lowercase letters and digits, all
of the digits are ranked below 21 of the letters; there is some interleaving of the letter and
digit frequency values at the lower end of the frequency ranks.
The discrepancy between frequencies of uppercase letters and digits is much
smaller and in the opposite direction: The average frequency of uppercase letters
(135,677) is lower than that of digits (283,418). Comparing these sets indicates that
digits are more frequent than uppercase letters (U = 44.0, N1 = 10, N2 = 26, p < .01).
Unlike with lowercase letters, the four most frequent characters among the combined set
of uppercase letters and digits are digits (0, 1, 5, 2); half of the letters are less frequent
than all of the digits. As with lowercase letters, when a subset of letters is used (e.g.,
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Starrfelt & Behrmann, 2011)12 the properties of those particular characters determine
whether sets of letters and digits differ.
Cross-case frequency (i.e., the average of lower- and upper-case frequencies)
differs from both lowercase (U = 230.0, N1 = 26, N2 = 26, p < .05) and uppercase
frequency (U = 41.0, N1 = 26, N2 = 26, p < .001). Given the numerically higher
frequencies of lowercase letters, their average with uppercase letters results in cross-case
frequency higher than digit frequency (U = 49.0, N1 = 10, N2 = 26, p < .01).
In summary, counts of uppercase, lowercase and cross-case frequency differ
significantly from digit frequency, but the latter two in the reverse direction of the
frequency hypothesis. The comparison between uppercase letters and digits revealed that
digits are of higher frequency than letters. However, with all three comparisons there
was considerable intermixing of the frequencies of the two character types.
Visual similarity
Pixel overlap
As it is directly computed from the visual appearance of the letters, pixel overlap
varies by font. For example, of the four fonts used here (Arial, Consolas, Courier New,
Times New Roman), cross-correlation ranged from .19 (Consolas with Times New
Roman) to .99 (Courier New with Times New Roman).
Pixel overlap was calculated for every pairwise combination of characters for
each font separately. Two measures were then computed: average overlap between a
12
The letter stimuli used by Starrfelt & Behrmann (A-J) include some high frequency letters (A, B,
C) as well as a low frequency letter (J), with the effect that the average for this letter set is very similar to
that found for the entire alphabet, though the minimum is much higher in the subset. Like comparisons to
the full alphabet, the frequencies of the digits are higher than the letters (U = 20.0, N1 = 10, N2 = 10, p <
.01).
94
given character and all other characters, and average overlap between a given character
and only the other characters of that same type (letters with letters, digits with digits).
Considering first the relationships among the full set of characters, there are significant
differences between letters and digits for only one of the fonts: Courier New (letter
average: .35; digit average: .29; U = 66.0, N1 = 10, N2 = 26, p < .05). In Arial, Consolas,
and Times New Roman there is no difference (Arial: p > .4; Consolas: p > .4, Times New
Roman: p >.1). Comparing pixel overlap computed only within category reveals
differences for 2 of 4 fonts; in Arial and Consolas (the sans-serif fonts) the letters and
digits differ (ps < .05) while in Times New Roman and Courier New they do not (ps >
.5). Both of these differences are in the reverse direction required for a pixel overlap
explanation of higher digit accuracy: Digits in Arial and Consolas have higher average
overlap than letters.
Feature overlap
Unlike pixel overlap, feature overlap involves more abstract visual properties
which do not vary by font (within a style; ‗uppercase print‘ is considered here). As
above, overlap of letters and digits was compared in two instances: including all
characters, and including only within-set characters. All analyses comparing letters and
digits on feature overlap failed to reach significance, regardless of whether the overlap
included all characters or just within-set characters (ps > .1). Feature overlap for letters is
.13 across all characters and .14 within letters only; for digits the average feature overlap
is .11 across all characters and .12 within digits only. The lower overlap values for
feature than pixel overlap reflect the fact the any feature can have pixel overlap with any
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other feature in the same location, while only features of the same class have any overlap
with each other.
Discriminability
Pixel overlap
I calculated the competitor with the highest overlap value for each character, from
the full set of characters and separately from the set of within-category characters, for
each of the four fonts. The set of maximum values for the letters was then compared to
that for the digits. Considering pixel overlap across all characters, letters and digits do
not differ in the value of their highest competitor in three of the fonts considered (ps >
.1). However, they do differ in Times New Roman: Average maximum overlap for
letters is .68 and for digits is .61 (U = 71.5, N1 = 10, N2 = 26, p < .05). Note that this
discriminability measure reflects the overlap of the most visually similar competitor,
which is independent of the number of competitors. Considering pixel overlap within set
only, letters with letters and digits with digits, three of four fonts show an advantage for
digits such that digits have lower highest-competitors than letters (ps < .05). The
exception is in the font Arial, in which letters and digits do not differ (p > .5).
Feature Overlap
The same discriminability measure (i.e., overlap value of highest competitor) was
also calculated from feature overlap. Highest competitor was computed among all the
characters as well as from within-set characters. Letters and digits do not differ in
discriminability computed across all characters (U = 116.5, N1 = 10, N2 = 26, p > .6).
However, letters and digits do differ in discriminability computed within set (U = 74.0,
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N1 = 10, N2 = 26, p < .05). On average, the highest competitor for digits has an overlap
value of .29, while for letters it is .37; letters have stronger within-set competitors than
digits.
Visual complexity
Number of features
The number of features for each character was counted from the feature set
described above. The average number of features for letters is 2.65; the average number
of features for digits is 2.3. The number of features for letters and digits was compared
using a Mann-Whitney test; no significant difference was found (U = 97.0, N1 = 10, N2 =
26, p > .2). The feature set was designed to capture abstract features of letters (e.g., does
not included serifs) and therefore does not differ by font (e.g., H in all four fonts is
described by two vertical lines and one horizontal line).
Perimetric complexity and number of pixels
Use of different fonts results in different values for number of pixels and
perimetric complexity and therefore the outcome of comparisons of these variables
depend on the font used. Tables 4.1 and 4.2 detail the comparisons for each font.
In Consolas, the perimetric complexity and number of pixels of letter and digit
stimuli do not differ (ps > .1). In Arial, perimetric complexity does not differ between
letters and digits (p > .3) while number of pixels does differ (p < .05). Courier New and
Times New Roman display significant differences in both perimetric complexity and
number of pixels between letters and digits (all ps < .05). In both fonts, digits have fewer
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pixels and lower perimetric complexity than letters; this is numerically true also for the
sans-serif fonts.
Table 4.1: Perimetric complexity comparisons
Font
Font type
Digit average
Letter average
Mann-Whitney U
p-value
All Digits v. All Letters†
CONSOLAS
0123456789
Sans serif
63.4
68.4
109.0
.475
ARIAL
0123456789
Sans serif
67.0
74.7
101.0
.320
COURIER NEW
Serifed
0123456789
116.8
148.6
23.0
< .001*
TIMES NEW
ROMAN
0123456789
76.2
107.2
22.0
< .001*
Serifed
†N1 = 10, N2 = 26; *Significant at p < .05 level, 2-tailed
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Table 4.2: Number of pixels comparisons
Font
Font type
Digit average Letter average
All Digits v. All Letters†
Mann-Whitney U
p-value
CONSOLAS
0123456789
Sans serif
1173.6
1224.8
111.5
.520
ARIAL
0123456789
Sans serif
1330.5
1608.6
70.5
.034*
COURIER NEW
Serifed
0123456789
622.9
738.0
70.5
.034*
TIMES NEW
ROMAN
0123456789
895.5
1251.9
44.0
.002*
Serifed
†N1 = 10, N2 = 26; *Significant at p < .05 level, 2-tailed
These three measures of complexity are intercorrelated. Number of pixels
correlates with perimetric complexity (Spearman‘s ρs range from .76 to .88, all ps <
.001). Across three of the fonts tested, number of features correlates positively with
perimetric complexity (Spearman‘s ρs from .25 (Arial, ns) to .45, all significant ps < .05).
On the whole, number of pixels does not correlate with number of features (ps > .1)
except with the font Courier New (Spearman‘s ρ = .35, p < .05). The positive correlation
between number of features and number of pixels in Courier New may be due to the large
serifs in this font; the number of serifs (and therefore the number of pixels) generally
increases as the number of features increases.
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Discussion
The analyses conducted in this study do not indicate systematic differences
between letters and digits. Broadly, the four variables considered were frequency of
occurrence, visual overlap, visual discriminability, and visual complexity. The latter
three were computed for both pixel- and feature-based metrics, which are assumed to
index different levels of processing in the identification system. Of these variables,
visual overlap and discriminability depends on the nature of visual relationships among
the characters, while frequency and complexity are properties of a single character. I
briefly review the results of each analysis, discussing the conclusions that can be drawn
from each.
Frequency
The analyses of character frequency revealed opposite patterns depending on
letter case. Considered as a set, lowercase letters are more frequent than digits while
uppercase letters are less frequent than digits. However, in both comparisons there is a
large amount of intermixing of character frequencies such that some digits are more
frequent than some letters and some digits are less frequent than some letters. Overall,
the lack of systematic difference in character frequencies is inconsistent with the
postulation of frequency as the cause of the performance discrepancy between digits and
letters.
Visual similarity
Visual similarity and discriminability comparisons were conducted with all
characters and within-set characters as separate comparison sets. Results from these two
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analyses differ in their ability to account for differences arising within a shared or
separate identification system: all characters are potential competitors in a shared system
while only within-set characters compete in separate systems.
Pixel and Feature Overlap
The pixel overlap comparisons are consistent with the observation that pixel
overlap measures vary widely across font. Comparisons between pixel overlap of letters
and digits to all other characters were nonsignificant in three of four fonts, but significant
in Courier New. On the other hand, when pixel overlap was computed relative only to
within-set characters, only Arial and Consolas letters and digits differed from each other,
but in the opposite direction. These results present a very inconsistent picture of any
letter-digit differences and do not suggest a role for this type of visual similarity in
explaining letter/digit identification performance.
The results of the feature-based visual similarity analyses are straightforward: No
differences were found between letters and digits in their feature overlap. The feature set
was designed to include features which are abstract, i.e., invariant to properties such as
size, absolute position, and line thickness, and reflect features at the character shape
level. To the extent that this attempt was successful, a lack of difference between letters
and digits on overlap at this level suggests that at the character shape level the set of
digits and the set of letters differ only in terms of their connections to higher
representations (i.e., allographs, abstract identities), not featural representations. The
conclusions from pixel and feature overlap measures are inconsistent with any ability of
these variables to explain letter/digit accuracy discrepancies.
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Discriminability
Discriminability is a measure of the strength of the highest competitor for a given
character. As with visual similarity, it was computed using two different overlap
measures: pixel overlap and feature overlap, and for each measure one analysis
considered all other characters as possible competitors, while a second analysis only
considered characters from within the same set (letters for letters and digits for digits) as
competitors.
When considering competitors across the entire set of characters, differences
between letters and digits were only found for Times New Roman. On the other hand,
three of four fonts tested showed a difference in within-set discriminability for letters and
digits: Letters have higher competitors within the set of letters than digits do within the
set of digits (exception: Arial font). In their 2011 paper, Starrfelt and Behrmann
conducted a discriminability analysis using pixel overlap of Times New Roman and
Arial, finding that digits have more high-valued within-set competitors than letters do.
Their result is consistent with the result presented here of differences between digit and
letter discriminability among within-set competitors.
Discriminability based on feature overlap revealed a similar outcome: No
differences when considering competitors across all characters, but digits have lowervalued highest-competitors within-set than letters do. The consistency of this result with
the general pattern obtained with three fonts in pixel-overlap suggests that it may be a
general property of the visual forms of letters and digits.
As discussed in the introduction, positing a variable such as discriminability as
the cause of the digit/letter performance discrepancy also involves a commitment to a
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particular architecture. The finding that discriminability largely only differs when
considering within-category rather than all-character would be consistent with separate
identification systems but not shared systems. However, given that the result of higher
digit than letter within-category discriminability only obtained at the pixel overlap level,
it is not obvious what relevance this result may have for processing. It is unclear how a
system might differentiate letters and digits based on pixel representations, before any
contact has been made to more abstract features (it is conceivable that distinct sets of
features could represent letters and digits, see Footnote 6, p. 59) or to stored
representations.
Visual complexity
Visual complexity was calculated in three ways: as number of features in each
character, number of pixels in each character, and perimetric complexity. Considering
features, the result is very straightforward: Letters and digits do not differ in the number
of features that comprise them. For pixels and perimetric complexity, results varied by
font; significant differences were found with two of four fonts. For both Courier New
and Times New Roman, letters have higher average perimetric complexity and number of
pixels than digits. These differences parallel the font types: Sans-serif fonts show no
difference while serifed fonts do (see Tables 4.1 and 4.2 for examples of letters and digits
in each font). In serifed fonts, the serifs on the letters are more prominent and frequent
than on digits (e.g., 6, 9 have no serifs in either font), which would reduce the number of
pixels and perimetric complexity relative to the serifed letter stimuli. In addition, Arial
showed a significant difference between letters and digits in number of pixels.
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Pelli and colleagues (2006) reported that the log of average perimetric complexity
for an entire alphabet (e.g., Latin letters, Chinese characters, Hebrew letters) correlated
highly with the log of identification efficiency (a measure of accuracy across varying
levels of visual noise): More complex alphabets were harder to identify. This observation
is in the same direction as the one observed here with the serifed fonts: Digits, which
show an identification advantage, were shown to be less complex than letters. However,
while Pelli‘s result was robust to a large number of alphabets and font styles—they
included both serifed and sans-serif fonts—the present results were only obtained with
serifed fonts. The relative frequency of observing letters and digits in serifed and sansserifed fonts is not known, but to a reasonable approximation most text read on a screen
uses sans-serif fonts (with the exemption of digital versions of newspapers/magazines)
while printed material tends to use serifed fonts. Furthermore, the studies reporting better
digit than letter performance likely used a mix of fonts. The lack of difference found
with sans-serifed fonts does not contribute to a uniform explanation for the finding that
digits are identified more rapidly and accurately than letters.
Moving beyond set-wise analyses
A number of the results in this study provided partial or suggestive evidence for a
role of character frequency or visual properties in facilitating digit over letter
identification, but consistent results were not found across analyses and some results
would be consistent only with separate identification systems. Stronger conclusions
could be drawn by comparing by-character performance to by-character measures of
frequency, visual similarity, and complexity (which were considered only collapsed
across sets in the current study). The ability of these variables to predict identification
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accuracy/RT would provide a more robust explanation of the digit and letter performance
discrepancy, and allow for examination of whether the setwise discrepancy is an accurate
portrayal of the relative difficulty of characters. This is the topic of Studies 2 and 3, in
Chapter 5.
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CHAPTER 5: LETTER AND DIGIT IDENTIFICATION STUDIES
In this chapter I consider the ability of the variables discussed in Study 2 to
account for empirical data: character identification errors and response times. Through
numerous studies have published confusion matrices and accuracy/RT measures for
individual letters, digit confusions have rarely been reported. The tasks used in the
current two studies—identification with a delayed typing response, and a same/different
judgment with character pairs—are both assumed to require representing the character(s)
through the character shape level, and either require (delayed typing) or may
automatically involve activation of abstract character identities (same/different).
Analyses of the results of these tasks will explore the nature of identification processing
for letters and digits and the degree to which the variables considered above are relevant
predictors of identification accuracy and speed. In addition, the relevance of the findings
to the existence of shared versus separate identification systems will be explored.
Letter identification: Confusions and response time
The vast majority of previous research considering performance on individual
characters has addressed letters and letter identification, without considering digits. Prior
suggestions for performance differences among letters have been in terms of three
variables: visual similarity to other letters, visual perceivability or complexity, and
written frequency of occurrence.
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Inter-letter similarity
Inter-letter visual similarity has often been investigated through confusability
matrices: errors produced in letter naming under conditions that induce low accuracy
(e.g., brief presentation, masking, peripheral presentation, low contrast, for recent
reviews see: Mueller & Weidemann, 2012; Simpson, Mousikou, Montoya, & Defior,
2012). Of studies presenting theses error matrices, many do not go beyond presenting the
matrix and comparing it to those collected by previous researchers, though it is common
practice to perform a clustering or similar analysis to reveal the structure of the confusion
data (Fisher & Monty, 1969; Gilmore, Hersh, Caramazza, & Griffin, 1979; Loomis,
1982; Phillips, Johnson, & Browne, 1983; Simpson, Mousikou, Montoya, & Defior,
2012; Townsend, 1971). Confusions are assumed to reveal similarity: if any two letters
X and Y have highly similar representations this will result in identification errors of X
for Y and vice-versa. Some authors have used a confusability matrix to derive a feature
set which could account for the observed confusions, or have attempted to predict
confusions using a feature set (e.g., Gervais, Harvey, & Roberts, 1984; Geyer & DeWald,
1973). Such feature sets often include such features as horizontal lines, vertical lines,
angles, and curves (e.g., Briggs & Hocevar, 1975; Gervais et al., 1984; Geyer & DeWald,
1973; Wiley, Wilson & Rapp, in prep.) These analyses have also been carried out on
response time data collected from same/different tasks on pairs of letters (Courrieu,
Farioli, & Grainger, 2004; Podgorny & Garner, 1979, WIley, Wilson & Rapp, in prep.).
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Visual complexity
The majority of attempts to characterize letter identification errors have focused
on inter-letter similarity. However, additional insight comes from analyzing performance
for each letter independently, in addition to confusions between letters. A number of
studies have attempted to explain the ―perceivability‖ or ―legibility‖ of particular letters,
particular fonts, or particular alphabets (e.g., Mueller & Weidemann, 2012; Pelli et al.,
2006; Roethlein, 1912; van der Heijden, Malhas, & van der Roovaart, 1984).
Perceivability is meant to index the difficulty in identifying a particular letter,
independently of inter-letter similarity (as a visual metric this is necessarily specific to a
given letter form, e.g., a and a may differ in perceivability). In a recent paper, Mueller
and Weidemann (2012) presented evidence suggesting that there is a role in identification
for perceivability after accounting for inter-letter similarity. They additionally found that
perceivability is influenced by a masking character in the identification task. Other
studies have used a measure of complexity—operationalized by the number of pixels in
the letter strokes, or perimeter normalized by pixel area—to account for perceivability,
and found negative correlations between letter complexity and letter identification
accuracy (Appelman & Mayzner, 1982; Pelli et al., 2006). However, it is unclear
whether complexity is independent of inter-letter similarity. These studies suggest that
the visual properties of a single letter contribute to identification performance, with some
evidence that it accounts for an independent source of variance from inter-letter
similarity.
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Letter frequency
Beyond visual variables, multiple authors have reported frequency effects on
identification performance. Frequency of occurrence is a property of a single letter,
though relative or summed frequency of two or more letters may also be relevant to
identification performance. Studies employing case-specific letter frequency metrics
were reviewed in a previous section (Chapter 2: ‗Evidence for stored letter forms‘).
Some researchers additionally investigated effects of case-collapsed letter frequency on
letter identification. In a review of 58 studies of letter naming and same/different
judgments, Appelman and Mayzner (1981) found evidence for a weak correlation
between by-letter accuracy for lowercase letters and frequency, but no correlation
between by-letter accuracy for uppercase letters and frequency. In studies collecting
response time to uppercase letters, these authors found a significant correlation between
by-letter reaction time and letter frequency. In a letter search task involving the detection
of a given letter target in a string of five letters, Pitchford, Ledgeway, and Masterson
(2008) found that by-letter correct response time correlated with letter frequency. These
results, and those reviewed previously, provide broad support for the notion that letter
frequency is a relevant variable in letter identification.
The studies reviewed here address inter-letter similarity and confusions, as well as
metrics of a given letter. They suggest that frequency and visual properties (similarity,
complexity) are relevant to the letter identification process, and have provided proposals
for the visual features used in identification. The shared system theory would be
strengthened by an understanding of the variables which are relevant to identification
performance for both types of characters. No study to date has considered these variables
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for the full set of characters: letters and digits. Only one study to my knowledge has
collected identification data for letters and digits (excluding some early experiments,
which have peculiarities of stimuli such as dot matrix fonts or fonts designed for radar
screens), but this study was limited by separately analyzing the data for letters and digits,
and not including all of the letters (Starrfelt & Behrmann, 2011). Additionally, they did
not report by-character accuracy or response time for post-hoc analysis. By collecting
identification accuracy and response time for all letters and digits I will gain a rich data
set to analyze for influences of character frequency, visual complexity, and visual
similarity, and inform the nature of character identification processing.
Predictions of shared and separate identification systems
Separate systems
In the version of separate digit and letter identification systems considered here,
processing diverges at the allograph level, at which point information is available about
the letter/digit category of the stimulus. Within such a system, described in detail in
Chapter 3, two broad predictions can be derived for the results of Studies 2 and 3. With
respect to identification errors (Study 1), separate systems predict that any errors which
arise after the allograph level will be within-category errors. This is due to the inhibitory
(or similar) mechanism which reduces activation of other-category representations in the
other system, only allowing representations of the stimulus category to compete for
selection. Errors arising earlier in the processing system could result in cross-category
errors due to the incorrect system being selected (the inhibitory mechanism would in that
case be erroneously inhibiting same-category representations). In addition to predicting
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the category of the errors with respect to the category of the stimulus, the separation of
processing also impacts the type of similarity that is expected to obtain among the
characters. In particular, character accuracy (Study 2) as well as response times (Study 3)
will tend to be predicted by visual similarity which is computed from same-category
representations (digits‘ similarity to other digits, letters‘ similarity to other letter) rather
than similarity computed from all representations (all characters‘ similarity to all other
characters). In both Studies two visual similarity independent variables are tested, one
that indexes within-category similarity (consistent with errors arising within a single
system) and one that indexes across-category/all-character similarity.
Shared system
Predictions can also be drawn from the shared identification system. They are
often opposing to those of the separate system, though one should note that processing in
both systems (shared and separate) is shared up through the allograph level. The shared
identification system places no constraints on the category of an error made; any stimulus
will activate representations from both categories and no restriction is made during
processing to limit representations to the category of the stimulus. Additionally, by
contrast to the separate systems, similarity across all characters is relevant to predicting
errors and response times. This entails that the variables which index similarity across all
characters (not restricted by category) should be more successful than those which index
only within-category similarity. The particular variables which make this distinction will
be highlighted in each study.
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Letter and Digit Identification Accuracy (Study 2)
In this study, I created a behavioral confusability matrix for letter and digit
stimuli, in mixed-category strings in a delayed typing paradigm. Intermixing the two
stimulus types allows for examination of letter and digit identification without top-down
knowledge that the stimuli belong to a single category, which could influence responding.
Strings were presented for brief durations to induce identification errors (which are rare
or nonexistent for single characters of standard size and contrast, even with limited
exposure). The choice to limit exposure duration rather than mask or distort the
characters was to not alter the visual forms of the letters, particularly since the mask or
distortion used may not uniformly affect all characters (Fiset et al., 2009; Mueller &
Weidemann, 2012).
The confusability method provides multiple subsets of data: identification
accuracy for each character (from the correct identification responses), and the set (and
rates) of characters reported in error for each target character (from the identification
errors). These correspond to the diagonal and off-diagonal cells of a target character-byresponse character confusion matrix. The first set of data was used to determine the
extent to which character frequency, visual complexity, and visual similarity predict
character accuracy. The error responses were analyzed to determine whether the same
variables (frequency, complexity, and visual similarity) affect the character given in
error. Regression was employed to determine the relative importance of these variables in
explaining the data.
There are numerous published behavioral confusability matrices for letter stimuli,
but no study to my knowledge has examined cross-category confusability for letters and
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digits. With increasing interest in digit identification and overlap between letter and digit
processing, such a matrix not only provides useful data for direct analysis but also a tool
for other researchers in designing and matching letter and digit stimulus sets.
Methods
Mixed letter and digit strings (e.g., R9XM) were presented briefly and subjects
asked to report the stimulus after offset. As indicated by pilot testing, 4-character strings
provide a balance between collecting as much data as possible per trial (long strings) with
constraints on working memory (short strings). All letters except O and all digits except
0 were used (these characters are not reliably distinguishable in mixed contexts). In the
experiment 442 strings were presented: each of the 34 characters appearing 13 times in
each position. In 34 practice trials (split into 3 short blocks) participants saw strings with
the same characteristics, one character appearing once in each position.
The fixed-width font Consolas was used. One feature of this font, as indicated by
Study 1 results, is that it does not introduce any categorical visual differences between
letter and digit characters. In visual similarity (average pixel overlap), discriminability
(maximum pixel overlap), and visual complexity (perimetric complexity and number of
pixels), the sets of Consolas letters and digits do not differ from each other. This
property of the font is beneficial for investigating effects of visual variables on bycharacter dependent measures because it means that any effects of these variables are not
confounded with the categorical distinction.
Stimulus duration was brief to induce errors; pilot testing revealed that central
presentation with a duration of 30-50ms is sufficient to induce errors on strings of this
length. Duration was calibrated individually for each participant through practice trials to
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obtain an approximately 60% accuracy rate. The trial structure was as follows: selfpaced display to begin trial (‗. . .‘ terminated by Spacebar), fixation for 200ms, blank
screen for 100ms, stimulus for set duration, untimed response period (terminated by Enter
key), and 500ms of blank screen. Twenty-seven individuals participated in this
experiment, which lasted about forty minutes including a brief mandatory break at the
halfway point.
A long duration version of this experiment was run with four participants to
investigate possible effects of working memory on the errors. The long duration
experiment included the same stimuli as the main experiment but stimulus duration was
1500ms to insure that participants had plenty of time to accurately identify all of the
characters presented. All other experimental parameters were the same. Errors due to the
memory demand of remembering the strings from the stimulus offset until the completion
of the typing response would be expected to also affect the long duration experiment; a
high accuracy rate would indicate that the working memory load is minimal and does not
contribute errors during the main (brief duration) experiment.
Analyses
Analyses explored error rate by character, proportion of times each character was
given as an error, modal error response to each character, and substitution error matrices.
Simple correlations and multiple linear regressions were used to assess the relationship
between independent variables and the dependent measures. Simple correlations were
run in MATLAB using corrcoef. Regressions were run with the stepwisefit function,
which evaluates the current model (beginning with zero predictors entered) with respect
to all variables and sequentially adds/removes predictors to improve model fit. All
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models included a constant term. Before model fitting began, all variables (dependent
and independents) were individually normalized by Z-scoring; the resulting model
coefficients are β-values which can be compared across models. A p-value of .05 was
considered significant.
By-character analyses. The modal error response given for each character was
compared to the target character to determine whether errors and responses differ in
frequency, number of pixels, number of features, perimetric complexity, visual overlap
(pixel and feature, over all characters or just within-set), or visual discriminability (pixel
and feature, over all characters or just within-set).
The error rate for each character and the proportion of times each character was
given as an error were correlated and regressed with the predictor variables listed in
Table 5.1. Many of these predictors are derived from measures described in Study 1:
frequency, perimetric complexity, visual similarity (average overlap), and visual
discriminability (maximum overlap). For the latter two variables, two versions of each
were computed which reflect the visual relationship between characters either across all
other characters, or within a given character category (letter or digit). The all-character
versions are most consistent with a shared identification system, while the withincategory versions are consistent with separate identification systems.
Table 5.1: Predictor variables for by-character error rate.
Predictor Variable
Binary category
Description
0 for digits; 1 for letters
Number of features*
Number of features in character
Number of pixels*
Number of pixels in character
Perimetric complexity*
Perimetric complexity of character
Character frequency*
Character frequency of character
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Average pixel overlap: All Char.*
Average pixel overlap: Within Categ.*
Maximum pixel overlap: All Char.*
Maximum pixel overlap: Within Categ.*
Average feature overlap: All Char.*
Average feature overlap: Within Categ.*
Maximum feature overlap: All Char.*
Maximum feature overlap: Within Categ.*
Average pixel overlap of character with
all other characters
Average pixel overlap of character with
other same-category characters (letters
with letters, digits with digits)
Maximum pixel overlap between
character and most-similar other
character.
Maximum pixel overlap between
character and most-similar samecategory character.
Average feature overlap of character
with all other characters
Average feature overlap of character
with other same-category characters
(letters with letters, digits with digits)
Maximum feature overlap between
character and most-similar other
character.
Maximum feature overlap between
character and most-similar samecategory character.
*Derived from measures described in Study 1
Substitution matrix analyses. Each cell of the substitution matrix (character target
by response character, 34x34) contains the raw number of times the two characters
indexing that cell were confused, in either direction; this matrix is symmetrical and only
one triangle was submitted to analysis. Fourteen predictor variables were created (listed
in Table 5.2). These variables included ones derived from the measures of frequency,
visual similarity, and complexity used in Study 1. Additional variables were designed to
represent possible sources of knowledge the participants may have used (either
intentionally or not) in responding, including character names, letter/digit category status,
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and distance between letters and digits in alphabetic/numeric order. In addition to
analyses of all the substitutions, separate analyses considered subsets: Digit-for-digit
errors, Letter-for-letter errors, and Mixed (Letter-for-digit and Digit-for-letter) errors.
Table 5.2: Predictor variables for substitution errors.
Predictor Variable
Binary category
Description
1 if characters of the pair belong to same category; 0
if characters of the pair belong to different
categories
Pixel overlap*
Pixel overlap of characters of the pair
Total number of pixels*
Summed number of pixels in pair
Feature overlap
Feature overlap of characters of the pair
Total number of features*
Summed number of features in pair
Total perimetric complexity*
Summed perimetric complexity of pair
Perimetric complexity
Difference between perimetric complexities of the
difference*
pair
Frequency difference*
Difference between character frequencies of the pair
Minimum frequency
Smaller of the two character frequencies
Maximum frequency
Larger of the two character frequencies
Total frequency
Summed character frequencies of the pair
Name similarity
Overlap of phonetic features of constituent
phonemes in character names of pair
Normalized distance
Alphabetic distance between two letters in pair;
numeric distance between two digits in pair,
normalized within category s.t. max distance = 1.
Set to 2 for all cross-category pairs.
*Derived from measures described in Study 1
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Long Duration Experiment Results
Accuracy in the long duration (1500ms) experiment was extremely high (mean:
96%, range: 93-99%), suggesting that the use of working memory does not cause errors
in this task. The near-ceiling performance in this experiment is consistent with
conclusions that visual working memory has a four-object capacity (Vogel, Woodman, &
Luck, 2001). Additionally, the main experiment had a shorter lag between stimulus onset
and responding due to the shorter (≤50ms) stimulus duration which would further reduce
the demand on working memory.
Main Experiment Results
Data from three participants were excluded from analysis due to very high or very
low accuracy (accuracies of 95%, 94%, and 16%). Extremely high accuracy will
contribute very few errors to the analysis, while the quality of the low accuracy data is
questionable. Data from twenty-four participants (10,608 total trials) were retained.
Average accuracy was 74%, with a range of 37% to 89%.
Character accuracy differs across positions (χ2 (1, N=42432) = 73.0, p < .001).
Highest accuracy was found at the first position from the left (98%), followed by the
second position, fourth, and finally third position (96.4%). This pattern of high accuracy
on leftmost and rightmost positions is characteristic of character string identification and
may be a due to a combination of factors including visual acuity, crowding, and the leftto-right reading direction (e.g., Hammond & Green, 1982; Tydgat & Grainger, 2009).
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By-character error rates
Letters were more accurate than digits: 5.5% error rate for letters and 6.8% error
rate for digits (χ2 (1, N=42432) = 27.1, p < .001). The five most accurate characters were
all letters (L, P, H, S, C), while the five least accurate characters were a mix of both types
(I, 1, T, 8, Y), see Table 5.3. Comparisons of the category of response by category of
target indicated that response category was independent of target category. Of error
responses to letters, 69% (1179/1704) were other letters and 31% (547/1704) were digits.
Of error responses to digits, 72% (547/764) were letters and 28% (215/764) were digits.
These rates do not differ based on target category (χ2 (1, N=2468) = 1.69, p = .19). The
rates of letter and digit responses approximate the relative prevalence of digit and letter
targets in the study (26.5% of target characters were digits), but differ from the expected
proportion if the response category was based only on category frequency in the stimulus
set (χ2 (1, N=2468) = 12.2, p < .01).
The proportion of times each character was given as an error and the error rate on
each character (Table 5.3) were submitted to correlation and multiple regression analyses
with the predictor variables described in Table 5.1. No significant results were found
with either dependent measure. These measures had very low variability on a bycharacter level, which likely contributed to the difficulty in predicting them.
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Table 5.3: By-character dependent measures. Each character was presented as a stimulus 1248 times.
Character
Error rate
(Number)
Proportion
of errors
Modal error response
to target (col 1)
Modal response prop.
of errors
1
2
3
4
5
6
7
8
9
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
0.06 (75)
0.02 (30)
0.02 (29)
0.03 (32)
0.02 (30)
0.03 (32)
0.01 (16)
0.04 (47)
0.03 (38)
0.01 (17)
0.03 (42)
0.01 (14)
0.02 (26)
0.04 (46)
0.01 (18)
0.04 (45)
0.01 (12)
0.08 (104)
0.03 (34)
0.02 (25)
0.01 (9)
0.02 (23)
0.02 (21)
-0.01 (10)
0.02 (24)
0.02 (22)
0.01 (13)
0.04 (48)
0.03 (40)
0.02 (23)
0.01 (17)
0.02 (29)
0.04 (46)
0.03 (34)
0.06
0.02
0.02
0.04
0.04
0.03
0.04
0.04
0.01
0.02
0.02
0.02
0.02
0.03
0.05
0.04
0.01
0.06
0.03
0.03
0.01
0.02
0.02
0.04
0.03
0.04
0.03
0.02
0.03
0.02
0.03
0.03
0.02
0.02
0.04
I
3
2
A
S
G
Y
B
P
4
8
G
B
F
E
6
0.87
0.12
0.15
0.16
0.39
0.36
0.13
0.19
0.19
0.31
0.38
0.12
0.14
0.36
0.24
0.19
†
†
1
7
X
I
N
M
6
G
P
5
I
V
Y
M
W
V
X
I
0.74
0.20
0.22
0.20
0.32
0.34
0.14
0.24
0.30
0.43
0.22
0.21
0.16
0.29
0.20
0.11
0.16
0.87
†H was excluded because three characters tied for modal error response: N, V, Z
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By-character modal error responses
For each target character, the modal error response character was extracted (see
Table 5.3). (The target H was excluded from this analysis because three characters tied
for its modal error response: N, V, and Z.) The modal error response given to both letter
and digit targets was generally a letter (letter responses to letters: 12/24, 71%; letter
responses to digits: 7/9, 78%), consistent with the pattern in the full set of substitution
errors.
The modal error responses were compared to their target characters on 12
variables, all listed in Table 5.1 (excluded: binary category). For each variable, the value
for the target was subtracted from the value for the error. The number of positive and
negative results was tallied for each variable and submitted to a sign test. None of these
variables differed reliably between the target and modal error response: None met the
critical value of 23 positive or negative outcomes out of the 33 observations (2-tailed sign
test). The maximum number of positive or negative results for any variable was 19 (also
nonsignificant with a 1-tailed test). The outcome of this analysis suggests that though for
some characters the modal error response forms a high proportion of errors to that target,
the influence of variables such as visual overlap, complexity, and frequency is better
investigated across the full range of error responses.
Substitution matrix
Five substitution errors were not included in the matrix: four responses of the
letter O (to J, Q, 1, and 9), and one response of the digit 0 (to 9); neither was ever
presented as a target. A total of 2466 substitution errors were included, of 2792 total
errors in the experiment. The entire matrix is reproduced in Appendix B.
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First, the raw counts of the substitutions for each character pair were correlated
with the variables listed in Table 5.2. Only two significant correlations resulted: a
positive correlation (r = .16) with feature overlap, and a positive correlation (r = .28) with
pixel overlap. Both of these correlations indicate an increase in errors on pairs which
have high visual overlap. Multiple regression run with all thirteen predictor variables13
produced a significant model including pixel overlap (β = 3.62), total pixels (β = -1.38),
and name similarity (β = -.95; model F(557,3) = 19.88, p < .05). These variables were
entered into the stepwise regression in the order listed, indicating that each subsequent
variable accounted for additional sources of variance; 8% of the variance could be
accounted for by only the first predictor, 9% with the first two, and 10% with the full
model. See Table 5.4 for a summary of these results.
By confusion type. The substitution data were also split into three subsets: Letterfor-letter errors, Digit-for-digit errors, and Mixed errors (Letter-for-digit and Digit-forletter). Of the total errors, 1179 were Letter-for-letter errors, 215 were Digit-for-digit,
and 1072 were Mixed errors. The substitution counts for these three subsets were each
correlated with twelve predictor variables from Table 5.2 (excluding binary category
match, also excluding normalized distance for the Mixed set).
Letter-for-letter errors correlated with feature overlap (r = .23), pixel overlap (r =
.33), normalized distance (r = -.13), difference in perimetric complexity (r = -.12),
difference in letter frequencies (r = -.19), maximum frequency (r = -.26) and summed
frequency (r = -.23). The visual overlap (pixel and feature) variables correlated
13
A stepwise regression with only feature overlap and pixel overlap as possible predictor
variables (the two variables significantly correlated with the dependent measure) also produced a
significant model including both variables (F(558,2) = 26.59, p < .05, R2 = 9%). This model was created
by first adding feature overlap (accounting for 8% of the variance, final model β = 2.97) and then pixel
overlap (final model β = 1.17).
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negatively, indicating more errors between pairs with higher visual overlap. The negative
correlation with normalized distance suggests that letters which are closer together in the
alphabet have higher confusion rates. A high difference in perimetric complexity
indicates that letters which differ greatly in complexity were less often confused. Letter
pairs with a larger frequency difference were also less often confused. The higher the
frequency of the more frequent letter, the less often confusions occurred. And finally, the
higher the combined frequencies of the two letters, the less often confusions occurred.
Stepwise multiple linear regression was run to reveal which of these variables could
jointly predict the confusability pattern; only three variables were entered into the final
model: pixel overlap, maximum frequency, and feature overlap (F(296,3)=21.90, p <
.05). These variables were added to the model in the order listed, with beta values of
1.25, -1.13, and .75 in the final model, together explaining 18% of the variance in the
Letter-for-letter data. (Models leading to the final model accounted for 11% and 16% of
the variance, respectively.)
The Digit-for-digit confusions were subjected to the same correlation and
regression analyses. Significant correlations were found with pixel overlap (r = .36),
normalized distance (r = -.50), and total number of pixels (r = .43). The positive
correlation with pixel overlap indexes more confusions between letter pairs which have
high pixel overlap. As with the Letter-for-letter data, increased distance, this time
numeric distance, resulted in lower rates of confusion. And finally, higher total number
of pixels of two digits, a measure of visual complexity, resulted in more confusions.
Stepwise multiple linear regression resulted in a model including normalized distance (β
= -2.78) and total number of pixels (β = 2.44; model F(33,2) = 13.43, p < .05). This
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model accounts for 45% of the variance in the Digit-for-digit data, and was built from a
model including just normalized distance (R2 = .27).
The Mixed-category confusion data were correlated with feature overlap (r = .20),
pixel overlap (r = .33), name similarity (r = -.14), minimum frequency (r = .14), and
summed frequency (r = .12). The positive correlations with feature and pixel overlap
indicate higher error rates on character pairs with high visual overlap. High character
name similarity was associated with lower error rates. The rarer the frequency of the
more-rare character, the lower the confusability of the pair. And finally, as total
frequency of the two characters increased, so did the number of confusions. Stepwise
multiple linear regression resulted in a model including only pixel overlap and character
name similarity (F(222,2) = 16.40, p < .05), accounting for 13% of the variance. Pixel
overlap was added first, and accounted for 11% of the variance alone.
Table 5.4: Significant predictor variables in regressions of substitution data (Beta values)
Predictor
Variable
Pixel overlap
Total number
of pixels
All
Substitutions
Letter-letter
Substitutions
3.62
1.25
-1.13
frequency
similarity
2.44
.75
Maximum
Name
Mixed
Substitutions
5.78
-1.38
Feature overlap
Digit-digit
Substitutions
-.95
-2.65
Normalized
-2.78
distance
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Total model R2
.10
.18
.27
.13
Discussion
Analyses of by-character error rate, proportion of times each character was given
as an error, and modal error responses to each character did not reveal any significant
influences of the variables considered. In addition to a variable representing the category
of the character (letter or digit), the independent variables tested were measures of visual
complexity: number of features, number of pixels, and perimetric complexity; character
frequency; visual overlap: feature and pixel, computed across all character and within
same-character pairs; and visual discriminability: feature and pixel, computed across all
character and within same-character pairs. The failure of these variables to correlate with
or predict the three dependent measures suggests either that none of these variables are
relevant to the identification process, or more likely, that there was not sufficient
variability in the dependent measures used here. Analyses in Study 3 will consider these
variables‘ abilities to predict response times in same/different judgments to character
pairs; higher variability in RT across characters may result in reliable relationships.
The two primary positive results of this study concern the independence of
response and target category, and variables predictive of the substitution matrix. The
failure of substitution errors to maintain the category (letter/digit) of the target character
was a dependable result. Chi-squared analysis revealed that target and response category
were independent in the overall substitution data, and a consistent pattern was also found
considering only the modal error response to each character. Rather than matching the
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category of the response, the substitution error categories were approximately consistent
with the overall relative frequencies of letters and digits in the experiment, though not
perfectly aligned with them.
Independence of response category with respect to target category in character
identification is consistent with a shared character identification system. In such a
system, letter and digit stimuli are processed without regard to their category designation
and errors take the form of other active character identities. By contrast, separate
identification systems would involve separation of letter and digit processing, with the
result that some identification errors (those arising after a determination has been made
about the category of the stimulus) would be constrained to be the same category as the
target. The pattern of independence of target and error category in identification was also
reported by McCloskey and Schubert (2014) in their study of acquired dyslexic
individual LHD, and formed a part of our conclusion in favor of shared system
processing. The lack of restriction of the error category by stimulus category implies the
presence of shared identification system, or alternatively, separate identification systems
combined with all errors having arisen prior to the category determination for the
stimulus was made.
Associations were found between character confusions and independent variables
which measure visual similarity, visual complexity, character name similarity,
alphabetic/numeric distance, and character frequency. The first analyses considered the
full set of substitutions: letter and digit error responses to both letter and digit targets.
This set was predicted by a combination of pixel overlap, total number of pixels, and
character name similarity. A combination of increased pixel overlap between two
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characters, fewer total pixels, and dissimilar character names were associated with higher
rates of character confusions. Pixel overlap and total number of pixels are properties of
low-level visual representations, such as those at the viewer-centered visual feature level.
The significant contribution of number of pixels beyond pixel overlap suggests an
independent influence of complexity (or ‗perceivability‘) on character identification,
consistent with similar reports by Mueller & Weidemann (2012) for letters. Character
name similarity is computed based on character name representations, accessed from
abstract character identities (by analogy to abstract letter identities, refer to Figure 2.2
and related discussion). The negative relationship between character name similarity and
confusion rates is in a counter-intuitive direction, but may indicate that participants took
particular care to distinguish identities with similar-sounding names, leading to errors on
those with dissimilar names14. Overall, the regression model indicates that both low- and
high-level variables influenced character identification errors.
Subsequent analyses considered the set of Letter-for-letter substitutions, which
were reliably predicted by a combination of pixel overlap, feature overlap, and maximum
frequency. As pixel overlap and feature overlap of a pair increased and the frequency of
the more-frequent letter decreased, the number of confusions increased. These variables
reflect the impact of visual similarity at low (pixel) and more-abstract (feature) levels, as
well as a benefit in processing for high-frequency letters. These conclusions are
consistent with a large literature of research on letter confusion matrices (reviewed in the
introduction to this chapter). The success of the feature overlap measure suggests that
this measure, designed to explain character shapes through a small set of abstract visual
14
This variable added only weakly to the overall explanatory capacity of the model (raising the R 2
from .092 to .097).
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features, is a sufficiently accurate model of visual similarity within the identification
system to correlate with identification performance.
Digit-for-digit substitutions were well-predicted (45% of the variance) by a
combination of numeric distance and number of pixels. The influence of numeric
distance implies involvement of semantic representations of number, which are more
similar for close numbers (see also the numeric distance effect, e.g., Moyer & Landauer,
1967). The equivalent variable for letters, alphabetic distance, did not predict the Letterfor-letter confusions, suggesting that numeric distance is a more influential factor in digit
identification, perhaps indicating that position of letters in the alphabet is not
automatically accessed in identification (Krumhansl & Thomas, 1977). An increase in
the number of pixels also increased confusions, which is a property of low-level visual
representations. Together these two variables, one strictly visual and one semantic, had a
large influence on digit-for-digit confusions.
Mixed character substitutions (Letter-for-digit and Digit-for-letter; 43% of the
overall substitutions) were predicted by pixel overlap and name similarity. These
variables overlap with those found to predict the Letter-for-letter substitutions (pixel
overlap) and the full set of substitutions (pixel overlap, name similarity). Identical
variables predictive of Letter-for-letter, Digit-for-digit, and Mixed confusions would have
provided strong evidence in favor of the shared systems hypothesis; the variables
affecting character identification would not differ depending on the character type. The
present findings are not of identical predictors, but there are consistencies (e.g., the role
of pixel overlap) which are suggestive of shared systems processing. Furthermore, one
major difference, that Digit-for-digit confusions were predicted by normalized distance
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while Letter-for-letter confusions were not, reflects a post-identification, semantic impact
on the responses. This result is not inconsistent with shared identification systems for
letters and digits.
With the results of regressions predicting the substitution matrices in mind, an
earlier conclusion can be fine-tuned. Previously, the result that response category was
independent of target category was discussed as either consistent with the shared system
hypothesis, or separate systems with the added requirement that all of the errors arise
prior to the determination of target category. However, regressions revealed the
importance of high-level variables (e.g., numeric distance, character names) which are
accessed only after character identity has been determined. The influences of these
representations on the confusability matrix suggest that all of the errors did not arise prior
to the determination of target category; some errors were affected by similarity at higher
levels. This finding somewhat strengthens the conclusion in favor of a shared
identification system for letters and digits. However, analyses did not test for the
presence of particular errors which arose after the determination of target category and
whether these particular errors did or did not maintain the stimulus category. Rather, the
result indicated that some errors arose at a high level and that overall the error did not
preserve stimulus category; it is possible that other errors arose prior to the hypothesized
split into letter and digit processes and did maintain category but their influence was not
evident in the overall error pattern. Additional stimulus manipulations or analyses could
search for the locus of particular errors through use of mixed case letter stimuli and/or
perseveration errors; perseverations of a letter identity but not its case would indicate
involvement of abstract letter identities, accessed only after the split. The presence of
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such errors and demonstration that they do not maintain the category of the stimulus
could strengthen the argument for a single system. However, additional theoretical
specifications would be required to describe the interaction between perseverations and
current trial activations and their effect on the determination of stimulus category.
Beyond character identification accuracy
Though the substitution matrix provided a rich source of data for analysis,
analyses of by-character error rates in this study failed to reveal any impact of the
independent variables. In Study 3 I continue to investigate the impact of visual
similarity, discriminability, complexity, frequency, and higher-level variables on
character identification, through data acquired in a same/different judgment task. Study 3
builds on the results of this study, providing both a second source of data relevant to
character identification, and potentially a more sensitive measure of performance in
response times. Unlike Study 2, which relied on errors to populate the character
similarity matrix, the same/different task ensures that every cell in the matrix contains a
value: the reaction time associated with the response to that pair of characters.
Response Times in Letter and Digit Same/Different Judgments (Study 3)
In this study I collected response times for all pairwise combinations of uppercase
letters and digits through a speeded same/different judgment. Though similar in many
ways to the studies by Courrieu and colleagues (2004) and Podgorny & Garner (1979),
the present study has multiple advantages: use of a same/different task requiring a
response on every trial (c.f. go/no-go for different pairs), unmasked presentation,
simultaneous presentation of both items of the pair, and inclusion of digits.
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As in Study 2, multiple data sets were derived from a single task. The first set of
data is the response times on same trials (e.g., ‗D D‘, ‗4 4‘), which provides a measure of
the relative difficulty of determining and indicating that two identical characters are the
same. The second set of data concerns the different trials (e.g., ‗D 4‘). These responses
provide a measure of the similarity of the characters presented on that trial. Higher
response times, and lower accuracy, on these trials correspond to higher
similarity/confusability of the two elements of the pair.
Methods
For a complete picture of the similarity of letter and digit stimuli one would use
all uppercase letters, lowercase letters, and digits, presenting all pairwise combinations.
However, the resulting 6084 combinations are impractical to test empirically. Instead I
restricted the stimuli, as in Study 2, to 25 uppercase letters and 9 digits (excluding 0 and
O) resulting in 561 different pairs. Along with these different trials, an approximately
equal number of same trials were presented (17 presentations of each of the 34 samepairs: 578 trials). Of the 561 different pairs, 225 presented one letter and one digit, 300
presented two letters, and 36 presented two digits. The font Consolas was used to display
the stimuli.
On each trial, the two characters of the pair were presented horizontally, centered
on fixation. Participants were instructed to respond as quickly as possible whether the
two characters were the same or different, using designated keys on the keyboard.
Stimulus presentation timed out after 1500ms; pilot data indicated that participants
responded well within 1000ms. The ordering of the stimuli in the pairs and the hands
used for the response keys were counterbalanced across participants. A short practice
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block (40 trials) using symbol stimuli (e.g., %, $, #) preceded the main experiment and
served to familiarize the participants with the procedure and response keys. The entire
experiment, including practice and a brief mandatory break halfway through the main
experiment took about 45 minutes.
Data analysis
Data cleaning proceeded in two steps on individual participants‘ RT data:
Removal of outliers (trials with RT less than 2.5SD below or more than 2.5SD above that
participant‘s mean RT), and normalization to the mean by condition (dividing each trial
RT by the participant‘s mean RT for that condition—same or different--calculated
without outliers). Cleaned data were averaged across participants and the resulting 34x34
matrix (character 1 of the pair by character 2 of the pair) was symmetrized by averaging
the matrix with its transpose. The diagonal of this matrix is the normalized RT to same
trials; the upper and lower triangular portions are normalized RT to different trials. Only
one triangle was used for correlation and regression analysis as the other triangle is
identical due to the symmetrization procedure.
Accuracy data were also analyzed; extracted as a 34x34 matrix, averaged across
participants and symmetrized. The diagonal of the matrix gives the accuracy for the
same trials, while the off-diagonal cells are accuracy for the different trials; only one
triangle was used for analyses of the different accuracies.
To visualize the similarity structure of the Different trial RT data, a clustering
analysis was conducted and plotted as a dendrogram. The process for creating the
dendrogram involved computing the pairwise Euclidean distance between each of the
data points, multidimensional scaling of the distances, and creation of a hierarchical
132
binary cluster tree (using the MATLAB functions pdist, linkage (‗ward‘), and
dendrogram, respectively).
Correlation and multiple linear regression analyses were conducted separately for
same and different trials. These determined which of the predictor variables (see Tables
5.1 and 5.2) were predictive of the behavioral confusions, and whether they made
independent contributions.
Different pairs. The same predictors used in Study 2 for the substitution matrix
were used for the Different trial RT and accuracy data. There are thirteen in total: binary
category match, pixel overlap, total number of pixels, feature overlap, total number of
features, total perimetric complexity, perimetric complexity difference, frequency
difference, minimum frequency, maximum frequency, total frequency, name similarity,
and normalized distance. These are described in Table 5.2.
In a second analysis, different responses to cross-category pairs (Mixed), withindigit pairs (Digit-digit), and within-letter pairs (Letter-letter) will be considered
separately to determine whether the same factors are predictive of RT across these
categories of different pair.
Same pairs. Analyses of the same pairs used the single character predictor
variables described in Study 2 (see Table 5.1). These variables are: binary category,
number of features, number of pixels, perimetric complexity, character frequency,
average pixel overlap across all characters, average pixel overlap within category,
maximum pixel overlap across all characters, maximum pixel overlap with category,
average feature overlap across all characters, average feature overlap within category,
133
maximum feature overlap across all characters, and maximum feature overlap within
category.
In addition to analyzing the average data to all same pairs, a second measure of
same pair performance was calculated based only on the first presentation of each same
pair to each participant. This dataset is referred to as SameFirst to distinguish it from the
SameAll dataset. Parallel analyses were conducted for SameFirst as for SameAll using
the predictor variables described in Table 5.1.
Results
Comparing Same to Different Trials
Same and different trials differ in accuracy: Different pair accuracy was higher
(92% correct) than same pair accuracy (89%, U = 6577, N1 = 34, N2 = 561, p < .01).
Comparing RT for same and different pairs (using data normalized by average correct
trial RT regardless of condition) revealed that same trials were responded to more quickly
than different trials (Same: .99, Different: 1.02; U = 4778, N1 = 34, N2 = 561, p < .001).
The RT matrix for Different, SameAll, and SameFirst data are reproduced in Appendix
C.
Different trials: RT
Dendrogram. The dendrogram computed from the RT values for different trials is
displayed in Figure 5.1. Characters with high similarity are grouped into (unordered)
clusters, with the height of the vertical branch connecting two clusters indexing their
similarity. Order of the clusters along the horizontal axis is arbitrary and depends only on
the constraint that branches are not allowed to cross for display purposes. One immediate
134
observation from the dendrogram is that letters and digits are highly intermixed, with
most digits having a letter as the other character in their immediate cluster (6-G, 8-B, 5-S,
9-Q, 1-I-T, 4-A, 7-Z). Furthermore, visual similarity appears to be a major organizing
factor of the clusters, as can been seen not only in the lowest level clusters but also
higher-order groupings containing characters which appear to share categories of features
such as curves (leftmost cluster: 6, G, 8, B, R, D, P, U) or the presence of two vertical or
near-vertical segments (rightmost cluster: H, W, M, N). These observations suggest that
the RT data are indexing similarity which is based in part in visual similarity; particular
types of visual similarity are explored in the following sections.
135
Figure 5.1: RT dendrogram computed from Different trials. X-axis labels are shown in
Consolas, the display font used in the experiment.
Quantitative analyses. Pairwise correlations were performed between the
predictor variables in Table 5.2 and the dependent variable of Different trial response
136
time. Five significant correlations were revealed: binary category match, feature overlap,
pixel overlap, normalized distance, and minimum frequency (all ps < .05). Binary
category match was positively correlated (r = .12) with RT, consistent with the result
reported above that Mixed pairs were responded to faster than Letter-letter/Digit-digit
pairs. Feature and pixel overlap were both positively correlated (r = .21) with RT,
indicating that higher feature and pixel overlap between the characters in a pair are both
associated with slower responding. Normalized alphabetic/numeric distance was
negatively correlated (r = -.13) with RT, indicating a time-cost associated with
letters/digits which are close together in the alphabet or numerically close. The final
significant correlation was between the minimum (smaller) frequency of the two
characters of the pair, which was positively associated (r = .12) with RT: The presence of
a rare character resulted in faster responding.
Stepwise multiple linear regression was conducted with all of the Table 5.2
variables included as possible predictors. The resulting best model included four
predictors and accounted for 18% of the variance in the RT data (F(4, 556)=29.46, p <
.05, R2 = .18). The predictors included are pixel overlap (β = .01), normalized distance (β
= -.0007), frequency sum (β = .005), and feature overlap (β = .004), which were added to
the model in that order. The intermediate models achieved R2 values of .14, .16, .17, and
.18, suggesting that the addition of each subsequent predictor increased the ability of the
model to account for the data. See Table 5.5 for a summary of these and subsequent
results.
By trial type. There are three types of different trials: Letter-letter pairs, Digitdigit pairs, and Mixed (digit-letter/letter-digit pairs). The average RTs for these pair
137
types are 1.00 for Letter-letter pairs, 1.01 for Digit-digit pairs, and .99 for Mixed pairs;
the former two do not differ while both are slower than the Mixed pairs (LL compared to
Mixed: U = 28691, N1 = 300, N2 = 225, p < .05; DD compared to Mixed: U = 3001, N1 =
36, N2 = 225, p < .05). This result suggests that the presence of a character from the two
different categories facilitated responding ―Different‖ to the pair.
Correlations of Digit-digit trials with the predictor variables (excluding binary
category match) revealed no significant correlations, likely due to the small size of this
subset of the data (only 36 trials). Correlations of Letter-letter trials revealed significant
correlations with feature overlap, pixel overlap, total features, total perimetric
complexity, minimum frequency, and summed frequency; all were positive. The
relationships with feature and pixel overlap indicated slower responding associated with
increased visual overlap (feature: r = .23, pixel: r =.34). The relationship with total
perimetric complexity (r = .14) and total number of features (r = .14) indicated slower
responding associated with increased letter complexity. The positive correlation with
minimum frequency (r = .14) indicated an increase in response time for higher frequency
letters, while the positive correlation with summed frequency (r = .12) indicated an
increase in response time as the overall frequency of the letters of the pair increased.
Correlations with the Mixed trials were largely consistent with the correlations found
with the Letter-letter trials: feature overlap, pixel overlap, difference in perimetric
complexity, and minimum frequency were all significant correlates. The relationship
between Mixed trial RT and the two types of frequency was positive (feature r = .21,
pixel r = .42). Difference in perimetric complexity correlated negatively (r = -.15),
indicating a decrease in response time as the difference in complexity of the two
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characters of the pair increased. Minimum frequency was positively correlated: As the
frequency of the less-frequent character of the pair increased so did response time.
Stepwise multiple linear regressions were run on the Letter-letter and Mixed
datasets, with the same variables used for correlations (normalized distance excluded for
Mixed). A significant model emerged for Letter-letter trials which included pixel
overlap, summed frequency, and feature overlap (F(296,3) = 17.57, p < .001). Beta
values were .01 for pixel overlap, .005 for summed frequency, and .005 for feature
overlap. These variables were added to the regression model in the order listed; R2
values for the subsequent models were .12, .14, and .15 for the final model. The final
model for the Mixed data included only two predictors: pixel overlap and feature overlap
(F(222,2) = 27.56, p < .001). This model accounted for 20% of the variance, with a beta
value of .13 for pixel overlap and .05 for feature overlap. The interim model included
only pixel overlap, accounting for 18% of the variance in the data.
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Table 5.5: Significant predictor variables in regressions of Different pair RT data (Beta values)
Predictor Variable All different RT
Letter-letter RT
Mixed pairs RT
Pixel overlap
.01
.01
.13
Feature overlap
.004
.005
.05
Total frequency
.005
.005
Normalized
distance
Total model R2
-.0007
.18
.15
.20
Different trials: Accuracy
Pairwise correlations were carried out between the predictor variables and
Different trial accuracy. Four significant correlations were revealed: binary category
match, feature overlap, pixel overlap, and normalized distance (all ps < .05). Negative
correlations were found with feature overlap (r = -.16) and pixel overlap (r = -.25); higher
levels of visual overlap were associated with lower accuracy. Binary category match was
also negatively correlated with accuracy (r = -.14): Same category pairs resulted in lower
accuracy than cross-category pairs. Finally, normalized distance was positively
correlated with Different trial accuracy (r = .14); increased alphabetic/numeric distance
between characters of a pair resulted in increased accuracy.
Stepwise multiple linear regression was conducted for all of the predictor
variables listed in Table 5.2 with the dependent variable of Different trial accuracy. The
resulting model included three predictors, accounting in total for 9% of the variance
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(F(3,557) = 18.35, p < .05). The included predictors were pixel overlap (β = -.01), binary
category match (β = -.005), and feature overlap (β = -.004); which were included in the
model in that order. The addition of each predictor increased R2 of the model from .07 to
.08 to the final .09 value.
By trial type. Comparisons between Letter-letter, Digit-digit, and Mixed pair
types on accuracy indicated that while the two same-category pair types did not differ
(Letter-letter: 91%, Digit-digit: 92%), Mixed trials were more accurate than Letter-letter
trials (Mixed: 92%, versus LL: U = 28442, N1 = 300, N2 = 225, p < .05). Parallel to the
analyses on RT, correlation and regression analyses were performed on accuracy of
Letter-letter, Digit-digit, and Mixed pairs. As with RT, Digit-digit trials did not correlate
significantly with any of the predictor variables. Letter-letter trials correlated negatively
with feature overlap (r = -.14), pixel overlap (r = -.22), total perimetric complexity (r =
.12), and summed frequency (r = -.13). Mixed trials correlated with only two variables:
feature overlap (r = -.13) and pixel overlap (r = -.35).
Stepwise multiple linear regressions were run on the Letter-letter and Mixed
datasets. The resulting model for the Letter-letter trials included pixel overlap (β = -.01)
and maximum frequency (β = -.006) and accounted for just 7% of the variance (F(297,2)
= 11.20, p < .05). For the Mixed trials, only pixel overlap (β = -.01) was included in the
model (F(223, 1) = 30.78, p < .05, R2 = .12).
Same trials
Accuracy did not differ between SameAll (89%) and SameFirst (89%) datasets.
However, RT did differ: SameFirst trials were slower than SameAll (1.02 versus 1.00
normalized RT, Mann-Whitney U = 270, N1 = 34, N2 = 34, p < .001).
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SameAll. Letters and digits do not differ in SameAll RT (both 1.00) or accuracy
(both 89%). Correlations between all of the predictor variables in Table 5.1 and the
SameAll RTs resulted in no significant correlations. Correlations between the predictor
variables and the SameAll accuracies revealed a single positive correlation with character
frequency (r = .36, p < .05). This small correlation indicates the tendency of characters
with higher frequencies to result in higher average accuracy on Same trials.
A stepwise multiple linear regression conducted on SameAll RT values did not
result in a significant model; in addition to predictors not making significant individual
contribution to explaining the data, a combination of predictors was also unable to do so.
The parallel analysis conducted instead on SameAll accuracies resulted in a model
containing only character frequency, which accounted for 12% of the variance in the data
(F(1, 32) = 4.86, p < .05, R2 = .12).
SameFirst. Considering only the first presentation of each same pair, letters were
responded to more quickly than digits (digits: 1.04, letters: 1.01; U = 46, N1 = 34, N2 =
34, p < .01). Pairwise correlations between SameFirst RT and the predictor variables
listed in Table 5.1 resulted in two significant correlations: binary category and average
feature overlap computed over all characters. The relationship between RT and binary
category was negative (r = -.47, p < .05), consistent with the result that digit characters
resulted in slower RT than letter characters. The relationship between RT and average
feature overlap (all characters) was also negative (r = -.39, p < .05), indicating that
participants were slower to indicate that two identical characters were the same when that
character has a high average featural overlap with other characters. Parallel correlations
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between SameFirst accuracy and the predictor variables resulted in no significant
correlations.
Multiple linear regression stepwise analysis on SameFirst RT data resulted in a
model containing two predictors: binary category (β = -.02) and average feature overlap
computed over all characters (β = -.19), the same variables which were independently
correlated with the dependent measure (F(2,31) = 7.14, p < .05). Together the variables
account for 32% of the variance in SameFirst RT. Parallel analyses on SameFirst
accuracy data resulted in no significant model; no combination of the predictor variables
provided a significant explanation of the dependent variable.
Discussion
Overall, attempts to explain the results for different trials were more successful
than for same trials. However, insights were gained in both instances about the variables
which influence speed and accuracy of responding in a same/different paradigm with
letters and digits. Overall, different trials were found to be more accurate while same
trials were responded to more quickly (faster same than different RT was also reported by
Podgorny & Garner, 1979; both patterns found by Wiley et al., in prep.).
Different trials
The dendrogram created from RT data for the different trials suggested
intermixing of response times to letter and digit stimuli and visual similarity as a strong
organizing factor. These observations were borne out in regression analyses, which
revealed that pixel and feature overlap between the two characters of the pair were
predictive of response times. The effect of visual overlap was to slow response time, a
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common finding with letter stimuli in similar paradigms (e.g., Courrieu et al., 2004;
Podgorny & Garner, 1979; Wiley et al., in prep.). The stepwise regression procedure is
informative as to the relevance of the two types of visual overlap tested. In all models
including both visual overlap variables (Different trial RT- All trials, Letter-letter
different trial RT, Mixed different trial RT), pixel overlap was added to the model first,
followed by feature overlap. Though pixel overlap made a larger contribution (verified
by the beta values, which were consistently larger for pixel than feature overlap), feature
overlap made a significant independent contribution to explaining the variance in
different trial RT. This finding is particularly striking in light of the fact that pixel and
feature overlap are significantly intercorrelated (r = .25, p < .001), and supports the
feature set as an approximation of abstract features involved in character identification.
In particular, that the feature set contributes to predicting not only Letter-letter different
trials but also the full set of all Different trials (and Mixed alone) suggests that the
features and overlap relationships are relevant for both letter and digit characters. To my
knowledge the feature set developed here is the first to explicitly describe both letter and
digit characters (though existing feature sets could be expanded to describe digits).
Multiple variables indexing character frequency were included in the regression
models (and are highly inter-correlated); summed pair frequency was found to be
predictive of different trial RT. As the total frequency of the two characters increased it
slowed responding, indicating a speed advantage for low frequency characters. This
effect arose despite the local frequency statistics of the experiment, in which every
character was presented equally frequently. As reported in Study 1 (Chapter 4), character
frequency for digits exceeds that for uppercase letters; the predictive effect of character
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frequency is not simply a result of this relationship because Digit-digit pairs were not
found to differ in RT from Letter-letter pairs.
Mixed and same-category different trials were found to differ in RT and
accordingly a significant correlation was found between binary category match (i.e.,
whether the two characters of a pair were from the same category) and different trial RT.
However binary category match was not found to be a significant predictor in the
stepwise regression. This outcome appears to suggest that the effect of binary category
match on RT was better accounted for through a combination of other variables,
specifically feature overlap, pixel overlap, normalized distance, and summed character
frequency (the significant predictors in the regression model). However, normalized
distance is highly correlated with binary category match due to the design of the variable:
Distance is only meaningful for within-category pairs, and the mixed pairs were assigned
the same arbitrary value. The result is that normalized distance also indexes binary
category match. To investigate this relationship, a stepwise multiple linear regression
was run excluding the normalized distance predictor; the resulting model includes binary
category match (also pixel overlap, feature overlap, and frequency minimum; model
F(556,4) = 29.27, p < .05, R2 = .18). A stepwise regression which excluded both
normalized distance and binary category match also resulted in a significant model,
though the explained variance is reduced relative to one including either binary category
or normalized distance (F(557,3) = 35.06, p < .05, R2 = .16). These investigations
indicate that the RT advantage for mixed-category pairs relative to same-category pairs
was fully explained by predictors which did not explicitly encode these two trial types. It
is unclear at this point whether the finding reflects the impact of one or more untested
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variable(s) which co-vary with category membership, or a categorical effect as assumed
by the binary category match predictor.
There was less variability in accuracy than response time in this experiment
(average performance was over 90% correct). However, some associations were still
revealed between the different trial accuracy data and predictor variables. In a regression
model, accuracy was predicted by pixel and feature overlap as well as binary category
match; higher visual overlap led to lower accuracy and pairs of characters from the same
category led to lower accuracy. The visual overlap result is consistent with that found for
RT; characters which are visually similar led to both slower RT and as well as lower
accuracy. Binary category information made an additional contribution beyond the other
included variables in accounting for variation in accuracy, though the overall variance
accounted for in the accuracy model (9%) was much lower than that in the RT model
(18%).
Subsets of the different trials were analyzed based on the type of different pair:
Letter-letter, Digit-digit, or Mixed. Analyses of Digit-digit trials revealed no significant
correlations, likely due to the small number of trials in this condition. Analyses of the RT
Letter-letter and Mixed trials both resulted in significant regression models including
pixel and feature overlap, with summed pair frequency making an additional contribution
to explaining the Letter-letter data. For accuracy, models predicting Letter-letter and
Mixed data included pixel overlap but not feature overlap, as well as maximum frequency
for Letter-letter pairs. That the by-type analyses revealed a subset of the variables found
to predict overall Different trial performance suggests that the same variables affect
performance regardless of the particular categories of characters presented on each trial,
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consistent with a single system, sensitive to certain variables (e.g., visual overlap) in
processing both letter and digit characters.
Regression models predicting different trial performance included binary category
information, and overall mixed pair performance was faster and marginally more accurate
than same-category pair performance. Though the number of mixed, Letter-letter, and
Digit-digit trials were not equal, it is not straightforward how Mixed trial performance
would have been boosted by trial counts: Mixed trials were approximately 40% of the
different trials, Letter-letter: 53%, and Digit-digit: 6%. Perhaps more likely is the
influence of explicit knowledge of character category within the identification system.
Investigations reported in McCloskey and Schubert (2014) pointed to the existence of an
explicit representation of digit/letter category, an output from the allograph level of
representation. We concluded in that study that the category representation does not
influence identification (i.e., does not bias selection of an identity of the same category as
the stimulus), but it is possible that the information was used in the same/different task.
Importantly, knowledge of the category of the two stimulus characters is relevant to the
same/different judgment: Any trial on which the two characters were from different
categories was a Different trial.
Same trials
Because same trials were repeated throughout the experiment, which may have
lessened the effects of various influences and facilitated processing due to repetition,
same trials were analyzed both as a whole and including only each participant‘s first trial
for each same pair. Speed on same trials increased when considering all trials compared
to just the SameFirst trials (accuracy did not differ). Considering SameAll trials, letters
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and digits did not differ in accuracy or RT, and no correlations were found between RT
and any of the predictor variables. SameAll accuracy was found to be predicted by
character frequency, with lower frequency resulting in lower accuracy; this variable alone
accounted for 12% of the variance in SameAll response time.
SameFirst response times were predicted by a combination of binary category
(letters v. digits) and average feature overlap between the presented character and all
other characters. The inclusion of the former predictor is consistent with the observation
that RT to letters exceeded that to digits. This pattern is the reverse of that commonlyreported; one possible explanation for the slower digit responding could be that digits
were less frequent in the experiment: Same digit trials were only 26% of the Same trials.
Accordingly, responding may have been facilitated for letter trials because the
representations will have been on average more recently and more often accessed. This
phenomenon remains to be tested with other paradigms to determine whether it reflects a
property of the task or of the identification system more generally.
The success of the average feature overlap computed over all characters is
suggestive of a shared letter and digit identification system. Other competing predictors
indexed average feature overlap between the presented character and other withincategory characters (e.g., digit characters with other digits) as well as the same measures
computed with pixel rather than feature overlap. The success of the average feature
overlap predictor indicates two properties of the underlying processing. First, this
predictor is computed with the assumption that all characters compete with each other;
average overlap is calculated with all character pairs rather than just same-category pairs.
This assumption is consistent with shared identification systems, in which letters and
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digits compete with each other (independently of the category to which they belong).
Second, the success of a feature rather than pixel overlap predictor suggests that the
relevant visual similarity was at a fairly abstract level at which character features are
represented (such as the character shape level), providing evidence that these features are
involved in both letter and digit representations.
Conclusions
Broadly, the results of this study indicated that both same and different responses
to pairs of letter and digit characters were affected by visual overlap and character
frequency. The results of Study 3 are largely consistent with a shared identification
system, suggesting that one of the first two possibilities is likely; but it remains to be
confirmed.
Furthermore, the results of this study have implications for interpretation of the
same/different task. This task could be accomplished purely on the basis of low-level
representations (i.e., the viewer-based visual feature level) without consultation of
information about abstract character shape, stored form, or identity. However, the results
suggested that representations at multiple levels of the identification system impacted
response times and accuracies. The effects of visual similarity were not limited to pixel
overlap; feature overlap was a significant predictor of both same and different pairs. This
effect suggests that though not necessary for the task, information about the visual
features present in the stimuli impacted performance, influencing the perceived similarity
of the pairs. Furthermore, effects of character frequency imply use of a stored level of
representation: allograph and/or abstract character identity representations. The type of
frequency employed here was case-specific, which is most consistent with activation of
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case-specific allograph representations. If explicit category information was used, this
implies activation beyond the allograph level. Alphabetic and numeric distance was also
found to predict accuracy and RT for different trials; this information is likely to be
linked to character identity representations (or allograph representations) and indicates
some impact of high-level semantic knowledge about the characters on performance.
Recent work comparing same/different judgments by naïve and experienced readers of
the Arabic alphabet found that both low-level (e.g., visual) and higher-level (e.g., letter
names, motor production patterns) information impacts performance (Wiley et al., in
prep.). The results of the current study are consistent with this task involving a range of
representations in the identification system.
General Discussion
The analyses of Study 2 and Study 3 data were largely parallel, addressing the
same underlying questions of how accuracy and speed of identification are influenced by
variables relevant to the character identification system. Identification error patterns were
considered to reveal the other active representations during processing of a given
character and the similarities between these representations. In terms of response time,
character pairs with high response time are assumed to be more similar, i.e., to have high
relative overlap between the character representations.
The results of Studies 2 and 3 suggest roles of visual similarity (both pixel and
feature), visual complexity, character frequency, character name similarity, and numeric
distance in character identification performance. Visual complexity (number of pixels)
and pixel overlap are assumed to reflect overlap and similarity of representations at
viewer-based feature levels. Feature overlap reflects a higher level of visual similarity in
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terms of somewhat abstract features represented at the character shape level. Character
frequency effects would arise at allograph or abstract identity levels, where stored
representations can differ in resting activation or threshold based on the frequency with
which that representation has been activated in the past (i.e., character has been
experienced and correctly represented). Name similarity and numeric distance are both
measures of similarity at levels beyond character identification; this information can be
accessed through character identity representations. Though effects of visual similarity,
complexity, and frequency have been reported in letter identification studies, these
studies are the first to investigate their effects on digit identification.
Differences between Study 2 and Study 3
A few key differences can be noted between the findings of Study 2 and Study 3.
First, while by-character independent variables were largely unsuccessful at predicting
by-character error rates in Study 2, robust relationships were discovered between these
variables and Same trial performance in Study 3. The positive results of Study 3 suggest
that the variables are not irrelevant to character identification but rather that the bycharacter dependent measures collected in Study 2 were not sufficiently variable to reveal
significant associations. Future studies eliciting by-character error rates should aim to
include higher and more variable values to increase the chance of successful prediction.
A second difference between the two studies concerns the role of feature overlap. This
variable was only found to predict one subset of the confusion data in Study 2 (Letter-forletter substitutions), while it was a robust predictor which accounted for independent
sources of variance in Study 3 data. The success of the feature overlap predictor in Study
3 suggests that the feature set approximates abstract featural representations in the
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character identification system, and furthermore that the method for computing overlap
between the features of two characters results in comparable similarities to similarity
relationships between character shape representations.
Shared identification systems
A number of results across both studies contribute to a growing body of evidence
consistent with shared identification systems for letter and digit characters. In Study 2,
the category (letter/digit) of error responses was found to be independent of the category
of the target character. This result suggests that the errors arose within an identification
system in which processing of letter and digit stimuli was not computationally distinct: a
shared identification system. However, this conclusion would be strengthened by direct
evidence suggesting that all of the errors (or particular ones which cross category) did not
arise at early processing levels prior to any letter/digit processing split.
Two additional findings from Study 3 support the shared systems theory. First,
average feature overlap, computed over all characters, was a reliable predictor of RT on
same trials. The relevance of this finding is that the predictor is consistent with the
assumptions of a shared system. In a shared system all characters compete with all other
characters, without regard to letter/digit category, and therefore the relevant visual
similarity is computed with respect to all characters. Another feature overlap variable,
which was unsuccessful in predicting RT, was computed over only within-category
characters, consistent with the assumption of separate systems that competition at some
levels is limited to same-category characters. Second, subsets of the different trials in
Study 3 coming from Letter-letter and Mixed (Letter-digit and Digit-letter) trials were
predicted by the same variables. This result is also consistent with the shared system
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assumption that performance on all characters will be sensitive to the same variables,
regardless of their category.
A note with regards to the shared systems theory is that it does not preclude the
presence of knowledge of digit/letter category membership. In fact, the ability of readers
to report the category of a stimulus suggests that this is information which is extracted
through the identification process. The claim of the shared systems hypothesis is that
category membership does not affect the process of determining the identity of a
stimulus. However, category membership can have other impacts on performance. One
possible example is the facilitation observed in Study 3 for Mixed category different
pairs; one source for this facilitation could be explicit knowledge of stimulus category
impacting the same/different judgment.
Stepwise regression analyses such as those used in Study 2 and 3 should be
interpreted with some caution as the particular ordering of variables entered may not
reflect the most optimum variables predictive of the dependent variable but rather a
sufficient set. There was a high degree of intercorrelation among the independent
variables used here (particularly between versions of the same variable, such as summed
and max frequency, which are based on the same underlying frequency values), and
strong conclusions cannot be drawn about the relative importance of these intercorrelated
variables on the basis of the results. For that reason conclusions refer to the importance
of visual similarity and frequency generally, rather than a specific measure (e.g., summed
pair frequency) which was revealed to be a successful predictor in the model found.
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CHAPTER 6: POSITION IN LETTER IDENTIFICATION (STUDY 4)
This study considers position representation in identification, specifically letter
identification during word recognition. Studies utilizing masked priming of lexical
decision and cross-case same/different paradigms, among others, have suggested that
letter position is coded in a flexible manner. More specifically, using evidence from
normal participants in an illusory word paradigm, Fischer-Baum and colleagues (2011)
provided evidence for graded both-edges coding of letter position. Through analysis of
errors of an individual with acquired dyslexia, McCloskey and colleagues (2013)
suggested that graded both-edges position is implicated in the coding of letter allographs
and abstract letter identities. However, both of these studies have limitations. First, the
illusory word paradigm depends upon setting up the opportunity for migration errors and
therefore requires careful design of stimulus items to test particular hypotheses about
letter position. This resulted in a small number of position schemes tested in that study.
The latter study, which involved analysis of perseveration errors in a large corpus of
unselected reading errors made by an individual with acquired dyslexia (LHD), tested a
larger number of position schemes, an improvement over the previous study. They
concluded in favor of a graded both-edges scheme used to code position of allograph and
abstract letter identity representations. However, the conclusions of the LHD study
would be strengthened by converging analyses of letter identification in unimpaired
participants. In Study 4 I aimed to address both of the limitations of previous studies
eliciting a large dataset of identification errors, from unimpaired participants, on which a
wide range of position schemes could be tested, including the commonly-posited openbigram scheme.
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According to the assumptions of cascading activation in letter identification,
multiple representations are active during letter identification. Under normal
circumstances (e.g., sufficient size and contrast of visual letter stimuli) in the unimpaired
identification system the activation for the stimulus letter is strong, preventing the other
active representations from being selected as the winning identity. By inducing errors in
the normal system one reveals the other representations which were active concurrently,
though they are normally not selected. To elicit errors from the undamaged identification
system one can provide weak input for the target letters by displaying word stimuli
briefly and away from fixation (Weinzierl, Kerkhoff, van Eimeren, Keller, & Stenneken,
2012). This technique results in letter substitutions and insertions, as well as smaller
numbers of deletions and transpositions, as seen in Study 2. To the extent that these
errors are perseveration errors, they reflect the residual activation of letters from previous
trials, and can be analyzed for the position maintained by these errors. These errors
reveal the underlying position coding used by the identification system: Due to the
position-specificity of letter representations, letters will intrude as errors in the same
position in which they first appeared (in a previous response). Analyses seek the position
code which can explain the position occupied by the perseverated letters with respect to
their position on a previous trial. Under the assumption of position-specific
representations in identification, residual activation will occur for a representation at a
particular position, and this representation will then re-appear at the same position in a
future response.
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Methods
Twenty participants were asked to report (by typing) briefly-shown word and
pseudoword stimuli. A fixation cross was presented in the center of the screen and on
each trial a single stimulus appeared just to the left or right of fixation. Pilot testing
indicated that left visual field presentation resulted in lower accuracy, while a fairly
balanced proportion of stimuli in the two visual fields ensured that participants did not
shift their focus from the central fixation and thereby inflate accuracy on the fixated side.
Therefore, sixty percent of stimuli were presented in the left visual field, the remainder in
the right.
Stimuli consisted of 600 words and 120 pronounceable pseudowords. Length
varied between 4 and 8 letters, with equal numbers of items of each length (120 words
and 24 pseudowords per length). The font Courier New was used and all stimuli were
presented in lower case.
Pilot testing indicated that stimulus durations of less than 70ms were sufficient to
produce a high proportion of errors. Stimuli were divided into ―short‖ (4-6 letters) and
―long‖ (7-8 letters) with different durations set for these two categories. Stimulus
duration was calibrated for each participant through 3 practice blocks of 10 trials each,
aiming to produce an accuracy of 60% correct.
After stimulus offset, participants typed in their response. They were told that
they would see some words and some stimuli that were not words, and encouraged to
type in whatever letters they saw regardless of whether they formed a word (the
pseudowords were included to encourage this). Responses were displayed on the screen
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as they were entered and participants were allowed to use the Backspace key to correct
typos or change their response; the response period was untimed.
The sequence of events in each trial was as follows: fixation cross for 200ms,
stimulus for duration set by individual‘s practice performance, response period for
unlimited duration (terminated by the Enter key), blank screen for 500ms, and self-paced
ITI (screen displaying ―…‖, terminated by Spacebar). A brief mandatory break split the
experiment into two halves; the entire experiment including practice trials took
approximately 50 minutes.
Long Duration Experiment
It is possible that errors could be introduced through the typing response; these
would not reflect the operation of the identification system. Though the population of
undergraduate research participants has extensive reading and typing expertise, typos
may be particularly rampant when participants seek to complete a tedious experimental
task as quickly as possible. Typing errors could take a different form than the
identification errors (e.g., typing errors may be non-perseverative while identification
errors contain perseverations) and act as noise in the analyses, reducing the possibility of
revealing a true effect in the data. Alternatively, typing errors could be of the same form
as the identification errors (e.g., both may be perseverative) and artificially inflate the
observed effect(s). The simplest solution is to attempt to collect the cleanest data
possible. Precautions in the main experiment consisted of: displaying the response on the
screen while it was entered, allowing the participant to make corrections before
submitting the response, and unlimited time for responding.
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In addition, to independently investigate the prevalence of typing errors, a
separate experiment was run with three participants. Stimulus items were a randomlyselected subset of the items used in the main experiment (4-8 letters in length). Testing
consisted of 360 trials: 59 pseudowords and 301 words. Stimuli were presented for 300
and 350ms (for short and long stimuli, respectively); all other presentation parameters
and the trial structure were the same as the main experiment. Identification accuracy in
the long duration condition should be at ceiling; any errors introduced can be assumed to
be typing errors. If error rates are small in this condition it is fair to assume that typing
errors make a negligible contribution to the letter errors in the brief presentation
condition.
Accuracy and Perseveration Analyses
Data were combined across participants to increase the corpus of errors for
analysis. However, chance analyses were conducted using trials from the participant‘s
data being tested. Initial analyses considered error rates for word and pseudoword
stimuli. Single letter errors were classified by an automated program (i.e., substitution,
insertion, omission, transposition, other error). Errors consisting of the repetition of an
entire response within a participant‘s data were excluded, as these could artificially
inflate the measures of letter perseveration errors. Substitution and insertion errors are
intrusion errors, which are possible perseveration errors. Perseveration analyses, as in
McCloskey et al. (2013), considered these intrusion errors and computed the number of
times the same letter occurs in the immediately preceding trial (‗I-1‘ for Intrusion trial
minus one) as a potential source for the perseveration. The proportion of times the letter
was present in a randomly selected trial (from outside the vicinity of the intrusion trial)
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was also calculated, as an estimate of the likelihood of a letter recurring in a response by
chance. In the event that the intruded letter was not found in I-1, the analysis (number of
times the letter occurs in the source trial and chance estimate) was repeated for trial I-2,
and so on until a potential source trial could be found or a limit of 10 trials prior to the
intrusion trial was reached (i.e., through I-10). The number of contiguous trials for which
there were intrusion sources present above chance rates was termed the perseveration
window. The perseveration window was then used in analyses of perseveration position.
The intrusions in the data set were matched with one or more possible source
trial(s): Trials within the perseveration window containing the intruded letter. The
intrusions are potential perseveration errors, now matched with their potential sources,
but it is not possible to know which particular intrusions are perseverations (i.e., caused
by presence of the letter in the source response). However, the number of true
perseverations was calculated from the number of intrusion-source pairs and the chance
rate of intruded letters in a prior response (see Appendix A of McCloskey et al., 2013 for
details). The number of true perseverations was then used to derive the position matches
as a proportion of the number of true perseverations for position schemes, which allows
comparisons among position schemes (see below). Throughout the results section,
reported p-values were derived from Monte Carlo chance analyses with 1,000 iterations.
Perseveration Position Analyses
Analyses determined which position scheme(s) best predicted the position
occupied by the intrusion errors with respect to their source letters. The analysis asked
whether the intruded letter in the intrusion trial and that same letter in the source trial
were in the same position, according to the particular position scheme under
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consideration. The number of actual position matches (where the letter was in the same
position) was compared to the number of chance position matches. Chance position
matches were calculated using randomly selected responses as the source trial, these
responses were required to be the same length as the source response, contain the
intruded letter, and be located outside the immediate context of the perseveration trial in
the experiment. In other words, the position matches were compared to an estimation of
the position matches expected if the position of the intruded letter is unrelated to the
position of the source letter.
Position Schemes
Broadly, the position schemes considered were: beginning-based, end-based,
both-edges, midpoint, preceding-letter and following-letter (i.e., closed-bigram), trigram,
open-bigram with preceding- and following-letter, and syllabic. These schemes have all
been previously proposed as manners of representing letter position in reading and/or
spelling; see Chapter 2 for review. Three both-edges schemes were considered: a simple
combination of beginning-based and end-based schemes, the beginning and end schemes
plus immediately-adjacent positions (narrowly-graded both-edges), and finally adding
second-adjacent positions (broadly-graded both-edges). Three midpoint schemes were
considered, which differed in how central letters were assigned to positions: Scheme
Midpoint1 assigns characters flanking the center of the string to positions -1 and 1, with
no character in position 0; Midpoint 2 assigns the character to the left of center position 0
and the character to the right of center position 1; Midpoint 3 assigns the character to the
right of center position 0 and the character to the left of center position -1. Closed bigram
and open bigram schemes were considered with and without explicit inclusion of word
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boundaries in the position representations. Additionally, open-bigram schemes were
considered which included one or two possible intervening letters.
Orthographic syllabification remains a topic of debate in the literature and
therefore the syllabic schemes were tested on two syllabifications of the data which
maximized the letters in either coda or onset positions, (CMax and OMax, respectively).
The syllabification algorithms labeled each syllable within the response with a syllable
number and delineated the role (onset, nucleus, coda, with the possibility of multiple
letters per role) held by each letter within a syllable. For example, the response
NEBULSH was coded as having two syllables: NE.BULSH (OMax) or NEB.ULSH
(CMax). Considering the CMax syllabification by way of example, syllable one15 (NEB)
would contain Onset1-Nucleus1-Coda1 roles and syllable two (ULSH) would contain
Nucleus1-Coda1-Coda2-Coda3 roles. Three syllabic schemes were tested in the position
analysis, varying in the manner in which they considered within-syllable positions. The
first scheme, Specific Roles, assigned position matches based on specific syllabic roles
(e.g., Coda2 position matches Coda2 position, HAND = CARD), the second scheme,
Graded Roles, assigned matches on basic syllabic role (i.e., any coda position matching
any other coda position in the same syllable), and the third scheme, Graded Adjacent
Roles, considered letters to match in syllable position if they occupied the same basic role
in the same or adjacent syllable within the response. Syllabic schemes were tested using
two position analyses: the retrospective method (described in the previous section) and
the prospective method, which is more appropriate to the syllabic schemes (described
below).
15
This is a simplification for explanation of the OMax/CMax distinction. In the analysis each
syllable was assigned position based on counting from the beginning of the response (NEB = syllable E+1)
as well from the end of the response (NEB = syllable B-1).
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The retrospective method gives the syllabic schemes an advantage in position
matches because position within syllables depends on letter identity. The identity of a
letter partially determines its syllable role (i.e., vowels are nuclei, consonants are onsets
or codas), and therefore searching for a particular letter identity in a source trial is not
independent from ascertaining whether that letter‘s position matches its position as an
intrusion. For example, in searching for a source for the intruded U in the response loup,
the analysis will consider the previous response, nebulsh, which also contains a U. The
retrospective position analysis considers whether these two Us are in the same position,
and they are both in a nucleus position, resulting in a match for the Graded Roles scheme.
However this match is misleading: U will necessarily be in a nucleus position in both the
intrusion and source responses due to its vowel status, resulting in an inflated number of
position matches for syllabic schemes.
To avoid this problem with syllabic scheme analyses, McCloskey and colleagues
(2013) developed an alternative position analysis method which does not search previous
trials for position matches but instead synthesizes intrusion errors and compares these to
the observed data. The prospective method uses the position of each source letter to
generate potential intrusion responses with that letter in the same position. For a given
stimulus, the generated response will contain an intrusion of the source letter at the same
position at which it appeared in the source trial, through either substitution of the letter in
that position or insertion of the source letter (if the position was unoccupied in the
stimulus). The generated responses are then compared to the observed intrusion
responses in the data set and any matching responses counted as position matches for that
scheme. Chance position estimates in the prospective method were calculated using
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randomly selected trials from outside the immediate context of the source trial,
generating predicted errors, and comparing these to the observed responses. Unlike the
retrospective method, the prospective method is limited to perseveration responses which
have only a single intrusion error because of the response generation process: it is unclear
how responses containing more than one error should be generated (using what order of
intrusions).
Result reporting is divided into two sections: evaluation of non-syllabic position
schemes (using the retrospective method), and evaluation of syllabic position schemes
(using the retrospective method and the prospective method). Retrospective analyses of
non-syllabic schemes first considered beginning-based and end-based position schemes,
followed by a both-edges scheme, as these schemes have been extremely successful in
previous work. Subsequently the graded both-edges schemes were tested. Other
schemes were then compared to this scheme. All analyses which compare schemes used
the residuals method described in McCloskey et al., (2013), which uses one scheme as
the base scheme, and considers the ability of the additional scheme(s) to correctly predict
the position of perseveration errors whose position is not predicted by the base scheme.
Long Duration Experiment Results
In the long duration experiment, accuracy was 99% for words and 86% for
pseudowords. Accuracy on short pseudowords approached ceiling (93%) while
performance on longer pseudowords was less accurate (75%). Perseveration analyses
revealed that letters did not intrude into later trials at rates higher than expected by
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chance (p > .4).16 This result suggests that typing errors do not surface as perseveration
errors in this task. Errors due to typing therefore only added noise to the perseveration
analysis, making it more difficult to reveal any perseverations from true
misidentifications in the brief duration experiment.
Main Experiment Results
Accuracy was 49.7% overall (14.0% for pseudowords, 56.8% for words), and
remained essentially constant over the experiment (50% correct in the first quarter, 51%
in Q2, 48% in Q3, 49% in Q4). For word stimuli, 83.6% of all responses were words,
and of errors, 62.4% were other words. Of these incorrect word responses, 54.4% were
more frequent than the stimulus word. For pseudoword stimuli, 52.8% of errors were
words. These results suggest a slight bias to respond with a word, which was stronger
when the stimulus was a word, suggesting that the participants may have had implicit or
explicit knowledge of the lexicality of the stimulus even when they were not sure of all of
the letter identities present.
There were 13,951 intrusion errors overall in the twenty participants‘ data. Error
types were very similar for the word and pseudoword stimuli: Errors were mainly
substitutions (words: 34% of errors, PWs: 38%), followed by deletions (words: 17%,
PWs: 24%), insertions (words: 9%, PWs: 8%), and transpositions (words: 4%, PWs: 5%).
16
For comparison, the perseveration analysis was run on the first 360 trials from three participants
(randomly selected) from the main experiment. This analysis revealed 1066 intrusion errors, with
significant perseverations present (p< .05 at I-1).
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Perseveration and position analyses
Perseverated letters were found with sources up to six trials prior to the intrusion
trial (I-6; p < .0001). The number of true perseverations was estimated at 1708 over the
perseveration window.
Position analyses first considered the ability of end-based and beginning-based
position schemes to account for the position of the perseveration errors. Beginningbased and end-based positions schemes correctly matched the position of the
perseveration errors (both ps < .0001), matching .442 and .376 of the true perseverations,
respectively. Allowing the end-based scheme to match additional perseverations not
matched by the beginning-based scheme, and allowing the beginning-based scheme to
match perseverations not matched by the end-based scheme both significantly increase
the position matches accounted for by the schemes (ps < .001). This both edges scheme
matches 68.0% of the true perseveration errors in the corpus. Adding immediatelyadjacent positions to the both-edges (beginning plus end) scheme—i.e., the narrowlygraded both-edges scheme—is a significant improvement (p < .002), and matches 95.1%
of true perseverations. All of the other schemes tested were also able to account for
significant proportions of the true perseverations, as shown in Table 6.1.
The broadly-graded both-edges scheme is also successful (p < .009) and matches
a near-perfect 98.2% of true perseverations. However, this scheme is considering nearly 4
positions as matching positions in the source trial and is therefore at an advantage relative
to other schemes, which generally predict only one position. For a more conservative
comparison, the narrowly-graded both-edges scheme (immediately-adjacent only) was
used as the baseline to which other position schemes were compared.
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Table 6.1: Results of non-syllabic position schemes
Proportion of position
Scheme
matches
Beginning-based
.442**
End-based
.376**
Both-edges (Beg + End)
.680**
Narrowly-graded both-edges
.951**
Broadly-graded both-edges
.982**
Midpoint1 (… -1| 1 …)
.334**
Midpoint2 (…-1 0 | 1…)
.297**
Midpoint3 (…-1 | 0 1…)
.273**
.343**
Closed Bigram† [AB]
.406**
.410**
Closed Bigram including word boundaries
.429**
.441**
Open Bigram-One [AXB]
.465**
.038**
Open Bigram-Two [AXYB]
.045
.673**
Open Bigram-One including word
boundaries
.561
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Proportion of position
Scheme
matches
Open Bigram-Two including word
.139**
boundaries
.110**
Trigram [ABC]
.166**
Trigram including word boundaries
.170**
*Significant at p < .05. **Significant at p < .001
†Two versions of bigram schemes were tested: considering the left letter as
context and the right letter as context. Listed in this order in the table.
Comparisons were made between the narrowly-graded both edges scheme and the
other schemes by allowing the other scheme to predict the position of perseverations left
unaccounted for by the both-edges scheme. Results are presented in Table 6.2; other than
the broadly-graded both-edges scheme only three schemes improved the narrowly-graded
both-edges scheme. The reported p-values refer to the ability of the additional scheme to
account for perseverations which are not matched by the narrowly-graded both edges
scheme; nonsignificant p-values indicate a scheme does not match a significant number
of the perseverations unaccounted for by the base scheme.
Three schemes (not including syllabic schemes) successfully accounted for
perseverations unaccounted for by the narrowly-graded both edges scheme. Of these,
two are midpoint schemes, differing in how positions from the midpoint are assigned to
the center characters of an even-length response. These schemes were successful in
accounting for true perseverations beyond the narrowly-graded both edges scheme. The
midpoint schemes were therefore compared to the broadly-graded both edges scheme.
The Midpoint1 scheme continues to account for seven perseverations beyond the
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broadly-graded both edges scheme (p < .05), taking the number of true perseverations
accounted for to 1528 (proportion of .986), from 1521 (proportion of .982) for the
broadly-graded both edges scheme. However, the Midpoint2 scheme did not account for
any perseverations beyond the broadly-graded both edges scheme (p > .6). The third
scheme with significantly improved the both-edges narrowly graded scheme was the
open-bigram scheme considering the left letter as context and word boundaries. When
this scheme was added to the broadly-graded both edges scheme, it did not match any
additional perseveration errors (p > .2).
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Table 6.2: Results of adding schemes to Narrowly-graded Both-edges scheme
Scheme added to Narrowlygraded Both-edges
Proportion of position
matches added by scheme
P-value of
adding scheme
Midpoint1
0.013*
.035
Midpoint2
0.011*
.024
Midpoint3
0.011
.081
-0.0091
.797
0.0172
.105
-0.00751
.816
0.0151
.115
0.0111
.352
0.0113
.297
0.0248
.206
0.0279
.115
0.0111
.386
0.0132
.310
0.0428*
.013
0.0407
.096
Closed Trigram
0.0095
.183
Closed Trigram with word
boundaries
0.0057
.186
Closed Bigram†
Closed Bigram with word
boundaries
Open Bigram-One
Open Bigram-Two
Open Bigram-One with word
boundaries
Open Bigram-Two with word
boundaries
*Significant at p < .05. †Two versions of bigram schemes: left letter as context, right letter as
context, in that order in the table. 1Negative change in proportion of position matches resulted
from an increased number of chance matches and an increased number of observed matches
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Table 6.3 presents values for the reverse comparison: The ability of the narrowlygraded both-edges scheme to match perseverations when added to another scheme. In
general, adding the narrowly-graded both-edges scheme to another (non-syllabic)
schemes significantly improved added perseveration position matches. However, four
exceptions exist, schemes to which the addition of the both-edges scheme did not cause a
significant improvement: Open-bigram with one and two intervening characters, both
with and without word boundaries (i.e., marking of letters at edge of the string as such).
The four schemes are all open-bigram schemes calculated based on the letter to the left of
the intrusion as context, rather than the letter to the right. An analysis was conducted to
determine whether adding the broadly-graded both-edges scheme would significantly
improve these four open-bigram schemes. For three of the schemes (open bigram-one,
open bigram-one with word boundaries, open bigram-two with word boundaries), the
addition of the broadly-graded both-edges scheme contributed significant position
matches beyond the base scheme (ps < .05); for the fourth scheme the broadly-graded
scheme contributed only marginally to accounting for the remaining perseveration errors
(p < .08).
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Table 6.3: Results of adding Narrowly-graded Both-Edges scheme to other schemes
Proportion of position matches added
by Narrowly-graded Both-edges
P-value of adding Narrowlygraded Both-edges
Midpoint1
0.630*
< .001
Midpoint2
0.665*
< .001
Midpoint3
0.690*
< .001
Closed Bigram†
0.576*
0.007
0.523*
0.012
0.523*
0.009
0.489*
0.001
0.451
0.085
0.453*
0.044
0.373
0.150
0.439*
0.030
0.279
0.171
0.332*
0.006
Base scheme
Closed Bigram with
word boundaries
Open Bigram-One
Open Bigram-Two
Open Bigram-One
with word
boundaries
Open Bigram-Two
with word
boundaries
0.112
0.128
0.180*
0.024
Closed Trigram
0.795*
0.006
Closed Trigram
with word
boundaries
0.764*
0.001
*Significant at p < .05. †Two versions of bigram schemes: left letter as context, right letter as
context, in that order in the table.
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Syllable-based schemes
Analyses of syllable-based schemes were conducted using two different analysis
methods, neither of which is ideal for testing syllabic schemes on this particular data set.
The retrospective method, used for all non-syllabic schemes, is not appropriate because it
gives the syllabic schemes an advantage for position matches. The prospective method,
which is appropriate for testing the contribution of syllabic schemes, suffers from the
requirement that only responses containing a single intrusion can be included combined
with the fact that the current data set has very few responses containing only one
intrusion error. Only 1394 potential perseveration-source response pairs could be
included in this restricted analysis, while the retrospective method analyzed 15534 pairs,
a much larger and more robust set of data. Despite these disadvantages, the syllabic
schemes were tested using both schemes and both results presented here, but they should
be interpreted with caution.
Using the retrospective method, all three syllabic schemes were highly successful
in accounting for position matches (see Table 6.4). As with the non-syllabic schemes,
these schemes were then compared to the both-edges narrowly-graded scheme. With the
CMax syllabification, only the graded adjacent roles scheme accounted for any
perseverations beyond those accounted for by the both-edges narrowly-graded scheme (p
< .01), and this scheme also accounted for perseverations beyond the both-edges broadlygraded scheme (p < .01). With the OMax syllabification, all three of the schemes were
successful at matching positions beyond the narrowly-graded both-edges scheme (ps <
.05) as well as beyond the broadly-graded both-edges scheme (ps < .01).
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Table 6.4: Results of syllabic scheme analyses
Specific Roles
CMax
OMax
Proportion of
position matches
Proportion of
position matches
Retrospective
.771*
.803*
Graded Roles
.878*
.878*
Graded Adjacent
Roles
.994*
.979*
Specific Roles
Prospective
1.10*†
1.09*†
Graded Roles
.902
.528
Graded Adjacent
Roles
1.23†
.827
*Significant at p < .05. †Proportion exceeding 1.0 suggests that insufficient data
was included in the analysis for accurate estimates.
With the prospective method, only the specific roles scheme was successful at
accounting for perseveration positions (with both syllabification schemes). Comparisons
to the both-edges narrowly-graded scheme were not conducted as this scheme was
unsuccessful at accounting for the position of perseverations in the restricted corpus
(added ps > .2 when adding end to beginning scheme or vice-versa to create both-edges
scheme). Instead, comparisons were made to the successful beginning-based scheme (p <
.05). With both syllabifications only the specific roles scheme improved the beginningbased scheme (added p < .05, adding 21 and 34 true perseveration matches under CMax
and OMax, respectively). Using the prospective method to calculate the proportion of
true perseveration matches for the narrowly-graded both-edges scheme gives an estimate
of .80 (no difference between CMax and OMax syllabification); the proportion of
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perseverations matched by the specific roles scheme numerically exceeds this value
(CMax: 1.10, OMax: 1.09).
The results of the prospective analysis are plagued by the small amount of data
which could be analyzed using this method. Estimates of the proportion of true
perseverations which exceed 1.0 indicate that the estimates of chance in the analysis are
unreliable. Therefore, the results of this analysis method should be interpreted with
caution and strong conclusions cannot be drawn.
Discussion
The analyses in this study were divided into three parts: retrospective analyses of
non-syllabic schemes, retrospective analyses of syllabic schemes, and prospective
analyses of syllabic schemes. Each of these results will be discussed in turn followed by
general observations and discussion of the particular level(s) at which the perseveration
errors may have arisen.
The vast majority of the non-syllabic schemes considered were able to account for
the position of significant numbers of the perseveration errors in the dataset.
Comparisons were made between the both-edges narrowly-graded scheme and the other
schemes to determine the relative success of these schemes. The both-edges narrowlygraded scheme was used as a base scheme, with the other schemes given the opportunity
to account for any perseveration errors not accounted for by the base. This analysis
revealed only three schemes which could significantly improve on the narrowly-graded
both-edges scheme. When the both-edges broadly-graded scheme was used as the base
scheme instead, only one of these schemes remained able to add position matches: a
midpoint scheme which matched seven additional perseverations (base scheme matched
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1528). Though this scheme significantly improved on the both-edges scheme, the
contribution of this scheme is extremely small.
In addition to considering the contribution of other schemes on top of the
narrowly-graded both-edges scheme, I also considered the ability of the both-edges
scheme to improve on the other schemes. If the narrowly-graded both-edges scheme
approximates the true positions of perseveration errors in the data, and to the extent that it
is making distinct predictions from the other schemes, adding this scheme to other
schemes should improve their ability to account for the perseveration positions. Four
open-bigram schemes were not significantly improved by the addition of the narrowlygraded both-edges scheme. Of these, one scheme—the open-bigram scheme with up to
two intervening letters and no marking of word edges—was only marginally improved by
the addition of the broadly-graded both-edges scheme (p < .08). On the whole, adding
the graded both-edges schemes to other schemes significantly improved the ability to
account for the position of perseveration errors in the dataset.
Syllabic analyses were analyzed using two distinct methods: the retrospective
method used for the non-syllabic schemes, and a prospective method. Of these, the
retrospective method is not wholly appropriate for testing syllabic schemes because the
syllabification of responses depends in part on the identity of the letters, resulting in an
over-estimation of syllabic position matches. As expected, use of this method results in
extremely high proportions of true perseverations accounted for by the syllabic schemes,
exceeding the both-edges narrowly- and broadly-graded schemes. When the syllabic
schemes were tested using the more appropriate retrospective method, the Specific
Syllabic Roles scheme was the only scheme which could account for significant numbers
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of the true perseverations. However, the retrospective analysis is limited to responses
containing only a single intrusion error, which vastly reduced the amount of available
data and resulted in unreliable chance estimates for all of the retrospective analyses.
Comparisons of the Specific Syllabic Roles scheme to the narrowly-graded Both-edges
scheme indicated that the syllabic scheme was more successful, though this result should
be interpreted with caution due to insufficient size of the restricted data set.
The primary result of this experiment is that perseverations made by unimpaired
readers tended to maintain graded both-edges position. This result leads to the
conclusion that graded both-edges position is used to represent letter position during
word recognition: representations are activated at particular positions defined by distance
from the beginning and end of the string and residual activation of these representations
causes them to intrude into later trials. This accords with previous results pointing to use
of the both edges scheme in other word recognition and reading paradigms (FischerBaum et al., 2011; McCloskey et al., 2013). A small contribution beyond the both-edges
scheme was made by a midpoint scheme (assigning characters flanking the center of the
string to positions -1 and 1, with no character in position 0). This empirical
demonstration of the utility of both-edges position coding builds upon previous work and
is consistent with a large corpus of masked priming and other behavioral results
suggesting that letters in adjacent and near-adjacent positions have similar
representations.
However, the conclusion that graded both-edges position is the most successful
position scheme is tempered by the fact that syllabic schemes could not be adequately
tested using this dataset. Previous authors‘ use of the prospective method with sufficient
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data revealed that the narrowly-graded both-edges scheme was more successful than
syllabic schemes. Whether those results contrast with the current results due to the
differing data sources (individual with acquired dyslexia versus unimpaired readers) or
the small size of the data set is unclear; future research should elicit responses containing
single intrusion errors from unimpaired participants for a more robust analysis of the
syllabic schemes.
Open bigram position schemes—frequently posited in models of letter
identification and word recognition—made some contributions to accounting for the
positions of the perseverations in this study. They generally performed inferiorly to the
both-edges scheme. However, when adding the both-edges graded schemes to openbigram schemes considering the left-letter as context, only the broadly-graded scheme
was able to significantly improve these open-bigram schemes. Both the open-bigram
schemes and the broadly-graded both-edges scheme consider a large number of positions
in the source response as matches due to their graded nature; a more robust test of these
schemes would be conducted on responses containing more letters than the 4-8 included
in this study.
Source of perseveration errors
On a more basic level, this experiment has demonstrated that perseveration errors
can be elicited from unimpaired participants performing a word recognition task. This is
consistent with assumptions that letter identification occurs in a cascaded system in
which multiple representations are active at any given time and compete for selection.
Considering the two underlying causes of perseveration errors discussed by FischerBaum and Rapp (2012), the errors observed in this study likely reflect a failure to activate
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representations on the current trial, rather than a failure to inhibit those active from
previous trials. As discussed previously, the experimental paradigm was designed to
limit visual information about the stimulus, which presumably leads to weak activation
throughout the identification system due to weak and/or noisy inputs. This allowed
representations which retain residual activity from previous trials to be successful
competitors in the identification process, resulting in perseveration errors. Therefore, the
results of this experiment suggest that it is a normal feature of the letter identification
system for letters to maintain residual activation in time. A question for future work
concerns the nature of this residual activation: Does it remain for a certain amount of
time or for a certain number of following uses of the identification system, or some
interaction of these two? Does a representation which was more strongly activated retain
activation for longer than one which was more weakly activated? Residual activation is
likely due to an underlying decay process, and these questions address the nature of that
process within the broader dynamics of the identification system.
Conclusions about the level of position representation
Within the letter identification theory under discussion, the errors elicited in this
task could have arisen at any of the five levels of representation involved in word
recognition (visual feature, character shape, allograph, abstract letter identity,
orthographic lexicon). The present task was to type the stimulus after it disappeared,
which is similar to a same-case delayed-copy task with the additional requirement of
translating the visual information to key press motor commands, a process which is made
possible by processing at least through the level of abstract letter identities. As with the
masked priming lexical decision studies (i.e., transposition and relative position priming),
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it is unclear whether a single level gives rise to the effect or if it results from the
combination of multiple levels of processing. However, some observations help to
delineate the likely sources of the errors.
One relevant aspect of the paradigm is that stimuli were presented at different
viewer-based positions (to the left and to the right of fixation); perseveration responses
with sources in the other position would suggest that the perseverations arose at a moreabstract level than the viewer-based visual feature level. To test this possibility I
conducted perseveration and position analyses limited to perseverations occurring in
trials in which the previous stimulus was in the opposite visual field; sources in this
analysis were restricted to the opposite visual field as the current trial stimulus. This
analysis revealed significant numbers of perseveration errors (p < .0001). Position
analyses revealed that position was maintained according to the both-edges narrowlygraded scheme (p < .0001, .98 of true perseverations accounted for). Perseverations
occurred despite the presentation of stimuli at different positions with respect to fixation,
ruling out perseverations at the viewer-based feature level, which would not consider two
stimuli on opposite sides of fixation to have any matching positions.
It is also likely, based on the higher accuracy found for word than pseudoword
stimuli, that lexical representations were used in this task, giving a boost to the ability to
recall word stimuli over pseudowords (a similar suggestion is made by Kinoshita &
Lagoutaris, 2010 to explain easier recall of pseudowords than nonwords). However,
given that the analysis depends on errors rather than correct trials, and many of the
responses are pseudowords or nonwords, it is unlikely that the errors arose solely in the
orthographic lexicon. In summary, though a clear delineation of the level at which the
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errors arise cannot be reached, it is likely that the perseveration errors under
consideration resulted from activation at the character shape, abstract letter identity
and/or lexical levels. In turn, this suggests that graded both-edges position is used to
code letter positions at one of more of these levels.
In summary, the results of this study suggest that graded both-edges coding of
letter position is employed in word recognition. Future work should pay particular
attention to potential roles of midpoint, open-bigram, and specific role syllabic schemes,
which were close competitors to the both-edges scheme across various analyses. These
results accord with previous results from Fischer-Baum and colleagues, as well as
providing a conclusion consistent with extensive evidence in favor of flexible position
coding in letter identification.
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CHAPTER 7: GENERAL DISCUSSION
In this dissertation I explored the cognitive processes of letter and digit
identification. This is the process of translating from visual letter and digit stimuli into
abstract representations of character identities and positions. In Chapter 2 I reviewed
extensive past research on letter identification and the position code(s) involved. Chapter
3 focused on digit identification, a topic which has seen little research, and the
relationship between letter and digit identification. I reviewed research leading to the
proposal of a shared letter and digit identification system, as well as outlining the
commitments of this theoretical position. Chapters 4 through 6 detailed behavioral
studies with unimpaired participants, summarized in the following section.
Summary of experiments
Study 1
Study 1 involved comparisons of the properties of lowercase letters, uppercase
letters, and digits, with the intent to determine whether various hypotheses for the digit
identification advantage are viable. The particular hypotheses are that digits are faster
and easier to identify due to higher digit than letter frequency, or lower
average/maximum digit overlap than letter overlap. Visual overlap was tested as pixel
overlap and feature overlap, through a feature set and overlap rules I developed. Overall,
the results of Study 1 indicated that the variables of character frequency, visual overlap,
discriminability, and complexity do not differ consistently between the classes of letter
and digit stimuli. Visual overlap, discriminability and complexity were all computed
using both pixel and feature metrics to provide a more general answer than using either
181
type of metric alone. For all variables tested there was considerable intermixing of
values for the two character categories, and in some cases (e.g., frequency for lowercase
letters) a difference between the categories was found in the reverse direction needed for
that variable to explain higher digit than letter accuracy. In some cases a difference arose
between similarity measures computed with just same-category characters as competitors
and those computed treating all characters as competitors. The shared system
architecture assumes that all characters compete with all other characters during
identification; if this theory is correct the relevant comparison class is to all other
characters rather than only same-category characters. A number of the results in this
study provided partial or suggestive evidence for a role of character frequency or visual
properties in facilitating digit over letter identification, but overall a consistent picture did
not emerge.
This study was meant to evaluate the preconditions of two classes of hypotheses
explaining the letter/digit performance discrepancy which has been reported in the
literature. However, the results did not suggest that frequency or visual properties
underlie this consistent empirical phenomenon. Rather, further consideration should be
given to the other two hypotheses discussed in Chapter 3: fewer digit identities, and
feedback from semantics and/or the right hemisphere. One or more of these hypotheses
may combine with the small effects found in Study 1; their influences on the
identification system remain to be tested in the future.
Study 2
In Study 2 I elicited errors in the identification of letters and digits in mixed
strings. Unimpaired participants viewed these strings briefly and then responded by
182
typing their response after stimulus offset. Most errors were substitution errors and
analyses considered the patterns of confusions among characters. One primary finding
was the independence of letter/digit category: response characters did not preserve the
category of their target character. Analyses of the full matrix (target character by
response character) of substitution errors revealed influences of visual similarity, visual
complexity, character frequency, similarity of character names, and numeric distance.
Though numerous previous studies have investigated visual similarity and complexity
effects on letter identification, this is the first to demonstrate their effects on digit
identification as well. The shared influence of some of these variables on Letter-forletter, Digit-for-digit, and Mixed category responses is consistent with the shared letter
and digit identification systems. Further, the lack of preservation of letter/digit category
in error responses, combined with the conclusion that some of the errors arise from late
and post-identification stages of processing are suggestive of a shared identification
system as described in Chapter 3.
Study 3
Study 3 analyses tested the same independent variables tested in Study 2, but with
dependent measures from a same/different judgment task on pairs of characters. Both
response time and accuracy were analyzed, to Same and Different trials. Results
suggested that both pixel and feature overlap made independent contributions to
explaining the RT on Different trials; the success of the feature overlap metric beyond
that of pixel overlap supports the feature overlap metric as an approximation of visual
similarity in the identification system. Frequency, normalized distance
(alphabetic/numeric), and the match of mismatch of the pair on category also contributed
183
to explaining the response time. Overall, mixed-category trials were responded to more
quickly than same-category trials, suggesting some impact of category knowledge.
Analyses of Same trials further validated the feature metric as well as providing
additional evidence in favor of a shared identification system. A successful predictor
involved feature overlap between a particular character and all other characters (rather
than other within-category characters); this is consistent with the assumption of the
shared system that all characters compete with each other. Other conclusions of the study
concern the nature of the same/different task, which showed influence of not only
character identification but also higher-order knowledge.
The results of Study 2 and Study 3 did not follow the commonly-reported pattern
of higher digit than letter accuracy. This suggests that though the finding is particularly
pervasive on a set-wise level (comparing average digit performance to average letter
performance); the performance on individual characters from both sets is determined by a
combination of factors and does not cleanly split along the category boundary. Bycharacter investigations of other paradigms and participant groups will reveal whether
any observed digit-letter distinction is a full separation of the two sets or a misleading
portrait of intermixed performance. Further consideration of underlying sources of this
performance are also warranted, as described above.
Study 4
In Study 4 I investigated position representation in letter identification. A large
body of research has addressed this topic in recent years, with differing conclusions about
the position code(s) used in letter identification. One main area of convergence has been
that the letter position code is flexible, with high similarity between letter representations
184
in adjacent positions. Study 4 introduced a novel source of data for this question:
perseveration errors elicited from unimpaired readers in a brief-duration delayed-typing
task. Perseveration errors reflect residual activation of letters from previous trials; due to
the position-specific nature of the identification process these representations persist at
particular positions. When they appear as perseveration errors, one can ask what
definition of position best describes the letter in both its original position and as a
perseveration error: these should be in the same position according to the position code
used in the representations.
The corpus of perseveration errors collected from the participants was analyzed to
determine what position scheme best described the position maintained by the
perseverated letters. The results favor a position scheme which considers letter positions
based on distance from the beginning and end of the letter string, with graded rather than
absolute position. Letters are considered to be most strongly represented at their precise
position (e.g., Beginning+3) but also weakly represented at immediately-adjacent
(Beginning+2) and second-adjacent positions (Beginning+1). This broadly-graded bothedges position scheme was highly successful in accounting for the position of the
perseveration errors with respect to their sources. Other schemes were also successful, in
particular open-bigram schemes considering the letter to the left of the perseverated letter
as context; future work should continue to compare these schemes. Syllabic position
codes were also tested, in which letter positions are assigned based on delineation of
orthographic syllables within the responses. These schemes had some success in
predicting the perseveration positions, but appropriate analyses for comparing these
185
schemes to the both-edges scheme were underpowered in this study and require
additional data with fewer errors per response.
Though this study provided support for graded both-edges position coding in
word recognition, it is unclear at precisely which level(s) of representation this code is
used. Prior work studying the graded both-edges scheme has suggested that it is
employed at allograph and abstract letter identity levels. The perseveration errors
analyzed in Study 4 may have arisen through residual activation at a combination of these
levels and through a combination of factors; future work should aim to pinpoint the
mechanism through which they arise and the particular level or levels of representation at
which both-edges position coding are used.
Conclusions
I have focused on two subtopics in letter and digit identification: the overlap of
letter and digit processing, and the nature of position coding specifically in word
recognition. The results of Studies 2 and 3 are consistent with a single shared system for
letter and digit identification. In the shared identification system, no distinction is made
between the computations carried out for letters and digits, and representations of both
category types compete for activation. This conclusion remains to be further tested and
expanded through future work addressing the dynamics of activation within such a
system.
The second avenue of investigation specifically considered position coding of
letters, explored through a word recognition task. Support was found for graded bothedges coding of letter position at work within the letter identification system. A broad
topic for future research is the integration of the shared systems theory with the large
186
literature on letter position representation, and the extent to which findings of flexible
position coding are unique to letters (e.g., applying at lexical levels) or can be extended to
digit position representation within identification.
Future directions
Specific questions for future research have been noted throughout this thesis;
additional topics are further delineated in this section. One broad topic concerns the
visual similarity and other relationships between lowercase letters and digits. Studies 2
and 3 only utilized uppercase letters, but the full picture of letter/digit similarity includes
both cases. Confusion matrices for lowercase letters and digits (and reaction times to
pairs) are expected to differ from those obtained for uppercase letters and digits due to
differences in visual similarity (e.g., 4 is visually similar to A but less similar to a).
Allographic variation in letters, such as g and g, also differ in visual appearance and
therefore visual similarity. A recent study by Simpson, Mousikou, Montoya, and Defior,
(2012) collected similarity ratings for a wide range of letters in both cases and included
different allographs of the same letter, and found differences in subject similarity
between the two allographs of lowercase a, providing further evidence for the importance
of considering allographic variation. Along with these questions comes the possibility to
refine the feature set developed here, in order to approximate as closely as possible the
character features used in identification. With the existing empirical datasets from Study
2 and 3 one could alter the feature set and test whether the resulting overlap measure was
more or less able to account for character confusability and same/different response time.
Some of the substitution and addition errors in Study 2 were perseveration errors
(as is unsurprising given the similarity between Study 2 and Study 4 methods). These
187
errors were not analyzed as such in the analyses presented here, but an interesting
question about the dynamics of character identification concerns the relationship between
residual activation (leading to perseverations) and current-trial activation (e.g., from
visual similarity). Schubert and McCloskey (2013) found that perseverations produced
by LHD in reading were often visually-similar to the target letters, suggesting that the
two sources of activation combine to jointly influence error patterns. Preliminary
analyses on this topic could compare the characteristics of substitution errors which are
likely to be perseverations to others which are unlikely perseverative. Perseverations also
might explain why the observed pattern of response categories in Study 2 only
approximated but did not match the frequencies of the categories in the stimuli; perhaps
residual activation boosted particular responses and altered the overall pattern.
Another aspect of the data (from Studies 2 and 3) to consider is the presence of
asymmetries in the confusion matrix and RT matrix. Both were symmetrized for
analysis, but analysis of the asymmetries may reveal properties of the character
identification system. In Study 2, asymmetries show instances in which character X was
more likely to be given as a response to character Y than character Y was to be given as a
response to character X. Particular properties of characters (e.g., frequency, complexity)
may make them more likely to be given as responses than others, which would cause
these asymmetries despite the symmetrical nature of inter-character similarity (e.g.,
visual overlap).
The analyses conducted in Study 2 and Study 4 only begin to scratch the surface
of the rich dataset of errors elicited in the delayed-typing character identification task.
Only substitution errors were analyzed in Study 2 and substitution and addition errors in
188
Study 4, but deletion and transposition errors were also present. Multiple letter position
schemes provide predictions for the prevalence of different types of transposition errors
due to the assumption of a positional gradient across letter positions (e.g., Davis, 2010;
Fischer-Baum, Charny, & McCloskey, 2011; Gomez, Ratcliff, & Perea, 2008;
McCloskey, Fischer-Baum, & Schubert, 2013; Norris & Kinoshita, 2012) These schemes
predict that immediately adjacent transpositions will be more likely than second-adjacent
transpositions. This question has recently been addressed in studies of individuals with
developmental dyslexia, another source of relevant evidence (e.g., Friedmann &
Rahamim, 2007; Kohnen, Nickels, Castles, Friedmann, & McArthur, 2012).
In Study 4 a small lexical bias was present, such that participants sometimes
reported a word when a pseudoword was presented. Though this effect is numerically
small, it is likely to exceed the chance rate of reporting a word through random letter
substitutions, transpositions, etc. in pseudowords. If this effect is reliable, and to the
extent that the word-errors also contain position-preserving perseveration errors, it may
suggest interactions between the orthographic lexicon and the identification of letter
identities at previous levels. For example, when multiple lexical entries are activated by
an incoming string (either word or pseudoword), feedback is thought to boost the
activation of letter identities present in these words. This top-down effect likely combines
with the demonstrated effect of residual activation of letter identities. If any of the
residually-active letter identities are present in the active lexical entries, these particular
entries would in turn be boosted. By hypothesis, these dynamics would result in a bias to
select (and respond with) with a word which is both orthographically related to (i.e.,
contains letters of) the current stimulus and orthographically related to previous stimuli.
189
This prediction remains to be tested, through existing Study 4 data and/or the collection
of additional relevant data.
Future work could also consider the underlying mechanism of perseveration
errors, asking whether residual activation remains over a number of trials/intervening
words read, or an amount of time. Analyses of data from a subset of participants in Study
4 revealed a surprisingly small incidence of perseveration errors in the first half of the
experiment (in the first 360 trials; see Footnote 16, p. 158) relative to the large number
present in the full dataset. This may relate to a successive buildup of residual activation
throughout the identification system. These questions can be addressed through careful
control of experiment ITI and duration as well as the number of intervening trials. For
example, trials eliciting errors (e.g., stimulus presented briefly) could be interspersed
with trials with ceiling performance to examine the resulting perseveration errors.
Digit identification has only recently become a topic of study despite a long
history of research on mathematical and numerical abilities. Similarities between the sets
of letters and digits have led me to consider both in this work, but much of the existing
body of knowledge about letters and letter identification remains to be considered for
digits and digit identification. This work was only a start to this enterprise. Future work
will consider questions of the position representation of digits, including consideration of
any differences that may arise due to the nature and later processing of the digit stimuli
(strings of random digits versus a six-digit number). Feedback from semantic
representations may interact with digit position representation and identification, just as
feedback from lexical entries may interact with the activation of letter identities.
Furthermore, the nature of digit allographs, posited by McCloskey & Schubert (2014 and
190
Miozzo & Caramazza (1998) has not been investigated: what allographic variation is
present among digit forms (e.g., 4 and 4)? Neuropsychological study such as the tasks
conducted with patients HR and LHD may provide a source of evidence for this question
(Rapp & Caramazza, 1989; Schubert & McCloskey, 2013).
The inquiries described above are only a few of the possible future research
directions stemming from the current research. As an automatic but not innate skill with
which modern humans have extensive practice, character identification is a fascinating
topic for addressing questions about recycling of cognitive and neural processes that
evolved to accomplish non-reading tasks (such as identifying objects or faces). Though
much work has been done on this topic, many open research avenues remain
191
APPENDIX A: CHARACTER FEATURE SET
The feature classes used are Orthogonal, Slant, and Curve. These describe the
large categories of visual features found in uppercase letters. Within the Orthogonal class
are Horizontal and Vertical features; within the Slant class are Slant-left and Slant-right
features, and within the Curve class are Curve-facing-up, Curve-facing-down, Curvefacing-left, Curve-facing-right, and Curve-Closed (loop) features. Each letter is
considered within a rectangle in letter-space, which has a vertical height of Full and a
horizontal width of Half (Half is also used as the size specification for a feature which
extends half the height in the vertical dimension). Slant lengths are approximate; a slant
extending from the top to bottom of letter-space gets a length of Full even though it is
physically longer than an Orthogonal feature extending from the top to bottom. Curves
have a size parameter indicating the length in degrees covered by the curve.
To specify positions in letter-space, the FullxHalf grid is subdivided into 4
sections, with the vertices of the grid labeled by their position in the horizontal dimension
(Top, Middle, Bottom) and in the vertical dimension (Left, Center, Right). These vertices
are abbreviated by their first letter, and each feature is defined by two positions
approximating the two ends of the feature. The system is arbitrarily set such that Position
2 is always downward and/or to the right of Position 1. For example, the Slant left
feature in A is described by Position 1 of Center-Middle (CM) and Position 2 of RightBottom (RB).
192
Table A1: Features for uppercase letters and digits
Character
A
B
C
D
E
F
G
H
I
J
K
L
M
N
Feature class
Slant
Slant
Orthogonal
Orthogonal
Curve
Curve
Curve
Orthogonal
Curve
Orthogonal
Orthogonal
Orthogonal
Orthogonal
Orthogonal
Orthogonal
Orthogonal
Orthogonal
Orthogonal
Curve
Orthogonal
Orthogonal
Orthogonal
Orthogonal
Orthogonal
Orthogonal
Orthogonal
Orthogonal
Curve
Orthogonal
Slant
Slant
Orthogonal
Orthogonal
Slant
Slant
Slant
Slant
Orthogonal
Orthogonal
Feature
Slant left
Slant right
Horizontal
Vertical
Curve facing left
Curve facing left
Curve facing right
Vertical
Curve facing left
Vertical
Horizontal
Horizontal
Horizontal
Vertical
Horizontal
Horizontal
Vertical
Horizontal
Curve facing right
Vertical
Vertical
Horizontal
Vertical
Horizontal
Horizontal
Vertical
Horizontal
Curve facing up
Vertical
Slant left
Slant right
Vertical
Horizontal
Slant left
Slant left
Slant right
Slant right
Vertical
Vertical
193
Size
Full
Full
Half
Full
180
180
180
Full
180
Full
Half
Half
Half
Full
Half
Half
Half
Half
180
Full
Full
Half
Full
Half
Half
Full
Half
180
Full
Half
Half
Full
Half
Full
Half
Half
Full
Full
Full
Position 1
CM
CM
LM
LT
LT
LM
RT
LT
LT
LT
LT
LM
LB
LT
LT
LM
RM
CM
RT
LT
RT
LM
CT
LT
LB
RT
LT
LM
LT
RT
LM
LT
LB
LT
LT
RT
RT
LT
RT
Position 2
RB
LB
RM
LB
LM
LB
RB
LB
LB
LB
RT
RM
RB
LB
RT
RM
RB
RM
RB
LB
RB
RM
CB
RT
RB
RB
RT
RM
LB
LM
RB
LB
RB
LB
CM
CM
RB
LB
RB
Character
O
P
Q
R
S
T
U
V
W
X
Y
Z
0
1
2
3
4
Feature class
Slant
Curve
Orthogonal
Curve
Curve
Curve
Orthogonal
Curve
Slant
Curve
Curve
Orthogonal
Orthogonal
Orthogonal
Orthogonal
Curve
Slant
Slant
Slant
Slant
Slant
Slant
Slant
Slant
Orthogonal
Slant
Slant
Orthogonal
Orthogonal
Slant
Curve
Slant
Orthogonal
Orthogonal
Slant
Orthogonal
Curve
Curve
Curve
Slant
Orthogonal
Feature
Slant left
Curve closed
Vertical
Curve facing left
Curve closed
Curve right
Vertical
Curve facing left
Slant left
Curve facing left
Curve facing right
Vertical
Horizontal
Vertical
Vertical
Curve facing up
Slant left
Slant right
Slant left
Slant left
Slant right
Slant right
Slant left
Slant right
Vertical
Slant left
Slant right
Horizontal
Horizontal
Slant right
Curve closed
Slant right
Vertical
Horizontal
Slant right
Horizontal
Curve down
Curve left
Curve left
Slant right
Vertical
194
Size
Full
360
Full
180
360
90
Full
180
Half
180
180
Full
Half
Full
Full
180
Full
Full
Full
Half
Half
Full
Full
Full
Half
Half
Half
Half
Half
Full
360
Half
Full
Half
Full
Half
180
180
180
Full
Full
Position 1
LT
CT
LT
LT
CT
CB
LT
LT
LM
RT
CM
CT
LT
LT
RT
LB
LT
RT
LT
CM
CM
RT
LT
RT
CM
LT
RT
LT
LB
RT
CT
LM
CT
LB
RT
LB
LM
LT
LM
CT
RT
Position 2
RB
CB
LB
LM
CB
CR
LB
LM
RB
CM
LB
CB
RT
LB
RB
RB
CB
CB
LB
RB
LB
RB
RB
LB
CB
CM
CM
RT
RB
LB
CB
RT
CB
RB
LB
RB
RM
LM
LB
LM
RB
Character
5
6
7
8
9
Feature class
Orthogonal
Orthogonal
Orthogonal
Curve
Curve
Curve
Orthogonal
Slant
Curve
Curve
Curve
Curve
Feature
Horizontal
Vertical
Horizontal
Curve left
Curve closed
Curve right
Horizontal
Slant right
Curve closed
Curve closed
Curve closed
Curve left
Size
Half
Half
Half
180
360
90
Half
Full
360
360
360
90
Position 1
LM
LT
LT
LM
CM
LM
LT
RT
CT
CM
CT
RM
Position 2
RM
LM
RT
LB
CM
RT
RT
LB
CT
CM
CT
LB
To generate the overlap matrix for all characters, the rules in Table A.2 were
followed for each feature in every pairwise combination of characters. The overlap
values for a character-pair where then summed and divided by 3 times the product of the
number of features in each of the two characters.
Table A2: Rules for computing feature overlap
Overlap type
Units of overlap assigned
Feature class only
.5
Feature class and feature
1
Feature class, feature, and feature size
2
Feature class, feature, feature size, and position
195
3 (maximum)
Table A3: Feature overlap matrix (lower triangle only)
2
3
4
5
6
7
8
9
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
0 0 0
0 0 0
.06 .17 0
.17 0 0
0 .26 .17
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
.06 .15 .11 .19 .15
.17 0 .06 .17 0
0 .19 .28 0 .25
.33 0 .06 .17 0
.17 0 .06 .25 0
0 .15 .17 0 .22
0 0 0 0
.06 0 0 0
.19 0 0 0
.06 .5 0 0
.08 .29 0 .5
.09 0 .17 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
.11
.17
.08
0
0
.06
.09
0
.14
.31
.28
.15
.06
.06
.06
.21
.17
.11
.24
.06
.19
.28
.28
.2
.17
.17
.13
0
0
.06
.02
0
.03
.21
.2
.07
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
.06
0
0
0
.28
.35
.19
.19
.33
.11
.11 0 .35 .2 0 .17 0 0 .15 .2 0 .31 .43
.2 0 .28 .28 0 .31 0 0 .17 .11 0 .17 .51
.11 .06 .22 .2 .06 .19 .06 .06 .09 .13 .06 .17 .31
.11 0 .19 .06 0 .08 0 0 .17 .11 0 .17 .13
.19 0 .28 .22 0 .21 0 0 .14 .19 0 .29 .5
.14 0 .11 0 0 .17 0 0 .22 0 0 0 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
4
5
6
7
8
9
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
1
.56
.17
.33
0
0
.06
.09
0
.14
.31
.31
.15
.11
.25
.08
0
0
.08
.03
0
.04
.31
.31
.14
.11
.17
.08
0
0
.06
0 0 0 0 0
0 0 0 0 0
.39 .08 0 0 0
.13 0 .19 0 0
.15 0 .22 .47 0
.09 .33 .11 .13 .13
.46
.48
.31
.15
.47
0
.2
.24
.17
.06
.22
0
0 0 0 0
.39 0 0 0
.31 .31 0 0
.2 .11 .09 0
.47 .47 .28 .19
0 0 0 .22
0 .2 .06 0 .24 .11 0 .08 0 0 .13 .19 0 .28 .22 .26 .11 .41 .22 .22 .24 .28 .11 0 0
1 0 .06 .17 0 .06 .17 0 .33 .17 0 .11 .17 .08 0 0 .06 0 0 .06 0 0 0 0 0
.08 .14 .08 .42 .14 .19 .08 .04 .08 .13 .03 .44 .08 .42 .19 .22 .08 .31 .17 .17 .17 .25 0 .28 .08
196
0
Q
R
S
T
U
V
W
X
Y
Z
1
2
3
4
5
6
7
8
9
A
B
C
.58 0 .06 .17 0 .06 .29 0 .25 .17 0 .11 .17
.06 .11 .06 .28 .11 .13 .06 .06 .06 .08 .07 .3 .06
.17 0 .06 .33 0 .14 .21 0 .17 .21 0 .28 .42
0 .33 .14 0 .28 .28 0 .29 0 0 .14 .14 0
.06 .19 .06 .06 .22 .13 .06 .06 .06 .06 .04 .22 .06
0
0
0
0
0
.08
.11
.08
.15
.26
.14
.11
.19
.07
.3
0
0
0
0
0
.14 0
.11 0
.14 0
.11 .09
.22 .22
0
0
0
0
0
.21
.17
.29
.11
.44
0
0
0
0
0
0
0
0
0
0
.28 0
.22 0
.28 0
.13 .02
.24 .04
0
0
0
0
0
D
E
F
G
H
I
T
U
V
W
X
Y
Z
.08 0 0 .08 0 0 .06 0 0 0 0 .58
.28 .13 .15 .11 .2 .11 .11 .2 .17 .1 .22 .06
.21 0 0 .14 0 0 .06 0 0 0 0 .17
.21 .46 .47 .22 .42 .53 .33 .14 .42 0 .28 0
.31 .22 .26 .13 .41 .22 .3 .19 .33 0 .37 .06
.08 0 0 0 0
.33 .06 0 0 0
.08 .17 .14 0 0
.21 0 .14 0 0
.31 .06 .2 .06 .28
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
.06 .07 .07 .09 .09 .07 .06
.06 .42 .37 .19 .22 .41 .22
0
0
0
.11
.06
197
J
K
L
M
.17 0 .33
.22 0 .33
.17 0 .33
.22 .06 .28
.09 .33 .1
N
.14
.11
.19
.13
.09
O
0
0
0
0
0
P
Q
0
0
0
0
0
R
.08
.11
.08
.13
.06
S
0
0
0
0
0
0 0 0 0 0 0
0 0 .33 0 0 0
0 0 .42 .33 0 0
.08 .07 .17 .22 .17 0
.33 .07 .14 .11 .19 .09
0
0
0
0
0
APPENDIX B: CHARACTER CONFUSION MATRIX
198
Table B1: Behavioral confusion matrix from Study 2 (lower triangle only)
1
2
3
4
5
6
7
8
9
A
B
C
1
2
4
5
6
7
8
9
A
B
C
D
E
F
G
H
I
J
K
L
M
N
P
Q
R
S
T
U
V
W
X
Y
Z
0
4
1
1
0
0 0 0
0 0 0
19 0 0
7 12 0
4 5 16
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
2
0
3
1
6
6
2
1
2 5 11
3 2 6
10 7 9
5 4 2
3 27 4
4 0 0
0
4
8
9
3
5
0
0
9
4
0
0
0
0
0
25
13
57
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
3
2
0
1
0
4 1
1 3
14 4
4 17
1 1
0 1
2
1
6
8
5
1
6
1
1
1
47
0
2
4
2
9
3
1
1
2
9
2
1
2
1
5
0
2
3
1
4
3
2
4
3
1
1 0
11 3
6 2
9 3
4 16
2 2
0
0
2
5
5
1
0
0
0
30
5
1
0
0
0
0
5
5
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
4
0
0
1
5
1
3
2
2
0
0
2
3
4
2
2
2
5
1
3
1
1
0
0
2
1
4
0
1
2
28
3
6
0
2
0
2
1
1
2
0
0
4
0
0
0
3
2
0
1
1
0
1
0
3
2
0
4
0
0
3
2
2
4
2
0
3
2
1
0
1
0
3
0
5
1
0
2
9
9
2
2
0
1
18
4
1
4
1
3
2
3
0
3
9
0
17
6
10
0
1
0
0
5
5
1
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
21
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
2
2
1
3
2
1
4
4
0
5
5
3
6
4
0
3
4 19
6 2
11 3
3
2
0
7
3
9
1
8
4
7
3
3
2
2
0
6
4
6
5
27
3
3
3
4
3
1
2
3
3
2
3
3
3
2
0
5
1
1
0
2
4
1
0
5
9
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
D 0
E 3
F 0
G 0
H 0
I 231
J 7
K 0
L 6
M 0
N 0
P 0
Q
R
2
1
3
199
S
T
U
V
W
X
Y
Z
1
2
3
4
5
6
7
8
9
A
B
C
D
E
F
G
H
I
J
K
L
M
N
P
Q
R
S
T
U
V
W
X
Y
Z
0
7
1
0
1
4
2
4
1
3
12
0
2
2
2
5
1
3
4
2
96
3
1
1
2
7
0
0
0
2
1
7
3
6
3
2
2
1
1
1
3
0
3
0
3
4
1
3
1
6
3
0
3
5
3
8
5
4
9
1
4
3
4
0
4
1
2
2
2
5
5
2
3
3
5
6
0
8
3
2
0
2
2
6
4
0
21
4
1
2
7
5
3
6
1
3
3
4
7
4
0
4
2
1
1
1
0
4
5
26
4
0
4
4
4
3
3
1
3
2
2
2
3
2
8
5
0
3
4
2
0
1
1
0
1
0
0
1
2
0
0 0
0 0
0 0
18 0
2 13
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
11
3
2
1
2
5
4
3
0
10
1
2
1
6
15
21
4
0
0
2
2
1
0
1
4
1
2
3
6
1
3
0
1
0
2
2
2
2
5
5
3
4
4
2
2
5
1
0
1
3 22
10 8
15 11
0
3
2
1
1
3
2
5
5
1
2
2
6
3
4
4
3
3
3
5
5
0
3
2
2
7
0
10 22 0
25 11 10
11 1 32
0
0
3
0
0
0
200
APPENDIX C: SAME/DIFFERENT RESPONSE TIMES
201
Table C1: SameAll (diagonal) and Different (lower triangle) response times from Study 3
1
1
2
3
4
5
6
7
8
9
A
B
C
D
E
F
G
H
I
J
K
L
M
N
P
2
3
4
5
6
7
8
9
A
B
C
D
E
F
G
H
I
J
K
L
M
N
P
Q
R
1.010
1.032 1.011
1.010 1.096 1.009
1.032 .989 .985 1.016
.
.952 .994 1.018 .997 1.005
.986 1.003 .995 1.021 .981 1.011
.998 1.001 .991 .995 .948 1.028 .993
1.005 1.023 1.061 .997 1.006 1.054 1.032 .985
1.084 1.061 .972 .990 1.011 1.019 1.001 .986 1.003
.996 1.076 .990 1.093 .939 1.004 .945 1.007 .956 .970
1.059 .958 1.040 .954 .997 1.044 .913 1.155 1.064 1.026 .975
.952 1.078 1.006 .990 1.058 1.025 1.028 .988 .989 1.004 1.005 .990
.918 1.032 .944 1.012 .985 1.008 .961 1.002 1.034 .996 1.055 1.014 .982
1.003 1.008 1.093 .918 1.046 .976 .959 1.023 .980 .996 1.045 .960 .981 1.001
1.039 1.033 1.003 .958 1.022 .961 .961 .939 1.026 1.063 .999 1.026 1.020 1.090 1.007
1.017 .966 1.014 .973 .974 1.175 1.036 1.040 .997 1.010 1.039 1.108 1.049 .968 .999 .996
.938 .971 .955 1.005 .979 .963 .949 .981 .958 1.028 1.033 1.000 .954 1.095 .944 1.036 .980
1.078 1.003 .977 .959 .939 1.011 .992 1.009 .950 .971 .956 1.003 .969 1.003 .954 1.039 .993 1.016
.959 1.023 1.013 .944 .982 .952 1.028 .982 .942 .942 1.006 1.000 .987 1.011 .960 .948 .973 1.017 1.024
1.046 .915 .946 .959 1.024 .988 .950 .942 1.012 1.001 .989 .970 1.010 1.032 1.007 .980 1.066 1.047 1.008 1.010
.986 .978 .933 .991 .975 .990 .935 .972 .976 1.009 .991 1.002 1.030 1.013 .976 .970 .996 1.080 1.045 1.047 .981
.981 .983 .966 1.004 1.022 .974 .961 1.014 .938 1.022 1.029 1.024 .989 .991 1.011 .989 1.113 1.005 .964 1.079 1.007 .986
1.017 .980 .987 .972 1.030 .964 1.015 .959 .956 1.001 1.017 1.023 .963 1.001 .956 1.054 1.044 .956 .933 1.057 .953 1.140 1.016
1.009 .987 1.005 .982 .961 1.015 .984 1.017 1.021 1.027 1.056 1.037 1.101 .987 1.007 1.010 .965 .961 .991 .982 .993 .940 .959 .985
Q .935 .982 1.015 .931 .981 .980 .965 1.005 1.128 .950 1.024 1.016 .999 .976 .991 .994 .992 1.003 .980 .986 .943 .992 .948 .995 .998
R .999 .966 .975 1.010 .977 .977 .937 1.058 1.025 1.027 1.119 .988 1.033 .992 1.070 .949 1.000 .961 .981 1.012 .995 1.029 .986 1.099 .954 1.002
202
S
T
U
V
W
X
Y
Z
1
S
T
U
V
W
X
2
3
4
5
6
7
8
9
A
B
C
D
E
F
G
H
I
J
K
L
M
N
P
Q
R
S
T
U
V
W
X
Y
Z
.908 1.086 1.068 .996 1.102 1.036 .998 1.016 1.066 .993 .947 1.071 .952 1.018 .962 1.061 .989 .992 .978 1.021 .978 1.038 .977 1.002 1.015 1.056 1.000
1.067 1.017 1.008 1.025 1.019 1.036 1.080 .998 .976 1.006 1.017 .939 1.004 .971 1.006 .945 1.025 1.089 .997 1.011 1.036 1.018 .993 .991 .962 .950 1.065 .994
.998 .960 .961 .987 .959 1.002 .998 .965 1.028 .983 1.021 1.012 1.066 .984 .954 .979 1.081 1.031 .983 .983 .964 1.031 1.053 1.040 .900 .988 .980 .946 1.002
.989 .952 .984 1.042 .993 .977 1.045 .942 .946 .983 1.002 .942 1.010 1.016 .962 .969 .966 .964 .998 .937 1.007 1.048 1.003 .982 .958 .969 .976 1.005 1.051 1.009
.906 .936 .983 1.014 1.021 .968 .982 .997 .984 .974 .983 1.003 .970 1.064 1.036 1.057 1.068 .985 1.022 .987 1.023 1.120 1.026 .985 .986 .998 .982 .994 1.023 1.045 1.008
.999 1.015 1.025 .931 1.026 .997 .975 .971 .969 1.019 .947 .980 1.007 .956 .971 .996 1.041 .974 .963 1.081 1.046 .976 .981 1.003 .965 .982 1.054 1.007 .975 1.018 1.040 1.016
Y .960 1.014 .999 .999 .997 1.027 1.073 .967 .950 1.063 .946 .990 .958 .991 .966 .950 .985 1.005 .979 .970 1.014 1.027 1.012 1.013 1.006 1.027 1.031 1.069 1.027 1.129 1.059 1.067 1.001
Z 1.005 1.061 .997 .980 1.020 .966 1.102 .961 .949 1.018 .961 1.036 .965 1.026 .990 1.019 .996 .982 1.081 .988 .962 1.023 1.009 1.005 .914 1.016 1.027 1.028 .977 1.010 1.022 .963 .985 1.015
203
Table C2: SameFirst RT from Study 3
Pair
SameFirst RT
1 1
1.022
2 2
1.048
3 3
1.056
4 4
1.01
5 5
1.042
6 6
1.062
7 7
1.013
8 8
1.036
9 9
1.079
A A
0.996
B B
0.992
C C
0.971
D D
1.002
E E
1.032
F F
1.031
G G
0.971
H H
1.001
I I
1.012
J J
1.025
K K
1.02
L L
0.965
M M
1.015
N N
0.999
P P
1.009
Q Q
1.029
R R
1.012
S S
1.016
T T
1.006
U U
1.042
V V
1.031
W W
1.045
X X
1.033
Y Y
1.064
Z Z
1.014
204
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VITA
Teresa Marie Schubert was born on October 9th, 1987 in Durham, North
Carolina. In May 2009 she received a B.A. with honors in Linguistics at the University of
North Carolina at Chapel Hill, with minors in Cognitive Science and Spanish. She joined
the Cognitive Science Department at Johns Hopkins University in September 2009 under
the mentorship of Drs. Brenda Rapp and Michael McCloskey. In January 2015 she will
join the ARC Centre of Excellence in Cognition and its Disorders in the Cognitive
Science Department of Macquarie University in Sydney, Australia as a Postdoctoral
Research Fellow.
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