CALIF'ORNIA S'I'ATE UNIVERSITY 1 NOR'l'FIH.IDGE
THE FILLED-· DURATION ILLUSION:
THE EFFECTS OF' STH1.ULUS
CONDITIONS AND DURATION
A thesis submitted in partial satisfaction of the
requirements for the degree of Master of Arts in
Psychology, General/Experimental
by
Ralph Curtis Ihle
Hay, 1982
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TABLE OF CONTENTS
Page
ACKNmvLEDGMENTS
iii
v
LIST OF 'l'ABLES
LIST OF FIGURES .
vii
ABSTRACT
. viii
CHAPTER
I INTRODUCTION
1
Time Perception
1
The 'Filled-Duration' Illusion
15
'l'he Hypotheses
24
II HETHOD
Experiment
29
I
.
.
29
Experiment II .
40
41
III RESULTS • •
IV DISCUSSION
V CONCLUSION
•
•
•
•
•
•
•
•
•
•
a
•
•
•
HEF'ERENCES
•
•
58
62
APPENDICES
A.
The raw scores of each subject under each
experimental condition
B.
67
The ratio transformation scores of each
subject under each experimental condition
iv
74
TABLE OF CONTENTS
Page
iii
ACKNOWLEDGMENTS
LIST OE'
v
Tl\~BLES
vii
LIST OF FIGURES . • . •
ABSTR.!'l.CT
• . • viii
. . . • • • •
CHAP'FER
I INTRODUCTION
1
Time Perception .
1
The 'Filled-Duration' Illusion
15
The Hypo-theses
24
... ...... .. .
II Iv1ETHOD
~
Experiment.
.
~
29
.
29
Experiment II •
40
I
III RESUL'l'S • •
41
IV DISCUSSION
53
V CONCLUSION
.58
REFERENCES
62
APPENDICES
A.
The raw scores of each subject under each
experimental condition
B.
'I'he
67
ratio transformation scores of each
subject under each experimental condition
iv
74
10
A-priori specific comparisons for
experiment II
.
.
.
Vi
.
.
• .
.
49
LIS'r OF :E'IGURES
Page
Figures
1
A graphic representation of the two
possible outcomes of the 'filledduration' illusion across relatively
short and long durations .
2
.
• •
27
• . • .
37
.
General paradigm of the filled stimulus
pattern presentation .
4
.
General paradigm of empty stimulus
pattern presentation .
3
.
.
.
.
.
.
.
. • . .
38
Graphical representation of the x ratio
transformation as a function of stimulus
conditions and duration for experiment I .
5
. .
51
Graphical representation of the x ratio
transformation as a function of stimulus
conditions and duration for experiment II
vii
52
ABSTRACT
THE
FILLED-DUR~TION
ILLUSION: THE
EFFECT3 OF STIMULUS CONDITIONS AND
DURATION
By
Ralph C. Ihle
Master of Arts in Psychology
Two similar experiments were conducted to determine
the veracity of the 'filled-duration illusion' being
independent of duration.
The 'filled-duration illusion'
(FDI) contends that intervals filled with stimuli are
perceived as longer than empty intervals of equal duration.
This phenomena has long been part of the time perception
literature, dating back to the era of William James.
In
addi t.ion, ·the effect of proportioned intra-interval stimuli
(i.e. the duration of the stimuli being proportional to the
duration of the interval) on perceived duration was
examined.
The experimental stimuli involved an auditorally
defined temporal interval demarcated by auditory
viii
boundaries.
The
co~tents
of the interval were either
empty, four equally spaced 10 msec. tones (filled nonproportioned) , or four equally spaced tones proportional in
duration to the duration of the interval (filled proportioned}.
Each stimulus pattern was presented for 1 second,
3 seconds, 5 seconds, 13 seconds, 20 seconds, 25 seconds,
30 seconds, 45 seconds, and 60 seconds.
In experiment I, 24 subjects were randomly assigned to
blocks of a counterbalanced design.
A 6x3x9 (presentation
order x condition x duration) mixed design with repeated
measures on the second and third factors was utilized.
For
experiment II, 24 subjects were randomly assigned to
receive an order of a complete randomization of experimental conditions, that is, experiment II served as a
replication.
A 3x9 (conditions x duration) repeated
measures designed was employed.
The psychophysical methods
of verbal estima·tion and single stimuli were utilized in
both experiments.
As hypothesized, "filled" intervals were judged longer
than.
u
empty" intervals (FDI) for only rela·ti vely shor-t
durations, while showing no appreciable differences at
relatively longer durations.
The hypothesis predicting
longer duration judgements for filled proportioned than
filled non-proportioned intervals was not substantiated.
ix
9
It was concluded that the 'filled-duration illusion' is
dependent on the examined duration.
The results supported
an extention of the attention model of time perception
developed by Thomas and Weaver (1975).
X
•
THE FILLED DURATION ILLUSION: THE EFFEC'l'S OF STIHULUS
CONDITIONS AND DURATION
RALPH IHLE
CALIFORNIA STATE UNIVERSITY, NORTHRIDGE
Introduction
'l'emporal experience has been of interest to
philosophers and scientists throughout history.
The
question of the nature of time has captured the attention
of philosophers such as Aristotle, St. Augustine, Kant:, and
Leibnitz.
The accurate measurement of time was and is of
importance to the physicist and astronomer.
Due to observ-
ations that certain biological and physiological functions
occur at regular intervals (e.g. Circadian and other
rhythms), time has been a common topic of study by
biologists and physicians.
For the average person, time
has been a practical problem in which life revolves around
certain time periods of a day.
Time perception has been a t.opic of investigation i..:hat
has endured in psychology.
For not only is an adequate
understanding of the nature of time important from a standpoint of scientific theory, but it is also relevant to an
1
2
understanding of many problems in conscious experience.
Time is im.rolved in psychological processes ranging from
the most complex memory processes down to the simplest
sensory experiences.
As a consequence of these diverse interests, the study
of time has been approached through different orientations
and methodologies.
This has led to an incoherence in the
empirical and theoretical work (Hicks, et. al., 1976;Hogan,
1978a, 1978b; Ornstein, 1969).
In another sense, this
diversity has propagated an accumulation of information on
the experience of time.
Despite the intense interest in
the area and subsequent informat.ion c:tccumulat:ion,
mechanisms underlying time perception are relatively
unknown.
Some of the earliest theories developed to clarify the
nature of time perception were associated with biological
and cognitive factors.
Physiologists and biologists were
among the first to seek an explanation for the perception
of tiue.
Intrigued by rhythmic behaviors and physiological
functions, they sought to determine the biological processes or mechanisms responsible.
Psychologists, fascin-
ated by the relativity of time, as well as the behavior
oscillations, sought to determine whether the experience of
time resulted from cognitive or biological processes.
3
Czermak (1865), a German physiologist, first
postulated the existence of a
the perception of time.
'time-sense' to account for
Years later other scientists (i.e.
l-'!ach, 1865; Vierordt, 1868) began the empirical investigation of the 'time-sense 1
,
however, their efforts were
directed at finding and developing laws in accordance with
the traditional psychophysics of Fechner and Weber.
As
such, they were mainly concerned with problems such as
absolute and difference thresholds assessed through various
sensory modalities.
Investigative efforts were also aimed
·at finding a sense organ since a • t_:ime-sense • implied the
existence of a sense organ, analogous to the eye for vision
or the ear for hearing.
Out of the research came the conclusion that, in
general Weber's Law was unsupported for time perception.
Ernst l'1ach (1865) concluded, as did Wund·t later, that the
ear contained the 'time-sense' organ.
Karl Vierordt (1868)
went against the bias toward a physiological mechanism and
posi t.ed the experience of time as a
judgement rather than
a sense (e.g. this ?Osition served to polarize the field).
Vierordt (1868) also found a phenomena, later called
Vi;;:cordt' s Law, where very short intervals of time are
overestimated (e.g. the estimate is larger than the
standard) and longer intervals are underestimated (e.g. the
estimate is smaller than the standard).
4
Wundt and Estel (1884) proposed a
11
leg swing 11 as a
biological process to account for duration judgement.
Propagated by Wundt and others, Munsterberg (1889) posited
rhythmic bodily processes of muscular activity (e.g.
breathing, heart beat, etc.} as the mechanism responsible
for the perception of time.
These investigators and others
led the way for an accumulation of evidence for an internal
timer or 'biological clock' theory of time perception.
The internal timer approach to time perception is
predicated on a time base metaphor (Hoagland, 1933).
This
approach relat:es physiological processes to the flmv of
subjective time.
An internal
'biological clock' regulates
subjective time flow through the functioning of some
'pulse-dispensin9 1 body mechanism (i.e. heartbeat, brain
waves, respiration rate, etc~) that acts in a periodic
manner.
It also implies +.:.he exis·tence of a
sensitive to tim.e
~,vhich
'sense organ'
gives us a 'sense of time'
(Dember
& Warm, 1979; Ornstein, 1969).
Over the years at:tempts were made to relate every
imaginable physiological and biological process to time
perception (i.e. metabolism, blood volume, stress,
temperature, drugs, arousal level, digestion, alpha waves,
etc.).
However, only three physiological variables have
endured the rigor of empirical investigation: temperature,
drugs, and alpha rhyt.hm.
Hoagland ( 19 3.3)
1
Francois (1927)
1
5
Lecomte du Nouy (1937) and Pieron (1952) postulated models
relating physiological activity to perceived duration.
The
relationship was perceived to be a function of the output
of a 'pulse-dispensing' mechanism (e.g. pacemaker) and the
rate of physiological activity.
Greater rates of physio-
logical activity were associated with increased output of
the pacemaker which in turn resulted in a quicker flow of
subject5. ve time.
Treisman (1963) incorporated this model
int.o her information processing model of an internal timer
governed by an arousal center.
General support for the internal timer model comes
from investigations of perceived dura·tion involving
t.e::nperature, drugs, and alpha waves.
Experiments involving
variations in body temperature have provided evidence that
higher temperatures (increased rate of physiological
activity) lead to an increase in the flow of subjective
time, whilE lower temper2.tures {decreased rate of
physiological activity) lead to a slower rate of subjective
flc,w· {Hoagland, 1933; Ornstein, 1969).
Research wit.h drugs
has shown that stimulant drugs lengthen perceived duration,
while depressant drugs tend to shorten or decrease
perceived duration (Ornstein, 1969).
Holubar (1969), based
on results of his experiments relating classical conditioning, GSR, and alpha waves; postulated that the rhythmic
activity of the brain or a part of it could represent a
6
funC.amental r8ference rhythm which serves the organism as a
time-measuring pacemaker.
Although there is some evidence for a 'biological
clock' interpretation of time perception, other evidence
supports a cognitive processing approach.
By far the most
appealing, plausible and widely supported approach
represents a purely cognitive process with no notion of a
continuous internal timer {Dember
1969).
&
lvarm, 1979; Ornstein,
Our experience of time according to this model,
depends on cognitive events or non-temporal information
occuring during a particular physically defined interval.
As Ornstein {1969) declared in support of a cognitive
persp2ct:ive,
11
Increases in body temperature {or the
speeding up of a
1
biological clock' with a drug) •.. are more
parsimoniously considered as effecting cognitive processing
rather than altering one of the maze of possible 'chronomel:ers' ... " (p. 34).
One of the earliest event processing theorists,
Condillac (1798), postulated that time perception consisted
of the succession and number of impressions sensed by an
organ.
Guyua (1890), a later theorist, developed and
perpetuated the concept of time experience as a mental
construct ccnsi sting of' ten factors.
.<;.mong others, he
included the number and intensity of stimuli within an
i:-:terva 1, the att.enti0n genc>rated by stimuli, ex;,Kctat.ions,
and interest.
William James
(1890) attributed a memory
factor to the perception of time.
He related time to the
decay of 'brain traces' and multitudinous memories.
In more recent times, Frankenhauser (1959) attempted
to subject previous theoretical speculations to more
rigorous experimental exam1nation.
He invest:igated
,
t.
a;Jra
_:r.on judgements of intervals ranging from 4 to 53
st~conds.
The subjects were required to read random digits
during each interval.
After which they were asked to
esti:nta.te the interval, the number of digits read, or both .
.R.esults showed that the perceived number of digits read and
th2 duration estimates were significantly related in a
positive direction (e.g. the more digits read the longer
Frankenhauser concluded that the
mental
ccnt~ent
of an i:ntsrval significantly determines i '\:' s
cognitive duration.
A model proposed by Fraisse
duration
interval.
t~
be a function of the
(~963)
1
posits perceived
mental content' of an
Fraisse maintained that factors which
contx ibu t.ed toward an al teratio:n in t.he number of changes
observed between two points, has the effect of lengthening
or shortening perceived duration.
elements of greater unity
Specifi.ca11y, stimulus
(e.g·. smaller number of perceived
changes} ;,.:hich occur during an interval lead t:o a shorter
appa~e~t
duraticn
t~~n
e!2ments of a dispa=ate
nat~r2.
8
Suppport for this contention comes from studies in which
investigators varied the unity of the task (i.e. the degree
to which activities are broken up) and found that the
apparent duration of the task decreased as the activities
become less broken up (Dewolf and Duncan, 1959; Loehlin,
1959).
Ornstein (1969) proposed a 'storage-size metaphor'
model of event processing.
According to this model
perceived duration depends on the amount and type of nontemporal information registered and stored in memory during
a physically defined interval of time.
Increases in the
number of stimulus events cr complexity
OJ..
.C
stimulus events
increases storage-size and hence perceived duration.
Encoding was also conceptua.lized. as influencing perceived
duration through manipulation of storaqe-size (i.e.
chunking can reduce storage-size relative to non-chunked
items) .
.More sophisticated models of time perception developed
by Thomas and Brown (1974) and Thomas and Weaver (1975)
expanded and improved on earlier cognitive models by
postulat1ng the existence of an attention dimension.
models of time
p~rception
These
are based upon two levels of
processing variables: a timing processor and an information
processor.
The information processor and timing processor
9
presented for a certain duration.
Estimates of duration
can decrease and become unreliable when attention, which is
shared between the two processors, shifts away from the
timing processor and onto the information processor.
In
general research has substantially supported the event
processing approach and the
'storage~size
metaphor' or it's
variants (Dember and Warm, 1979; A.llen, 1979).
As a consequence of the popularity of the cognitlve
processing approach the study of the non--temporal content
of intervals has ddminated time perception research.
However, most reviews of the literature have shown only
proportionally small consistent effects of the content
variable.
A relatively recent review by Hicks, et.
al.
(1976) delineated a supposition that many of the
inconsistencies and incoherence involved in the research
are a result of the ambiguous use of terms
estimation and underestimation) and
and/or methodological congruity.
~
(i.e. over-
lack of procedural
This state of affairs has
led to an inability to build a strong structural base upon
•.vhich to develop a coherent theoretical network.
However f
Allen (1979), in a review of the time perception
literature, contends that amid the incoherence there arc a
number of methodological factors which influence the
perception o£ time.
10
From past attempts to impose order on the me-thodology
of time perception emerged four basic methods: verbal
estimation, production, reproduction, and the method of
paired comparisons.
For verbal estimation the experimenter
presents a given duration and the subject responds by
giving a verbal estimate of the duration in clock time.
In
the method of reproduction the experimenter presents the
temporal interval and the subject reproduces it.
In
production, the experimenter states the duration in clock
time and the subject produces the interval.
In t.he me·thod
of paired comparison, the experimenter presents two
temporal intervals ·in succession and the subject makes a
category judgement of relative duration.
Most early research was non-theoretical.
The
subject's responses were generally treated as a direct
estimate of perceived duration.
Later studies showed that
the methods of assessing time judgements were of uncertain
validity and generalizability.
No single method proved
superior and there emerged a general lack of correlation
amonq the methods.
Contemporary research has generated
quantitative models.
Consequently, new methods have been
developed and improvised in which the older methods have
become sub-categories.
There are now considered to be two
basic research methodologies: duration scaling and duration
discrimination (Allen, 1979).
li
In a duration scaling task the subject is asked to
judge the perceived durations of a set of easily
discriminable temporal intervals.
Included under duration
scaling are verbal estimation, magnitude estimation,
category rating, production, ratio-setting, and synchronization.
A variant of verbal estimation is magnitude
estimation, where the subject assigns a number to represent
the magnitude of the perceived duration.
In category
rating the experimenter presents the temporal interval and
the subject locates its perceived duration among a number
of ordered categories.
A subcategory of ratio-setting is
reproduction, where i:he experimenter presents the temporal
interval and the subject generates a specified proportion
of that interval.
When the proportion is 1.00 the task is
reproduction; less than 1.00, fractionization; greater than
1.00, multiplication.
With synchronization the experi-
menter presents an interval and the subject responds in
synchrony.
A duration discrimination task requires that the
subject distinguish among a set of highly similar
intervals.
Included under duration discrimination are the
method of comparison, method of single stimulus, and two
variations on method of single stimuli; many to few, and
ident:ification.
In t.he method of comparison, two durations
are presented sequentially which the subject must determine
whether cne was short or long relative to the other.
With
12
the method of single stimuli one of two possible durations
are presented and the subject indicates whether it was a
shorter or longer value.
In the many-to-few variation of
the method of single stimuli, the number of possible
stimulus values is increased but the binary response is
maintained.
With the identification variation, both the
number of stimulus values and response alternatives are
increased.
The nature and or form of the response has been shown
to affect duration estimates (i.e. rnethod of production,
method of reproduction, etc.).
The nature of the judgement
to be made also affects duration estimates (i.e. paired
comparisons method of single stimuli, etc.),
along with
the subjects knowledge of the task (i.e. prospective
judgements vs. retrospective judgements}.
When these
factors are controlled, other consistencies do emerge.
RE::search on the energy values of the presented stimuli
indicate t:hat i·t is an important factor in perceived
duration (Allen, 1979; Treisman, 1963).
The intensity of
the signal involved, particularly with bounding signals,
appears to be directly related to judgements of absolute
duration.
While judgement.s of relative durat.ion appear to
be independent of signal intensity (Allen & Kristofferson,
1974) .
Other evidence suggests that duration estimates are
independent of both signal intensity and frequency
13
(Steiner, 1964).
The sensory modality involved with the
signal also effects judgements of duration, although the
results are less conclusive.
Duration judgements of
intervals involving visual stimuli are perceived as shorter
than those involving audition and cutaneous stimulation
(Goldstone, 1968; Hawkes, et. al., 1961).
However, other
investigators (e.g. Buffardi, 1971; Hockerman & Ben-Dov,
1979) using visual, auditory, and tactual modalities found
performance to be independent of modality.
The nature of the task involved with duration
estimates may affect
perc~ived
duration.
Intervals filled
with diverse and interesting activities appear to pass more
quickly relative to intervals containing less diverse and
interesting activit.ies (Dember
Ornstein, 1969).
&
Warm, 1979; Fraisse, 1963;
When subjects are required to perform
concurrent non-temporal tasks (i.e. arithmatic problems,
maze tracing, etc.) perceived duration of
interv~ls
tend to
decrease {Burnside, 1971; Wilsoncroft & Stone, 1978).
Stimulus familiarity and similarity affect perceived
duration by decreasing duration judgements with increasing
similarity and familiarity of intra-interval stimulus
events (Ornstein, 1969; Thomas & Weaver, 1974).
1'he configurations of int.ra-interval stimuli, stimulus
complexity, and the number of stimulus events have been
found to influencs perceived duration.
Configurations of
14
stimuli within the interval affect duration estimates, in
tha·t intervals containing stimulus events near the end of
an interval are perceived as shorter relative to those with
regular spac1ng (Buffardi, 1971).
Perceived duration also
appears to vary directly with the complexity of the stimuli
utilized and the amount of informa.tion in a s·t.imulus
(Ornstein, 1969; Thomas & Brown, 1974).
It has been
conjectured that complex stimuli increase attention and
awareness, thereby increasing the amount of subjective time
{Ornstein, 1969).
In general, it has been observed
tha~
the greater the number of intra-interval stimuli, the
longer the interval is judged to be.
This is dramatically
displayed in comparisons of 'filled 1 and 'empty' intervals
of time (Allen, 1979; Buffardi, 1971; Hawkes, et. al.,
1972, Ornstein, 1969; Thomas & Brown, 1974).
Some of the psychophysical research on perceived
duration involves
t~vo
types of stimulus patterns..
One
stimulus pattern is termed a filled interval, it is marked
off by a signal
(i.e. such as a flash of light or tone
burst) which may last continuously for a physically defined
interval or consist of two marking signals with discrete
stimulus events in between.
The other stimulus pa·ttern is
termed an unfilled or empty interval.
It consists of a
physically defined interval delimited by two brief bounding
signals.
.'\.lt:hough the same amount of physical time can be
delineat0d by both stimulus patterns, the response to thesa
patt.erns has been shmm to be disparate, resulting in what
has come to be called the 'filled-duration illusion'
(Allen, 1979).
The 'filled-duration illusion' is a frequently discussed issue in time perception.
Basically, the phenomenon
refers to the empirical observation that a given interval
of time which is filled with events or stimuli is perceived
as longer than an empty interval of equal physical duration
(Allen, 1979; Buffardi, 1971i Ornstein, 1969; Thomas &
Brown, 1974).
model
"tt)
This phenomenon is congruent with Ornstein 1 s
(1969) and Thomas and Brown's model (1974), accordinq
which stimulus event:s
\~Ti thin
an interval tend to prolong
the perception of the interval involved (e.g. the 'storagesize
rnetap~1or
1
.:md chunking model respectively).
Hall & Jastrow (1886), breaking away from other
psychophysical approaches to the study of time perception,
discovered what is now called the 'filled-duration
illusion'.
They observed that intervals containing clicks
tended to elicit longer judgements of duration than a
'vacant' interval of equal physical duration.
The authors
drew an analog between the illusion, and the illusion of
visual extelit.
Later researchers (i.e. Ejner, 1889;
Neumann, 1896; Munsterberg, 1892) studying the difference
between filled and vacant intervals reached the same conelusion and attributed the illusion to various factors in
16
accordance with the Zeitgiest (e.g. physiological
functions, muscular sensations and activities).
William James (1890), in a philosophical rhetoric concerning the nature of time, attributed a memory factor to
time perception in general.
He related the decay of "brain
traces" and "multitudinous memories" to the perception of
time.
According to James (1890} the 'filled-duration
illusion' was also due in part to retrospect duration
judgements.
varied and
He felt that,
int:erest~ing
11
In general, a time filled with
experiences seems short in passing 1
but long as we look back, on the other hand, a tract of
time empty of experiences seems long in passing, but in
retrospect short,"
(pg.
624)~
Contempory researchers have leaned toward the cognitive event processing approach for an interpretation of the
'filled-duration illusion'.
Fraisse~s
model (1963) would
predict that a filled interval would contain a succession
of ideas or change of events and hence elicit a longer
judged du:cation than an empty interval of equal physical
dw:aticn.
According to Ornstein's model (1969) a filled
interval. uses more storage space in memory than an empty
interval, eliciting a longer judged duration.
The Thomas &
Brown rnodel ( 197 4} predicts that. filled intervals d:caw
attention away from the time processor and segments the
interval during encoding (e.g. produces chunks of information), while an empty interval is encoded as one "chunk".
General support for the illusio_n has accumulated from
experimental situations where the principal parameters have
involved relatively short time intervals (100 msec. to 7
sec) , a.nd use of the psychophysical method of paired camparisons or category judgements.
(Adams, 1977; Allen, 1979,
Buffardi, 1971, Craig, 1973; Goldfarb & Goldstone, 1963;
Thomas
&
Brown, 19 7 4; Thomas
&
Heaver, 19 7 5) •
See table 1.
Goldfarb & Goldstone (1963), comparing filled and
unfilled durations, presented subjects with an ascending
and descending series of both filled durations of light and
unfilled durations bounded by light flashes.
Each duration
was to be judged by the subject as more or less than his
concept of one clock second.
The results indicated that
filled durations were judged significantly longer than
unfilled durations.
They concluded that the presence or
absence of stimulation in an interval influenced perceived
du.:.-ation.
Buffardi (1971} investigated factors affecting the
'filled-duration illusion 1 in different sensory modalities
using the method of paired comparisons.
Subjects \vere
18
'!'ABLE 1
SUMMARY OF' THE MAJOR STUDIES OF THE
'FILLED-DURATION ILLUSION'
AUTHOR
DATE
INTERVALS
METHOD
Hall &
Jastrow
!.886
0.089 to
0.052 sec.
counted
clicks
+
Goldfarb &
Goldstone
1963
1. 00 sec.
category
judgement
+
Buffardi
1971
1056 msec.
paired
comparisons
+
Thomas &
Brown
1974
750 to
5500 msec.
reproduction
+
Thomas &
'Neaver
1975
40 to
80 msec.
category
+
judgements &
paired comparisons
Adams
1977
800 to
1200 msec.
category
judgements
+
Swift &
McGeoch
1925
30 to
300 sec.
verbal
estimation
+,-
Spencer
1921
15 to
100 sec.
reproduction
+,-
Gulikson
1927
200 sec.
verbal
estimation
+,-
Goldstone &
Goldfarb
1963
0.15 to
1.95 sec.
category
+,judgements
single-stimuli
Warm, et. al.
1967
6 to
48 sec.
verbal
estimation
reproduction
+,-
Long & Mo
1970
3.25 to
7 sec.
production
+,-
·Essman
1958
60 sec.
reproduction
Cohen
1971
30 to
120 sec.
verbal
estimation
i.
+
=
RESULTS
the observation of the 'filled-duration illusion'
19
given 14 different experimental durations (each for 1056
msec.).
The number of intervening elements varied from 0
to 5 with each element being presented for 35 msec.
The
elements occured symetrically or asymetrically, depending
upon the desired manipulation, with durations presented
separately in the auditory, tactual, and visual modalities.
Subjects were presented with all pairs twice and were
required to judge whether one duration was longer or
shorter than the other duration.
The results indicated
that the number of intervening elements proved to be the
most important factor in the 'filled--duration illusion'
across auditory, tactual, and visual modalities.
However,
the conclusions seemed unwarranted, since not all duration
pairs consisted of an empty interval paired with a filled
interval (e.g. that is what the illusion is all about).
In
the instances where they were compared, they found wha-t has
been termed as the 'time-order error', that is, when empty
intervals were preceded by filled intervals the illusion
was enhanced, \vhen empty intervals preceded filled
intervals there were no substantial differences.
Investigators such as Allen (1979), Goldstone and
Goldfarb (1963), Jamieson & Petrusic (1975, 1978), and
Doehring (1967) have found that time estimation tasks in
the absence of feedback are subject to a strong and
systematic 'time-order error 1
•
Empty intervals lead to an
overestimate of subsequent filled intervals while filled
20 ,,
intervals lead to an underestimate of subsequent empty
intervals.
This seems particularly true with small inter-
stimulus values, as in paired comparison tasks, when a
subject is given two intervals and asked to judge whether
one is longer or shorter than the other.
Thomas & Brown (1974) found the 'filled-duration'
illusion to be 'independent of duration'.
Subjects were
presented with four interval lengths (750 msec., 1000
msec., 1500 msec., and 1750 msec.) for an average 1.25 sec.
set and four intervals (5000 msec., 5300 msec., and 5500
msec.) for an average 5.1 sec. set all delimited by 10
msec. tones.
The i!ltervals were of three stimulus types:
empty (bounding tones only), filled-regular (three tones
regularly spaced within the interval) , and filled-irregular
(three irregular spaced tones).
to reproduce the given interval.
The subjects were required
The results indicate that
filled intervals seemed longer than empty ones of equal
physical duration and that the effect was "independent of
duration".
Thomas & Brown (1974) provided a chunking model
to account for their findings
(e.g. attention focused on
information processor, where tones segment an interval
causing storage of a number of chunks ra·ther than one as in
an empty interval).
Even though the investigation was a
particularly well controlled one, a conclusion that the
effect was "independent of duration" seems to be an
'
21
inappropriate generalization (e.g. only intervals from 250
msec. to 5 sec. were investigated).
Although not all designed to directly study the
'filled-duration illusion'
1
other investigations (e.g.
Burnside, 1930; Cohen, 1971; Essman, 1958; Goldstone &
Golfarb, 1963; Gullikson, 1927; Hogan, 1975, 1978; Long &
Mo, 1970; Spencer, 1921; Swift & McGeoch, 1925; Warm, et.
al., 1967;
~vhitley
&
Anderson, 1930) have failed to show
consistent support for the illusion.
Among the principal
experimental parameters involved in these investigations
were longer time intervals
(2 sec. to 300 sec.), use of
methods other than paired comparisons,
and/o~
controlled
for and evaluated confounding factors such as the
'time-order error'
(Table 1).
According to the results of
these studies, the illusion appears to break down or
reverse as the judged interval increases in physical
duration.
However, the intra-interval stimuli vJere not
very well controlled in most of the studies (e.g. one study
used read.ing as a filler, one used muscular activity,
another used the recitation of prose, etc.).
Cohen {1. 9 71) investigated empty and filled interva.ls
using 30 sec., 75 sec. and 120 sec. durations.
The filled
interval consisted of blindfolded maze tracing while the
empty in:terval consisted of 'blindfolded rest 1
•
Verbal
duration estimates were required after each period of
blindfolded rest or maze tracing (i.e. the method of singl0
22
stimuli was used).
Results indicated that subjects over-
estimated actual elapsed time for all periods, with the
greatest overestimations ocurring during the empty task
periods.
The author concluded that empty intervals are
judged as longer in duration than filled intervals of equal
physical duration and that the effect is enhanced with
increases in physical duration.
Thus ·the author found a
reversal of the 'filled duration illusion' for intervals
ranging from 30 sec. to 120 sec. while using the method of
verbal estimation.
Goldstone & Goldfarb (1963) investigated the
difference between filled and unfilled intervals of time
using the method of single stimuli wi·th durations ranging
from 0.15 sec. to 1.95 sec.
They looked at the effects of
auditory and visual stimuli on perceived duration using
category judgements of duration magnitude.
One category
scale involved a "social standard" in which
subj~cts
were
to respond with one of nine response alternatives, from
very much less than to very much more than one clock
second.
Another category scale, the subjective standa.rd,
used nine response alternatives, from very, very short to
very, very long.
mag~itude
Subjects made category judgements of the
of durations consisting of continuous auditory or
visual stimuli or empty intervals bounded by discrete,
short lights or sounds.
Results indicated that in general,
both filled and unfilled auditcry durations were jucged
23
longer than filled and unfilled visual intervals of equal
physical duration.
Filled intervals were judged longer
than unfilled intervals only for social s·tandard judgements
of auditory durations.
In addition the filled-duration
illusion was only found in instances where the order of
presentation was empty intervals followed by filled
intervals (e.g. time order error).
Long & Mo (1970) investigated the relationship between
perceived duration and the amount of stimulus change within
an interval.
Utilizing the method of production and
durations of 3. 25 a·nd 7 sec. they investigated the effects
of interrupted, divided and no stimulation on perceived
duration.
For an auditory
condition, subjects were
presented with a buzzer once, twice, continuously or not at
all while producing the respective duration.
Results
indicated that, when considering the number of stimuli in
an interval alone, empty intervals are judged longer than
filled intervals.
When considering stimulus change,
interrupted intervals (e.g. filled) are judged longer than
empty in-tervals.
arr~iguous
However, the results are somewhat
in terms of the 'filled-duration illusion', since
not all reported comparisons were in t.erms of empty
intervals versus filled intervals.
As a final example of the dependence of the
'filled-duration illusion' on duration, Warm, et. al.,
24
(1967), investigated the effects of muscle tension on the
judgement of 6, 12, 24, and 48 second durations.
Induced
muscle tension was manipulated by having subjects maintain
different relative loads on a hand dynometer (0%, 10%, 20%,
30%, and 40% of maximum grip strength).
Subjects were
required to reproduce or verbally estimate a period of time
engaged in the manipulated muscle tension delimited by two
lights.
Result.s suggested that for 6 _and 12 second
intervals there were relatively no differences in estimates
across percent maximum strength.
While for 24 and 48
second intervals, 0% load was judged longer than 10%, 20%,
30%, and 40% loads;
However, due to the nature of the
task, the exact stimulus characteristics and hence, the
nature o£ the filled interval cannot be determined (e.g.
were there three stimulus events in terms of muscular
activity or 50, etc.).
The present research is an attempt to investigate the
veracity of the 'filled-duration illusion' across
relatively short and long durations.
An additional
investigative purpose was to determine the effect of
proportional intra-interval stimuli - the duration of each
stimulus being proportional to the duration of the
interval - on perceived duration.
The investigation
employed three types of stimulus patterns: empty, filled
non-proportioned, and filled proportioned; and nine
25
durations: 1 sec, 3 sec, 5 sec, 13 sec, 20 sec, 25 sec, 30
sec, 45 sec, and 60 sec).
According to the relevant literature, one of two
outcomes is possible.
There is the position that the
'filled-duration illusion' is depende_nt on t.he examined
durations.
Short intervals should result in the
observation of the 'filled-duration illusion', while
relatively long intervals should result ±n no appreciable
differences between the stimulus conditions or even a
reversal of the illusion (i.e. empty intervals judged as
longer than a filled interval).
This being the case, a
significant interaction of conditions (empty vs. filled
in·tervals) by duration should be observed.
Specifically, a
filled interval should result in significantly longer
duration judgements than an empty interval for relatively
short durations (under 5 sec.) while the illusion should
break down cr reverse for relatively
~ong
durations (over 5
sec.) as in figure la.
On the other hand, established research suggests that
the illusion is independent of duration, dependent solely
on non-temporal information.
Accordingly, the 'filled-
duration illusion' should be observed irrespective of the
examined duration.
Hence, a significant main effect of
conditions should be observed.
That is, filled intervals
26
should be judged as significantly longer in duration than
empty intervals across durations (figure 1b).
The only
viable alternative is that an interaction effect would be
found.
Specifically, empty intervals should be judged as
shorter than filled intervals for intervals under 5 sec.,
while there should be no appreciable.differences between
empty and filled intervals at durations greater than 5 sec.
Shorter intervals in all probability yield duration
estimates based on non-temporal information alone, that is,
attention is focused an information processor.
But longer
intervals in all probability yield judgements based on the
experience of the passage of time, not based solely on
non-temporal information, that is, a balance of attention
between an information and time processor, as seen in
figure 1.
Another issue of the perceived duration apparently not
previously assessed involves the nature of the stimuli
which ''fill" a given interval.
Supposedly, the "more
filled" a particular interval seems the longer it will be
judged (Ornstein, 1969).
If the judgement is between two
intervals of equal physical duration but with different
filler events (e.g. one has 4 tones at 10 msec. each, the
other has tones at 100 msec.) the responses should depend
on whether one appears "more filled" than the other (i.e.
the "more filled" yielding longer judgements).
Given two
intervals of unequal physical dm.:ation (but not >coo
27
DURATION
JUDGEMENT
1
3
5
13
20
25
DURATION (SEC)
30
45
60
FIGURE l(a): Outcome of stimulus conditions if
dependent on duration.
1
3
5
13
20
2.5
30
45
60
FIGURE l(b).
Outcome of stimulus conditions if
independent of duration.
FIGURE 1: Graphical representation of the two
possible outcomes of the 'filled-duration'illusion
across relatively short and long durations, (a)
dependence on duration, and (b) independence of
duration.
'
28
disparate) with identical filler events (e.g. all 10
rnsec.), the shorter duration should appear "more filled"
than the longer and hence elicit a longer duration
judgement.
Intervals with filler events which are
proportional in duration to the duration of the interval
should yield subjectively equally filled intervals.
In
accordance with earlier reasoning on the filled duration
illusion, the effect of proportional filler events would
probably be observed with relatively short intervals while
breaking down for relatively longer intervals.
Experiment I
Method
A:ep~ratus
An Apple Computer Disk II
(Model # A2M0003), was
utilized to generate the experimental stimuli.
Except for
the preparatory and response cues all experimental stimuli
were auditory, consisting of bounding tones
and intra-interval tonss
(565 Hz, 50 dB)
(950 Hz, 48-53 dB).
The experiment was conducted in a room measuring 7' x
14'.
A curtain separating the subject from the experiment
divided the room in halves
(7' x 7').
Th-e subject sat in a
chair in front of a monitor screen (12 11 diagonal), while
the experimenter sat behind the curtain in front of the
Apple computer and another monitor screen (12" diagonal).
The room ambient noise level (no more than 45 dB) and
ambient luminance level (23 ft/lamber:ts)
remained constant
throug-hout t.he experiment.•
Subjects
The subjects were 24 undergraduate students at the
California State University, Northridge.
from 18 to 39 years
years).
The age ranged
(median age =- 21 years, mean age
=
25
All subjects were required to have normal hearing
(self report) and no prior participation in time perception
experiment.s.
29
30
The design was a three way factorial with repeated
measures on two factors
(order x conditions x duration) .
Order was used as a blocking factor
(discussed later).
Stimulils conditions was at three levels: empty intervals
{E) filled intervals with non-proportional discrete filler
stimuli (Fl)
1
and filled intervals with proportional
discrete filler stimuli
(F2).
1 sec.
1
(Dl),
sec.
(D5),
sec.
(D9}o
3 sec.
25 sec.
(D2)
Duration was at nine levels:
5 sec.
{D3), 13 sec.
(D4), 209(
(D6), 30 sec.
(D7), 45 sec.
(DB), and 60
Repeated measures were obtained on both
conditions and duration.
The result was a 3x9 factorial
with each subject receiving all 27 conditions
(Table 2).
Presentation orders, with each order being a randomization of the nine durations for a particular condition were
gene:~:.-ated
by a table of random numbers
(Wike, 1971).
Orders were in turn randomly assigned to subjects within
the framework of a counterbalance design: each subject
received rJ.ne -order of randomized empty durations, one order
of randomized filled non-proportional durations, and one
order of proportioned filled durations
(Table 3).
This
mode of stimulus presentation was used as pilot studies
indica_tec1 that complete randomiza:ti<X1 of orders may have
lead -to hypothesis guessing (e.g.
that the experim,:!ntal
31
TABLE 2
3 x 9 TABLE OF STIMULUS CONDITIONS BY
DUR.l>.'I'IONS
DURATIONS
1 sec.
3 Bee.
t.;
sec .
13 sec.
20 sec.
25 sec.
30 sec.
..>
STIMULUS CONDITIONS
EMPTY(E)
FILLED (Fl)
NON-PROPORTIONED
1
2
3
4
5
6
7
45 sec.
8
60
9
se(~.
FILLED (F2)
PROPORTIONED
10
11
12
13
14
19
20
21
22
23
15
24
16
17
18
25
26
27
purpos•.:: was ·to study the difference between empty and
filled intervals).
Each sequence of the counterbalance
design was ra.ndomly assigned to subjects.
Procedure
The presentation and judgement mode of stimuli
employed in this work was the psychophysical method o£
sin·gle stimuli with the variation of identification, to
a.void the maximal effect of the time order error conunonly
found with other methods.
each
i~terval
That is, subjects were given
one at a time and asked for a
imn:.cdi-::t te l.y following each presentation.
judgement
The response mode
was that of verbal estimation (i.e. the subjects gives the
~uration
estimate verbally, in physical duration units}.
The experimenter recorded each estimate in seconds and
~
seconds.
'l'he methods of verbal estimation and single .stimuli
~1 e.v:e
used 1 as cont:casted with the method of comparison ancl
the reethod of reproduction, these methods have the advanta.ge that c.-s·t.imates are both more readily made and more
In addition, verbal estimation has
been found to yield more accurate estimates
\vakesberg:
l956i Hornstein
&
Each subject was tested
t~2
(Bindra &
Rotter, 1969).
individual~y.
After entering
expcrixcntdl situation the subjects were asked to be
3.3
'l'ABLE 3
COUNTERBALANCE DESIGN
E
Fl
F2
E
Fl
F2
Fl
F2
F2
E
Fl
Fl
F2
E
F2
E
Fl
E
E=ernpty st:imulus condition Fl=non-proportioned condition
F2=filled proportioned condition
34
seated in a chair directly in front of the Apple monitor
screen and given a sheet of paper with the following typed
instructions:
I.
This is a time estimation t.ask.
You will be
given a series of time intervals and asked to
judge the length of each interval in seconds.
Please remove your watch and please do not use
any counting strategies during the task (i.e.
tapping, foot swinging; counting 1000, 2000,
3000, etc.).
I know it is hard not use counting
strategies but it is imperative that you give an
intuitive estimate of the interval.
II.
Before each interval begins, you will see the
word ready appear on the screen.
When you see
the word ready, you know the interval is about to
start.
Each interval will consist of tones, you
will give an estimate of the length from the
first tone you hear to the last tone you hear.
After the last tone the phrase, What is your
estimate?, will appear on the screen.
When you
see the phrase, What is your estimate?f you will
have 5 sec. to give a verbal estimate in seconds
or minutes (e.g. you will say aloud what you
thought the length of the interval to be).
Please feel free to give fraction estimates as
35
well as whole number estimates (i.e. 3.5 sec., 25
sec., 93 sec., 6.5 sec., etc.).
After 5 sec. the
program will continue so it is imperative that
you give your estimate as quickly as possible.
Remember, try not to use counting strategies.
Below is the diagram of the procedure.
Ready
----Tones----
What is your estimate?
Your estimate
When you are done reading, let me know.
We will
go through a few practice trials before we
actually begin the experiment.
When the subjects finished reading the instruction
sheet E reiterated what the estimate consisted of and that
they were not to use counting strategies.
The Ss were then
presented with practice trials so that they would be
familiar with what was to be estimated as well as how to
make the estimate.
The experimenter then went behind the
curtain and sat in a chair facing the apple computer.
Sub-
sequent to 5 practice trials - in which all were given the
same randomized order, which was not used in the experiment
- the Ss were presented with the 27 experimental trials
(Table 2) .
Each experimental trial consisted of a warning signal,
a waiting period, the interval of time to be estimated, and
a response period, all performed and displayed by the Apple
Computer.
The warning signal consisted of a visual display
of the \·lOrd ready on the Apple monitor, followed by a five
second waiting period.
All other stimuli except the
response cue, were auditory.
The intervals to be estimated were of three stimulus
pat·terns: empty, filled non-proportional, and filledproportional.
Empty intervals.consisted of two bounding
stimuli demarcated the relevant duration (each 100 msec. in
duration, 565Hz, and 50 dB), as in figure 2.
The filled stimulus patterns consisted of bounding
stimuli iden·tical to the empty condition, demarcating the
relevant duration, with four intra-interval stimuli (tones
of constant 950 Hz), diagraiPmed in Figure 3.
For the non-proportional filled stimulus patterns
(Fl) , the discrete intra-interval stimuli were each 1·msec. in duration (tones of a constant 950 Hz) with each
equally spaced within the interval (WIS) .
The mathmatical
definition is:
WIS
where DI
lS
=
(DI - 4X)
/ 5
the duration of the interval and X is 10 msec.
100 msec.
xxxxxxxx
X
X
X
X
X
X
100 msec.
xxxxxxxx
-----DI-----
X
X
X
X
X
X
Ready xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxWhat is
your estimate?
Figure 2:
General paradigm of t.he empty stimulus pattern
presentation.
38
100 msec.
xxxxxxxx
X
X
X
X
X
X
XX XX XX
X
X
X
X
X
X
xxxxxx
xxxxxx
X
X
X
X
X
X
X
X
-----DI-----
X
XXX XXX
X
X
X
X
X
X
100 msec.
xxxxxxxx
X
X
X
X
X
X
Ready xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
What is your estimate?
Figure 3:
General paradigm of the filled stimulus pattern
presentation.
39
For the proportioned intervals (F2) the discrete
intra-interval stimuli occurred four times for a
proportioned duration (PD), mathmatically defined as:
PD
=
DI/100
where DI is the duration of the interval.
The resultant
durations of the intra-interval stimuli were 10 msec, 30
msec, 50 msec, 130 msec, 200 msec, 250 msec, 300 msec, 450
msec, and 600 msec (950Hz, 48-53 dB)r
The intra-interval
stimuli wer:e equally spaced throughout the interval (WISP) ,
mathmatically defined as:
WISP= (DI- 4(PD)) / 5
where PD is the proportioned duration of the intra-interval
stimuli.
Following the phrase, What is your estimate?, and a 5
sec. response period the program continued by displaying
the word Ready again.
This procedure continued until the
subject had completed all 27 trials.
After completing all
trials, the subject was given a brief questionnaire, which
assessed familiarity with the topic of time perception,
assessed what the subject conjectured the hypothesis to be,
how many intervals there were thought to be, whether the
subject used counting strategies, sex, and age.
Upon
completion of the questionnaire the subject was debriefed
on the purpose of the experiment.
Experiment II
Method
Experiment II was conducted in order to determine if
different results would be obtained under a complete
randomization mode of stimulus presentation, as opposed to
a counterbalanced mode, and to provide a replication of the
earlier results.
Subjects
The subjects were a different population of 24 undergraduate students from the California State University,
Northridge.
The age range was 18 to 42 {median age
years, mean age= 25 years) .
=
23
.All subjects were required to
have normal hearing (self-report) and no prior participation in time perception experiments.
~tus
and Environment
Identical to experiment I.
Procedure
The procedure was identical to experiment I except
that subjects received one order of a comple·te
randomization of the 27 conditions instead of in a
counterbalanced mode of presentation {Table 2).
Results
Based upon a priori criteria, the data from subjects
who reportad using counting strategies were not used in the
analyses, leaving 20 subjects in experiment I and 22
subjects in experiment II.
Raw and ratio transformation
scores for both experiments are found in Appendices A and B
respectively.
For the purpose of analysis, raw data were
converted into ratios of the subject's response to the
experimental presentation.
Use of difference scores for a
wide range of interval times is often misleading (e.g. a
d.i.f.ferez1ce. score of 5 sec. error in judgement would be
treated as belng equally inaccurate whether the standard
~nterval
wa3 2 sec. or 29 sec.).
Ratio transformation is
one method of equating scores and allowing for direct
comparisons across intervals· and me·thods.
In addition, a
comparison of estimates to physical time reduces the
analysis of ?erceived duration to an external process.
(Allen, 1979; Harnstein and Rotter, 1969; Ornstein, 1969).
In experiment I ratio scores were used in a 6x3x9
(order x
co~dition
x duration) mixed design analysis of
vz.ri.ance v:i·th repeated measu:ces on condi i.:.ions a:r:d durai::ion.
In experiment II ratio scores were used in a 3x9
(conditions x duration} repeated measures analysis of
variance.
Both analyses of variance were performed by a
41
BMDP2V computer program.
Assumptions underlying the
analysis of variance were evaluated using a BMDP2D
(from a computing facility)
descriptive statistics computer
program and found to be satisfactory.
The results for
experiment I are presented in Table 4.
standard deviations are presented in
respectively.
7.
The means and
~ables
5 and 6
The results for experiment II are in Table
The means and standard deviations are presented in
I'able 8.
'Iher:e were no significant ::nain or interaction effects
of the order factor in experiment I,
(p>.05).
The main
effect o£ conditions proved to be non-significant as well,
in both experiment I, F(2,28)
Il
1
F(2,42)
=
0.22, p>.OS.
=
2.11, p>.OS and experiment
The main effect of duration
proved to be significant in both experiment I, F(8,112) 25.70, p<.OOl and experiment II, F(8,168)
~~e
=
24.14,
p~.001.
interaction of conditions by duration proved to be
significant as well, for both experiment I, F(16,224)
5.12,
p~.001
and experiment II, F(l6,336)
=
=
4.20, p£.001.
Although result3 were in the predicted direction,
(see
Tables 5 and 8, Figures 4 and 5) a-priori comparisons were
pefo.nner:i between empty, filled non-proportioned, and filled
proportioned conditions across the 1 sec., 3 sec., and 5
sec. drt:ra.t.ions for !:>oth experiments.
The method of least
significant differerce (LSD) wae utilizPd for the
43
TABLE 4
ANOVA SUMMARY TABLE
FOR EXPERIMENT I
SOURCE
DF
ss
MS
F
p
ORDEH
5
14
54.204
56.632
10.480
4.045
2.68
p>. 05
2
4.198
2.099
2.11
p>. OS
10
28
8.176
27.824
0.817
0.994
0.82
p>. 05
8
84.682
10.585
25.70
40
112
13.625
46.127
0.340
0.411
0.83
p>.OS
16
27.992
1. 749
5.12
p~.001
80
224
27.365
76.500
0.342
0.342
1. 00
p>. 05
ERROR: BE'l'HEEN
CONDI'fiONS
CONDI'1'IONS X
ORDER
ERF.OE
DURATION
DURATION
p-<..001
v
~
ORDEH
ERROR
CONDITIONS X
DUR..li~'I'ION
CONDI'I'IONS "
DURA'r!ON X
ORDER
ERHOR
'"
TABLE 5
RATIO TRANSFORMATION MEAN (N
=
20) TABLE
FOR EXPERIMENT I
COND- DURAIT ION TION
E
5
13
20
25
30
45
60
1.50000
.97667
1.00000
.84333
.76667
.83333
.92000
.79000
.75333
1. 60000
1.59000
1.66667
1. 20667
1. 45667
1.09000
1.08333
.90000
1.73333 1.00000
.70000
1.15667
•. 9 8 50 0 1.16250 .55333
1. 36667
.90000
.83750 .70000
1. 30000 1.06000
.73500
.91333
1. 05667
.81750 .97667
.87500
.83500 1.14500 1. 02000
1. 36000
.98250
.98000 .68667
1. 443.33
.1
3
5
13
20
25
30
45
60
3. 33333"
1. 21000
.80000
.54000
.50000
.78667
.61000
.53333
.96667
4.66667
1.44333
1. 60000
1.98000
1.48333
1. 77333
1. 05667
1.44333
1.69000
3.00000
2.10000
1. 20000
.98000
1.11667
.90000
1. 22333
1. 06000
1. 05000
2.87500 2.50000 1. 66667
1. 35750 1.00000
.65667
1. 25000
.90000 1.33333
1.06500 1. 02000 1.59333
1.12500 .97500
.95000
.82000
.96250
.69333
.85750 .66667
.97500
.92750
.77667
.95500
.91750 .96500
.67000
1
1.10000
.93333
• 76667
.43667
.53333
.64000
.46667
.• 83000
.55333
3.50000
3.83333
2.30000
1.47333
1.50000
1.. 38667
1. 74000
1.12333
1.32333
3.00000
2.43.333
1. 93333
1. 60667
1. 60000
1.53333
1. 26667
1. 46000
.78000
3.25000 2.25000 1.16667
1.55000 1.17500
•
i 00 .
1. 30000
.90000
.76667
.85000
.95000
.79333
.90750
.65000 .58333
1. 08000
.99500
.68667
.88250
.74750 .74333
.96000
.65750
.71333
.78000
.70000
.70500
1 sec.
...,
:i
FNP
FP
ORDERl ORDER2 ORDER3 ORDER4 ORDER.S ORDER6
E,Fl,F2 Fl,F2,E F2,E,Fl E,F2,Fl F,E,F2 F2,Fl,E
3
5
13
20
25
30
45
60
ACROSS
CONDITIONS
1. 83333 1.66667 1. 50000 J.. 00000 1.16667
.44333
1. 03333 1.12333 1.32500 1.16750
.88605 1. 77321 1.19935 1. 02892
8~..-..-7
.86210 1.19959
45
Tl\..BLE 6
RATIO TRANSFORMATION STANDARD DEVIATION (N = 20)TABLE
FOR EXPERIMENT I
COND- DURAIT ION TION
E
FNP
1 sec.
3
5
13
20
25
30
45
60
1
3
5
13
20
25
30
45
60
ORDERl ORDER2 ORDER3 ORDER4 ORDERS ORDER6
E,Fl,F2 FJ.,F2,E F2,E,F1 E,l1'2,.F'1 F,E,F2 F2,Fl,E
.86603 .76376
.53985 .55076
.40000 .40000
.27465 1. 24952
.07638
.76376
.31005 .69002
.34395 .85594
.27731
.45310
.21939 .55752
2.08167
.76374
.40000
.08000
.13229
.53116
.35679
.14572
.45092
.57735
.52596
.46188
.36692
.40415
.26458
.33858
.46130
.58705
.57735 1. 00000 1.15470
.47170 .43843 .34429
.16330 .20000 .43589
.28337 .26887 .21032
.17795 .19738 .32787
.37736 .24406 .24194
.29861
.276.57 .2926.3
.20857 .68918 .41569
.36537 .25351 .38812
2.88675 1. 00000 2.09662 1.47196 .57735
.58705 1. 05830
.65769 .61585 .65010
l. 21655
.34641
.78951 .25820 .50332
1. 41905 .39345 .42470 .47357 1.47886
1. 02510 .31754 .49917 .45185 .55000
1. 04026 .26458 .24549 .22127 .44602
.51926 .39213 .34043 .25736
.87558
.64933 .• 21633 .30348 .37748 .15503
1. 22609
.25981 .23782 .24960 1.00000
-·---·
PP
1
3
5
13
20
25
30
45
60
.79373
.40415
.25166
.21939
.20207
.31749
.31501
.67668
.25423
1. 32288 1. 00000 1.50000
3.88887 .80829
2.33880 1.79258
1. 41384
.87757
1.00000 .65574
.93837 .64291
1.35602 .75056
.58535 .67439
.78015 .62354
.42032
.47610
.38236
.26437
.37094
.18025
.25599
.35062
.28868
.35000
.25820
.40546
.28577
.36529
.28964
.30380
.24718
.76376
.49662
.60277
.21939
.42525
.54271
.39577
.33620
.12767
4.0::
- '-•t
TABLE 7
ANOVA SUMMARY TABLE
FOR EXPERIMENT II
F
p
0.183
17.447
0.091
0.415
0.22
p.>. 05
8
168
73.208
63.695
9.151
0.379
24.14
p<.001
16
15.765
0.985
4.20
p<.001
336
78.858
0.234
DF
CONDI'riONS
ERROR
2
42
DURATION
ERROR
CONDITIONS X
DUHATION
ERROR
ss
MS
SOURCE
TABLE 8
RATIO TRANSFORMATION NEAN (N = 22) AND
STANDARD DEVIATION TABLE
FOR EXPERIMENT II
DURATION (SEc;)
ENPTY
DURA-TION
M
SD
FILLED
NON-PROPORTIONED
.t-'1
SD
FILLED
ACROSS
PROPOR'riONED CONDITIONS
M·
SD
M
1
1. 436
1. 057
2.29
1. 065
2.20
0.983
1. 975
.3
1. 067
0.539
1. 213
0.533
1. 29
0.568
1.190
5
0.859
0.338
0.875
0.336
0.977
0.509
0.904
13
1. 036
0.935
0.747
0.406
0.769
0.353
0.851
20
0.827
0.379
0.783
0.267
0.783
0.250
0.798
,I.._,
~~:;
0.745
0.247
0.794
0.342
0.848
0.427
0.799
30
1. 212
1. 314
0.716
0.293
0.910
0.489
0.946
45
0.984
0.651
0.841
0.297
0.874
0.413
0.899
60
1.158
0.726
0.891
0.393
0.879
0.451
0.976
48
TABLE 9
A-PRIORI SPECIFIC COMPARISONS USING
THE METHOD OF LEAST SIGNIFICANT DIFFERENCES
(LSD) FOR EXPERIMENT I.
VALUE~
0.475, pc.01.
COMPARISON
1.
2.
3.
4.
5.
6.
CRITICAL
DIFFERENCE VALUE
Filled interval vs. empty
interval for the 1 sec.
duration
1.27*
Filled interval vs. empty
interval for the 3 sec.
duration
0.485*
Filled interval vs. empty
interval for the 5 sec.
duration
0.103
Filled non-proportioned
interval vs. filled
proportioned interval for
the 1 sec. duration
0.56*
Filled non-proportioned
interval vs. filled
proportioned interval for
the 3 sec. duration
0.473
Filled non-proportioned
interval .vs. filled
proportioned interval for
the 5 sec. duration
0.135
*p~.
01
49
TABLE 10
A-PRIORI SPECIFIC COMPARISONS USING
THE METHOD OF LEAST SIGNIFICANT DIFFERENCE
(LSD) FOR EXPERIMENT II.
VALUE= 0.376,
CRITICAL
p~.01
·-----------------------COiviPARISON
1.
'')
'"•
3.
4.
5.
6.
DIFFERENCE VALUE
Filled interval vs. empty
interval for the 1 sec.
duration
0.809*
Filled interval vs. empty
interval for the 3 sec.
duration
0.185
Filled interval vs. empty
interval for the 5 sec.
dur-a·tion
0.067
Filled non-proportioned vs.
filled proportioned for the
1 sec. duration
0.090
Filled non-proportioned vs.
filled proportioned interval
for the 3 sec. duration
0.077
Filled non-proportioned vs.
filled proportioned interval
for the 5 sec. duration
0.102
*p<.Ol
50
For experiment I, filled
comparisons (Keppel, 1973).
intervals were found to be judged significantly longer than
the empty intervals for the 1 sec. and 3 sec. durations
(LSD= 0.475, p<.01;comp. 1
=
1.27, comp. 2
=
0.485).
The
non-proportioned filled interval was judged significantly
longer than the filled proportioned
~nterval
duration (LSD= 0.475, p<.01;Cornp 4).
proved significant (Table 9).
for the 1 sec.
No other comparisons
A graphic representation of
the results can be seen in Figure 4.
For experiment II, filled intervals were judged
significantly longer in duration than the empty interval
for the 1 second duration (LSD
0.809).
10).
No other
comparison~
=
0.376, p<.01; cornp. 1
=
proved significant (Table
A graphic representation of the results can be seen
in Figure 5.
Since subjects were not randomly assigned to experiments, no quantit.ative comparisons between experiment I and
experiment: II were attempted.
~_,
0---
3.00
i-t
E-<
2.75
....
·o 2.50
~
~
p:
f.x.,
u:
2.25
<
p:;
~_.,
!!--·
t- 2$00j
0
H
~'
~r
l. 75
~):
~ 1.501~
~
~~
t:'
1. 2
1. 0
"'"---x.-__
sl
L-~
-
,. -STANDARD- _
-
C; 0. 7:.•
.....
~
1
1
-------------------------25
3
5
13
20
DURATION
30
45
60
(SEC. )
FIGUR.E 4. Average ratio transformation duration
estimates based upon 60 responses in each of the nine
duration conditions of 1 sec, 3 sec, 5 sec, 13 sec, 20
sec~" 25 sec, 30 sec, 45 sec, ant~- 60 sec for empty (E) ,
filled non-proportioned (FNP) , and filled proportioned
(FP) stimulus patterns for Experiment I.
52
z
0
H
E-<
~
~
rr
0
f,I..;
(j~
:z:
oet
(:t.
E-<
0
i-1
E-.;
1 .. 75
1.50
~
p:~
:z:
H
E:-t
..t~
1.25
1. 00
j:J:'
~
0.75
0
0.50
4.:
Ci
~
1
3
5
13
20
25
30
45
60
DURATION (SEC)
FIGURE 5. Average ratio transformation duration estimates based upon 60 responses in each of the nine
duration conditions of 1 sec, 3 sec, 5 sec, 13 sec, 20
sec, 25 sec, 30 sec, 45 sec, and 60 sec for empty (E),
filled non-proportioned (FNP) , and filled proportioned
(FP) stimulus patterns for Experiment II.
DISCUSSION
Apparently, the 'filled-duration
not independent of duration.
illusion~
(FDI} is
Both experiments conformed to
the first experimental hypothesis in that a significant
conditions by duration effect was obtained.
However, the
illusion was not observed for all durations under 5 seconds
as originally hypothesized {e.g. earlier studies had
indicated that the FDI dissipated somewhere between 1 and 5
seconds).
Filled intervals were judged significantly
longer irl duration than empty int.ervals for the 1 and 3
second du:r-ation.s in experLnent I and only for the 1 second
duration in experiment II.
Although the conditions were in
the predicted direction for the 5 second duration in
experiment I and the 3 and ~ second durations in experiment
II, the
~npty
and filled intervals did not significantly
differ:.
Neither exper.:i_ment: conformed to t.he second experimental hypothesis, that is, intervals containing proportioned intra-interval s·t:imuli were not judged significant.ly
longer in duration than intervals containing nonpro_;?~Jrt:ioned
intra-interval stimuli.
Apparent.l:y, the
d-c.1ati.::m of the intra-interval stimuli was not a crucial
fact:or in thi.s experiment, only
being
"filled~
t~he
per se was crucial.
53
number of stimuli or
54
According to Ornstein's model (1969} of time
perception, a significant main effect of conditions should
have been obtained.
This model predicts that stimulus
events within an interval tend to prolong the perception of
the interval involved by virtue of occupying "storagespace" in memory.
Hence, filled
int~rvals
should have been
judged longer than empty intervals across all durations.
In addition, filled proportioned intervals should have
yielded longer judgements than filled non-proportioned
intervals, by virtue of being "more filled", across
durations.
Obviously the data in the present investigation
.fail to support such a model.
Ornstein's model (1969) .is
perhaps best applied to relatively short durations
sec~
(e.g. 1
or less).
Although only investigated for very short intervals
(e.g. 100 msec. or less), the model of time perception
developed by Thomas and Brown
(1974} .and Thomas and Weaver
(1975) provide an adequate explanation of the present
resul·ts.
Perceived duration, according to this model, is a
function of the attention given a time processor and/or
informat.ion processor.
(I)
an
Stimuli consisting of information
and duration (t) are processed at different levels.
Processing results in the encoding ,g(I,t) of I and an
encoding ,f(t,I}, o f t .
The information and time
processors simultaneously encode the information (I,t} of a
stimulus presented for a certain dura.·t.ion.
Estimates of
duration decrease and become unreliable when attention,
which is generally shared between the two processors,
shifts away from the time processor and onto the
information processor.
When more attention is focused on the g or information
processor, the relative influence of g(I,t) on perceived
duration increases because of the increasing unreliability
of f(t,I) or time processor.
When attention is focused
more on the time processor, the influence of f(t,I) on
perceived duration increases resulting in more accurate
estimates of
durati~n
based on the experience of time.
The 'filled-duration illusion' results when the time
spent processing non-temporal information g(I,t)
1
is
greater than the time spent processing temporal information, f(t,I).
For a "filled" interval attention is
focused on the non-temporal information and hence perceived
duration is then influenced to a greater extent by the
information processor g(I,t)> f(t,I)
est.imate of the
11
filled in·terval".
leading to an overFor an empty interval
attention is focused on the temporal information and hence
is influenced to a greater extent by the time processor f{t,I}> g(I,t) - leading to more reliable duration estimates and less of an overestimate than the filled, since a
relatively small amount of non-temporal information is
encoded.
When comparing the responses to the t";vO types of
56
stimulus patterns, one sees that "filled" intervals are
judged as longer than empty intervals of equal physical
duration based on the amount and type of non-temporal
information.
From the same type of reasoning, the 'filled-duration 1
illusion is dependent on duration.
As the duration {t)
increases, the amount. of time spent. processing temporal
information, f(t,I), increases toward or surpasses the time
spent processing non-temporal information, g(I,t), and
hence perceived duration is influenced to a greater extent
by the time processor, f (t, I) , for both filled and empty·
inte:cvals leading to more reliable duration estimates and
decreasing or dissipation of the 'filled-duration
illusion 1
•
Thus, for relatively short intervals the duration is
too abrupt to be adequately processed and hence Attention
is shifted toward non-temporal information for the
11
filled"
interval, while focused on ·temporal information for the
empty interval, leading to disparate responses for the two
stimulus patterns and the observation of the 'filledduration illusion'
(i.e., g(I,t)>f(t,I)).
As duration
increases {e.g. relatively longer durations) attention is
focused more on the time processor for both types of
intervals leading to more reliable duration estimates and
no appreciable differences between the two stimulus
patterns or dissipation of the 'filled-duration illusion'
(i.e.,
(g(I,t)< f(t,I)).
Closer inspection of Figures 4
and 5 indicates such a trend.
Filled intervals for 1 and 3
seconds are overestimated (greater than a ratio of 1.00) to
a greater extent than empty intervals of equal duration.
Longer duration estimates tend to fluctuate around a
nperfect" estimate (a ratio of 1.00).
For the "filled" conditions, the same type of
reasoning can be applied.
The filled interval containing
non-proportioned intra-interval stimuli and the filled
interval containing proportioned intra-interval stimuli
were originally thought to be different due to differing
non-temporal and temporal information (eog. different
intensities and duration levels).
However, no appreciable
differences in duration estimates were found between these
two types of stimulus pat.t.erns.
Hence, in terms of the
attention model, the same type of non.-temporal information
must have been extracted and encoded resulting in the same
amount of processing time,
g{I,t)
1 ~g(I,t) 2 , leading
to no appreciable differences in perceived duration,
t~g
(I,t.) tt.f (t,I)
i~g
(I,t) +f (t,i) •
2
2
Thus the Thomas and
Weaver (1975) model, extended to longer durations seems to
account for the present results.
Conclusion
The veracity of the 'filled-duration illusion' being
independent of duration was questioned.
It was hypothe-
sized that the illusion would only be observed at relatively short durations and that there would be no appreciable differences between
11
empty" and "filled r• intervals at
relatively longer durations.
In addition, two types of
''filled" intervals were investigated (non-proportioned
intra-interval stimuli and proportioned intra-interval
stimuli) to determine the effect of proportioned intrainterval stimuli ( i.. e. "filler" stimuli proportional in
duration to the duration of the respective interval) on
perceived duration.
Specifically, it was hypothesized that
proportionally "filled" intervals would yeild longer dura·tion estimates than non-proportioned "filled" intervals for
short durations, while yielding no appreciable differences
for longer durations.
The first experimental hypothesis was confirmed.
The
!filled-duration illusion' was observed at relatively short
durations, while there were no appreciable differences
between empty and filled intervals at longer durations .
. The second experimental hypothesis was not confirmed.
'There were no appreciable differences in duration estimates
between proportioned and non-proportioned
intervals.
58
11
filled"
59
The obtained data failed to support Ornstein's model
(1969) of time perception.
Essentially, Ornstein
proclaimed that "filled" intervals should yeild longer
duration judgements than empty intervals of equal physical
duration regardless of the examined duration.
Filled
intervals which seem '1 more" filled should yield longer
duration judgements than filled intervals of equal physical
duration which seem "less filled".
Instead the obtained
data supports an attention model developed by Thomas and
Brown (1974) and Thomas and Weaver (1975).
According to
this model, duration estimates are a function of the
attention given to
processor.
a
time processor and information
At relatively short durations non-temporal
information is crucial and hence results in disparate
responses to "filled" and "empty" intervals.
Whereas, at
relatively longer intervals temporal information is
crucial! resulting in more reliable duration estimates and
more congruent estimates between "empty" and "filled 11
intervals.
in
cancer~
However, a number of factors must be considered
with the findings.
Using only the method of verbal estimation has
subjected the experimental results to a mono-method bias in
terms of the construct validity of the dependent variable.
Even though the attention model seems pervasive and should
predict duration estimates independently of response
factors, investigators have found that perceived duration
60
is influenced by the method of response (Bindra and
Wakesberg, 1956; Harnstein and Potter, 1969.
Hence, the
results should be confined to the method of verbal estimation.
In addition, the experimental
r~sults
are subject to a
mono-opEration bias in terms of the construct validity of
the independent variable.
"Filled" intervals were defined
as intervals containing 4 intra-interval·stimuli.
Inter-
vals containing more intra-interval stimuli may lead to
different outcomes.
The effect of mul tiple-trea.tment interference presents
a problem as well, as in all investigations in which
multiple levels of a treatment are presented to the same
set of persons.
As the effects of prior treatments are not
usually erasable, the effect of treatment can not be
generalized beyond conditions of repe.ti tious and spaced
presentations of treatment.
All factors considered, the study represents an
initial exploration of the effects of relatively short and
long durations on the perceived duration of "empty" and
11
filled" intervals.
Further exploration should encompass
other methods of response {i.e. reproduction, production,
etc.), different "filler" stimuli (i.e. increasing the
number and complexity}
r
and a random effect model of
61.
durations.
Emphasis should be placed on testing the
attention model of time perception, particularly in
relation to the 'filled-duration illusion'.
The illusion,
according to this model, may be maintained across durations
if increases in duration are accompanied by increases in
the amount of time spent processing fl:On-temporal
inform~
ation (i.e. the subject is required to solve one math
problem for a 2 sec. duration, 3 problems for a 6 sec.
duration, 10 problems for a 60 sec. duration, etc.).
If
this were the case, the 'filled-duration illusion' would be
dependent on duration and ·the type of non-temporal inform&tion which "fills" an interval of time.
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267-287.
Hocherrnan,S.
& Ben-Dov,G. Modality-Specific Effect.s on
Discrimination of Short Empty Intervals.
Perceptual and Motor Skills, 1979, i8, 807-814.
Hogan,H.W. A Theoretical Note on Time Perception.
Perceptual and r~lo_tor Skills, 1978a, i§_, 1338.
Hogan,H.W. A Theoretical Reconciliation of Competing
Views of Time Perception. ]',merican Journal
Psychology, 1978b, 21, 117-128.
Holuba.r t.J. 'rhe sens.:= of time: an electrophysiological study
of its mechanism in man. Cambridge, Mass.:
M.I.T. Press, 1969.
Hornstein,A.D. & Rotter,G.S. Research met.hodology in temporal perception. Journal of Experimental
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.James v W. 'fhe Princioles of Psychology. New York: Dover
Publications, Inc. 1950 •
•Jamieson,D.G., & Petrusic,W.M. Pairing effects and timeorder errors in duration discrimination.
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Jamieson,D.G., & Petrusic,W.M. Feedback versus an illusion
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65
MacktE. Untersuchungen uber den zeitsinn des ohres. Sitz.
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391-401.
66
Wilsoncroft,W.E. & Stone,J.D. Temporal Estimat.es as a
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APPENDIX A
THE RAW SCORES OF EACH
SUBJECT UNDER EACH EXPERIMENTAL
CONDITION
67
58
THE RAW SCORES OF EACH SUBJECT UNDER
EACH EXPERIMENTAL CONDITION
EXPERIMENT I
EMPTY
OR
1
3
5
13
20
25
30
45
60
51 1
00.5
02.0 ' 03.0
10.0
15 • .0
13.0
25.0
29.0
41.0
S2 1
02.0
02.0
02.0
05.0
08.0
14.0
21.0
19.0
28.0
S3 1
02.0
05.0
07.0
15.0
17.0
40.0
40.0
50.0
60.0
S4 2
02.5
01.5
08.0
39.0
50.0
48.0
56.0
62.0
78.0
85 2
01.0
05.0
10.0
15.0
30.0
30.0
60.0
60.0
90.0
S6 2
02.0
03.0
06.0
08.0
20.0
13.0
14.0
23.0
27.0
S7 3
02.0
05.0
10.0
20.0
35.0
40.0
40.0
65.0
90.0
.)
01.0
03.0
06.0
10.0
25.0
30.0
20.0
40.0
50.0
S9 3
02.0
02.0
10.0
15.0
20.0
28.0
35.0
80.0
0120
SlO 4
01.0
03.0
05.0
11.0
15.0
20.0
24.0
33.0
41.0
811 4
01.0
04.0
06.0
10.0
15.0
26.0
15.0
40.0
58.0
Sl2 4
02.0
03.0
04.0
12.0
20.0
20.0
30.0
28.0
47.0
Sl3 4
02.0
06.0
05.0
18.0
21.0
40.0
35.0
50.0
90.0
S14 5
01.0
05.0
05.0
15.0
15.0
15.0
20.0
30.0
60.0
Sl5 5
01.0
02.0
03.0
11.0
12.0
16.0
17.0
23.0
37.0
816 5
02.0
04.0
05.0
20.0
20.0
28.0
25.0
65.0
65.0
517 5
01.0
03.0
05.0
14.0
20.0
15.0
35.0
90.0
70.0
818 6
00.5
00.5
02.0
04.0
07.0
28.0
40.0
69.0
67.0
819 6
00.5
02.5
02.5
07.0
15.0
25.0
22.0
35.0
38.0
S20 6
02.5
01.0
06.0
10.0
/.0.0
16.0
27.0
35.0
20o0
S8
..,_
69
FILLED
NON-PROPORTIONED
OR
1
3
5
13
20
25
30
45
60
81 1
01.0
01.0
02.0
08.0
09.0
12.0
09.0
25.0
30.0
S2 1
35.0
05.0
05.0
04.0
06.0
08.0
12.0
16.0
17.0
S3 1
04.0
05.0
06.0
07.0
13.0
35.0
30.0
30.0
60.0
S4 2
03.0
02.5
15.0
35.0
50.0
45.0
08.0
70.0
90.0
ss
2
08.0
06.0
05.0
45.0
30.0
70.0
60.0
90.0
0180
S6 2
03.0
04.5
04.0
09.0
09.0
18.0
27.0
33.0
34.0
S7 3
03.0
05.0
05.0
18.0
25.0
27.0
40.0
60.0
70.0
S8 3
03.0
04.0
05.0
08.0
15.0
25.0
20.0
45.0
45.0
S9 3
03.0
10.0
08.0
12.0
25.0
15.0
50.0
40.0
70.0
SlO 4
01.5
02.5
03.0
07.0
12.0
12.0
17.0
28.0
36.0
Sll 4
06.0
07.0
12.0
20.0
20.0
25.0
30.0
50.0
65.0
Sl2 4
02.0
04.0
05.0
17.0
22.0
20.0
25.0
36.0
52.0
813 4
02.0
03.0
05.0
12.0
35.0
25.0
45.0
60.0
65.0
814 5
00.5
01.0
03.0
15.0
25.0
20.0
30.0
60.0
50.0
S15 5
03.0
02.0
05.0
05.0
09.0
19.0
12.0
19.0
44.0
S16 5
04.0
05.0
06.0
20.0
15.0
27.0
35.0
50.0
60.0
S17 5
02.0
04.0
04.0
13.0
28.0
30.0
25.0
40.0
80.0
818 6
01.0
02.0
09.0
43.0
19.0
13.0
24.0
42.0
40.0
S19 6
02.0
00.0
04.0
09.0
08.0
09.0
11.0
28.0
40.0
S20 6
02.0
04.0
07.0
10.0
30.0
30.0
25.0
35.0
40.0
);>,-
70
FILLED
PROPORTIONED
OR
1
3
5
13
20
25
30
45
60
S1 1
00.5
01.5
02.5
09.0
10.0
13.0
08.0
32.0
30.0
S2 1
.30.0
02.0
03.0
05.0
04.0
07.0
10.0
15.0
20.0
83 1
04.0
04.0
07.0
04.0
15.0
25.0
25.0
25.0
50.0
S4 2
02.5
25.0
25.0
40.0
50.0
55.0
95.0
70.0
0120
S5 2
05.0
06.0
05.0
10.0
30.0
40.0
45.0
60.0
90.0
S6 2
03.0
03.0
04.0
07.0
10.0
09.8
15.5
21.0
28.0
S7 3
15.0
07.0
20.0
25.0
30.0
45.0
60.0
60.0
25.0
S8 3
02.0
05.0
05.0
08.0
20.0
20.0
15.0
40.0
25.0
S9 3
03.0
10.0
04.0
30.0
45.0
50.0
40.0
0100
90.0
S10 4
02.0
03.0
05.0
09.0
15.0
18.0
20.0
32.0
41.0
511 4
05.0
06.0
10.0
20.0
25.0
35.0
25.0
45.0
25.0
Sl2 4
02.0
04.0
05.0
09.0
16.0
20.0
33.0
37.0
72.0
Sl3 4
04.0
05.0
06.0
12.0
15.0
35.0
28.0
60.0
30.0
Sl4 5
02.0
03.0
04.0
06.0
10.0
25.0
25.0
35.0
40.0
815 5
02.5
03.0
03.0
07.0
07.0
12.0
10.0
13.0
24.0
S16 5
02.0
05.0
06.0
15.0
15.0
20.0
30.0
45.0
60.0
S17 5
02.5
03.0
05.0
15.0
20.0
30.0
25.0
25.0
45.0
S18 6
00.5
01.0
01.0
12.0
03.0
01.5
35.0
48.0
55.0
819 6
02.0
04.0
03.5
07.0
12.0
25.0
16.0
22.0
40.0
S20 6
01.0
03.0
07.0
12.0
20.0
2.5. 0
1.5. 0
25.0
45.0
THE Rl\W SCORES OF EACH SUBJECT UNDER
EACH EXPERIMENTAL CONDI'I'ION
EXPERIMENT II
EMPTY
3
1
5
1-..:J
20
25
30
45
27.00 40.00
60
Sl
2.00
1. 50
3.00 10.00 12.00 15.00
60.00
S2
2.00
3.00
8.00 55.00 30.00 25.00 200.00 60.00 180.00
S3
1.-50
2.50
2.00 10.00 13.00 12.00
54
5
7
6
4
18
S5
1
4
4
12
S6
1
4
6
57
0.6
2
S8
.l.
'
S9
18.00 2.5.00
30.00
22
30
35
90
12
20
45
23
90
10
25
22
27
50
60
.3
7
12
15
22
25
38
3
3
10
15
30
30
40
60
1
2
5
10
·15
15
25
30
60
SlO
0.5
2
5
45
20
30
60
60
180
Sll
2
5
4
10
11
17
15
14
25
S12
0.5
4
5
10
25
25
40
55
80
S13
2
4
3
10
10
15
20
30
40
Sl4
2
4
5
10
15
20
20
35
70
SJ.S
2
2
5
10
15
15
20
30
45
516
0.5
2
2.5
8
10
12
13
20
"7I
S1"7I
~
1
1
6
15
23
23
35
60
75
Sl8
3
5
6
18
30
25
35
65
85
Sl9
0.5
6
2
8
30
15
40
70
30
S20
0.5
2
2
6.5
4
8
30
45
110
821
1
5
6
10
7
9
24.5
10
60
522
1
1.5
2
8
12
20
25
40
60
72
FILLED
NON-PROPORTIONED
1
3
5
13
20
25
30
45
60
S1
3.00
4.00
4.00
5.00 15.00 21.00 27.00 38.00 50.00
S2
3.00
5.00
7.00
8.00 25.00
S3
3.00
3.00
3.00
8.00
S4
2
2
6
10
15
20
30
45
90
S5
2
3
4
10
16
12
25
37
55
S6
3
.J
t::
9.5
11
17
19
35
43
60
S7
2
3
6
6
17
20
20
25
35
88
3
5
5
15
15
20
25
30
45
S9
1
3
5
10
20
20
20
40
60
810
2.5
8
4
20
25
35
10
50
70
Sl1
2
2
5
7
12
10
11
15
16
Sl2
1
3
5
10
20
30
30
60
75
Sl3
3
2
3
7
10
12
20
35
40
S14
4
6
7
10
10
17
25
35
100
S15
1
3
3
7
12
15
9
30
90
Sl6
1
1.5
2.5
10
13
15
13
22
24
517
2
4
4
10
17
22
32
55
68
518
3
5·
8
25
25
35
34
45
65
S19
1.5
3
4
15
20
40
10
65
60
S20
1.5
2
2.25
2
15
10
20
40
. S21
5
2.5
2
3
13
25
30
26
10
S22
1
2
2
5
14
15
24
50
40
9.00 10.00 45.00 52.00
9.00 10.00 19.00 22.00 30.00
4.5
7.3
FILI,ED
PROPORTIONED
1
3
5
Sl
3.00
5.00
4.5
t)2
3.00
6.00
7.00 11.00 15.00 20.00
S3
2.00
4.00
3.00
S4
3
8
13
12
17
18
40
50
66
8~
,,
2
3
5
13
14
15
15
25
120
S6
3
5
5
14
12
23.5
30
19
45
87
2
4
4
8
20
17
15
25
35
S8
3
6
6
15
20
15
20
30
25
S9
1
2
8
10
15
25
25
45
50
S10
2
2.5
5
20
25
35
60
90
90
s:u
3
3
3.5
5
15
13
9
16
20
812
1
3
4
10
25
30
35
43
50
S13
2
4
30
8
12
15
21
30
32
S14
4
6
7
12
13
19
30
35
40
815
1
5
5
5
15
15
60
5
120
816
1
1
2.5
9
7
18
16
26
35
S17
3
3
8
13
17
42
27
40
60
Sl8
4
5
4
20
22
30
40
55
70
819
1.5
2
3
6
25
50
30
60
50
S20
1
3
3
2.5
6
15
·s21
2
3
2
13
21
7
7
27
31
S22
1
2
2
7
12
20
24
45
50
13
20
25
30
45
60
7.00 13.00 23.00 22.00 40.00 40.00
8.00 65.00 60.00
6.00 13.00 11.00 17.00 24.00 32.00
.
5 "r;
2.5
40
APPENDIX B
THE RATIO TRANSFORMATION SCORES
OF EACH SUoJECT UNDER EACH
EXPERIMENTAL CONDITION
74
75
THE RATIO TRANSFOill4ATION SCORES
OF EACH SUB,JEC'r UNDER
EACH EXPERIMENTAL CONDITION
EXPERIMENT I
EMPTY
OR
1
3
5
13
20
25
30
45
60
81 1
0.50
0.66
0.60
0.76
0.75
0.52
0.83
0.64
0.68
82 1
2.00
0.67
1. 00
0.62
0.70
0.84
0.63
0.62
0.58
S3 1
2.00
1. 60
1. 40
1.15
0.85
1.14
1. 30
1.11
1. 00
S4 2
2.50
0.50
1. 60
3.00
2.50
1.90
l. 90
1. 40
1. 30
S5 2
1. 00
1. 60
2.00
1.15
1. 50
1. 20
2.00
1. 20
1. 50
S6 2
2.00
1. 00
1.20
0.62
1. 00
0.52
0.47
0.57
0.45
S7 3
2.00
1. 70
2.00
1. 50
1. 80
1. 60
1. 30
1. 40
1. 50
sa 3
l. 00
1. 00
1. 20
0.77
1.30
1. 20
0.67
0.88
0.83
S9 3
2.00
0.67
2.00
1. 20
1. 00
1.10
1. 20
1. 80
2.00
SlO 4
1. 00
1. 00
1. 00
0.85
0.75
0.80
0.80
0.73
0.68
Sl1 4
1. 00
1. 30
1. 20
0.77
0.75
1. 04
0.50
0.89
0.97
Sl2 4
2.00
1. 00
0.80
0.92
1. 00
p.80
1. 00
0.62
0.78
Sl3 4
2.00
2.00
1. 00
1. 40
1.10
1. 60
1. 20
1.10
1. 50
814 5
l. 00
1.70
1. 00
1.20
0.75
0.60
0.67
0.67
1. 00
Sl5 5
1. 00
0.67
0.60
0.85
0.60
0.64
0.57
0.51
0.62
S16 5
1. 00
1. 30
1. 00
1. 50
1. 00
1.10
0.83
1. 40
1.10
517 5
1. 00
1. 00
1. 00
1.10
1. 00
0.60
1. 20
2.00
1. 20
S18 6
0.50
0.17
0.40
0.35
0.35
1.10
1. 30
1. 50
1.10
519 6
0.50
0.83
0.50
0.54
0.75
1. 00
0.73
0.78
0.63
820 6
2.50
0.33
1. 20
0.77
1. 00
0.64
1. 90
0.78
0.33
~
.
76
FILLED
NON-PROPORTIONED
OR
Sl 1
1
3
5
13
20
25
30
45
60
LOO
0.33
0.40
0.62
0.45
0.48
0.30
0.55
0.50
..L
1
5.00
1. 60
0.80
0.46
0.40
0.48
0.53
0.38
1.40
S3 1
4.00
1. 70
1. 20
0.54
0.65
1. 40
1. 00
0.67
1. 00
S4 2
3.00
0.83
3.00
1. 75
2.50
1. 80
0 .. 27
1.60
1. 50
ss
2
8.00
2.00
1. 00
3.50
1 .. 50
2.80
2.00
2.00
3.00
S6 2
3.00
1. 50
0.80
0.69
0.45
0.72
0.90
0.73
0.57
S7 3
3.00
1. 70
1. 00
1. 40
1. 30
1.10
1. 30
1. 30
1. 20
S8 3
3.00
1. 30
1. 00
0.62
0.75
1. 00
0.75
2.00
1. 70
S9 3
3.00
3.30
1. 60
0.92
1. 30
0.60
1. 70
0.88
1. 20
S10 4
l. 50
0.83
0.60
0.54
0.60
0.48
0.57
0.62
0.60
Sll 4
6.00
2.30
2.40
1. 50
1. 00
1. 00
1. 00
1.10
LlO
S12 4
2.00
1. 30
1.00
1. 30
1.10
0.80
0.83
0.80
·0. 87
813 4
2.00
1. 00
1. 00
0.92
1. 80
1. 00
1. 50
1. 30
1.10
S14 5
0.50
0.33
0.60
1. 20
1. 30
0.80
1. 00
1. 30
0.83
S15 5
3.00
0.67
1. 00
0.38
0.45
0.75
0.40
0.42
0<73
S16 5
4.00
1. 70
1. 20
1. 50
0.75
1.10
1. 20
1.10
l. 00
S17 5
2.50
1. 30
0.80
1. 00
l. 40
1. 20
0.83
0.89
1. 30
Sl8 6
1. 00
0.67
1. 80
3.30
0.95
0.52
0.80
0.93
0.67
S19 6
2.00
0.00
0.80
0.69
0.40
0.36
0.37
0.62
0.67
S20 6
2.00
1. 30
1. 40
0.79
1. 50
1. 20
0.83
0.78
0.67
S2
r:-.·
77
FILLED
PROPORTIONED
OR
1
.J.
3
5
13
20
25
30
45
60
S1 1
0.50
0.50
0.50
0.69
0.50
0.52
0.27
1. 60
0.50
S2 1
2.00
1. 00
1. 00
0.31
0.35
0.40
0.30
0.33
0.33
83 1
0.80
1. 30
0.80
0.31
0.75
1. 00
0.83
0.56
0.83
S4 2
2.50
8.30
5.00
3.10
2.50
2.20
3.20
1. 60
2.00
S5 2
5.00
2.00
1. 00
0.78
1. 50
1.60
l. 50
1. 30
1. 50
S6 2
3.00
1. 20
0.90
0.54
0.50
0.36
0.52
0.47
0.47
S7 3
4.00
2.30
4.00
1. 90
1. 50
1. 80
2.00
1.30
0.42
sa
3
2.00
1. 70
1. 00
0.62
1. 00
0.80
0.50
O.B8
0.42
S9
'}
.J
3.00
3.30
0.80
2.30
2.30
2.00
1. 30
2.20
1. 50
SlO
4
2.00
1. 00
1. 00
0~69
0.75
0.72
0.67
0.71
0.68
S11 4
5.00
2.00
2.00
1. 50
1. 30
1. 40
0.83
1. 00
0.42
Sl2 4
2.00
1. 50
1. 00
0.69
0.83
0.80
1.10
0.83
1. 20
S13 4
4.00
1. 70
1. 20
0.92
0.75
1. 40
0.93
1. 30
0.50
Sl4 5
2.00
1. 00
0.80
0.46
0.50
l. 00
0.83
0.78
0.67
Sl5 5
2.50
1. 00
0.60
0.54
0.35
0.48
0.33
0.29
0.40
S16 5
2.00
1. 70
1. 20
1. 20
0.75
1. 30
1. 00
1. 00
1. 00
Sl7 5
2.50
l. 00
1. 00
1. 20
1. 00
1. 20
0.83
0.56
0.75
51. . r•o 6
0.50
·o. 33
0.20
0.92
0.15
0.06
1. 20
1.10
0.92
Sl9 6
2.00
1. 30
0.70
0.54
0.60
1. 00
0.53
0.49
0.67
S20 6
1. 00
1. 00
1. 40
0.92
1. 00
1. 00
0.50
0 .::JJ
r:·c:
0.75
78
THE RATIO TRANSFORMATION SCORES
FOR EACH SUBJECT UNDER
EACH EXPERIMENTAL CONDITION
EXPERI.tvlENT II
EMPTY
,
..1.
3
5
13
20
.25
30
45
60
Sl
1. 00
0.50
0.40
0.62
0.60
0.80
0.83
0.89
1. 00
82
1. 00
1. 67
1. 20
0.77
0.35
0.36
0.82.
0.22
1. 00
83
0.50
0.67
0.40
0.50
0.20
0.32
1. 00
1. 00
1. 83
S4
0.50
2.00
0.40
0.62
1. 50
0.60
1. 33
2.92
0.50
S5
3.00
1. 67
1. 20
1. 38
1. 50
1. 00
1.17
1. 44
1. 42
56
1. 00
0.33
1. 20
1.15
1.14
0.92
1.17
1. 33
1. 25
S7
0.50
0.67
0.50
0.62
0.50
0.48
0.43
0.44
0.12
S8
2.00
0.67
1. 00
0.77
0.75
0.60
0.67
0.67
0.75
59
2.00
1. 33
1. 00
0.77·
·a. 75
0.80
0.67
0.78
1.17
SlO
2.00
0.67
0.80
0.77
0.50
0.60
0.30
0.67
0.67
Sll
0.50
1. 33
1. 00
0.77
1. 25
1. 00
1. 33
1. 22
1. 33
812
2.00
1. 67
0.80
0.77
0.55
0.68
0.50
0.31
0.42
Sl3
0.50
0.67
1. 00
3.46
1. 00
1. 20
2.00
1. 33
3.00
Sl4
1. 00
0.67
1. 00
0.77
0.75
0.60
0.83
0.67
1. 00
815
1. 00
1. 00
0.60
0.77
0.75
1. 20
1. 00
0.89
1. 00
Sl6
0.60
0.67
0.60
0.54
0.60
0.60
0.73
0.56
0.63
S17
1. 00
1. 33
1. 20
0.77
1. 25
0.88
0.90
1.11
1. 00
818
1. 00
1. 33
0.80
0.92
0.60
0.80
1. 50
0.51
1. 50
S19
5.00
2.30
1. 20
0.31
0.90
0.88
1. 00
0.78
1. 50
520
1. 50
0.83
0.50
0.77
0.65
0.48
0.60
0.53
0.38
821
2.00
1. 00
1. 60
4.20
1. 50
1. 00
7.00
2.50
3.00
822
2.00
0.50
0.60
0.77
0.60
0.60
0.90
0. 8-9
1. 00
79
FILLED
NON-PROPORTIONED
1
3
5
13
20
25
30
45
60
Sl
1. 00
0.67
0.40
0.38
0.70
0.60
0.80
1.11
0.67
82
5.00
0.83
0.40
0.23
0.65
1. 00
1. 00
0.58
0.17
83
1. 50
0.67
0.45
0.15
0.23
0 •. 60
0.33
0.44
0.67
S4
l. 50
J.. 00
0.80
1.15
1. 00
1. 60
0.33
1. 44
1. 00
ss
3.00
1. 67
1. 60
1. 92
1. 25
1. 40
1.13
1. 00
1. 08
S6
2.00
1. 33
0.80
0.77
0.85
0.88 '1. 07
1. 22
1.13
S7
l. 00
0.50
0.50
0.77
0.65
0.60
0.43
0.49
0.40
S8
1. 00
1. 00
0.60
0.54
0.60
0.60
0~30
0.67
1. 50
S9
4.00
2.00
1. 40
0.77
0.50
0.68
0.83
0.78
1. 67
SlO
3.00
0.67
0.60
0.54
0.50
0.48
0.67
0.78
0.67
Sll
l. 00
1. 00
1. 00
0.77
1. 00
1. 20
1. 00
1. 33
1. 25
Sl2
2.00
0.67
1. 00
0.54
0.60
0.40
0.37
0.33
0.27
513
2.50
2.67
0.80
1. 53
1. 25
1. 40
0.33
1.11
1.17
514
1. 00
1. 00
1. 00
0.77
1. 00
0.80
0.67
0.89
1. 00
Sl5
3.00
1. 67
1. 00
1.15
0.75
0 ..80
0.83
0. 67
0.75
Sl6
2.00
1. 00
1. 20
0.46
0.85
0.80
0.67
0.56
0.58
Sl7
3.00
1. 67
0.90
0.85
0.85
0.76
1.17
0.96
1. 00
818
2.00
l. 00
0.80
0.76
0.80
0.48
0.83
0.82
0.92
519
2.00
1. 67
l. 20
0.77
1. 75
0.80
1. 00
1. 00
1. 50
S20
3.00
1. 00
0.60
0.62
0.45
0.40
0.76
0.49
0.50
S21
.3.00
1. 67
1. 40
0.62
1. 25
0.36
0.33
1. 00
0.87
S22
3.00
1. 33
0.80
0.38
0.75
0.84
0.90
0.84
0.83
80
FILLED
PROPORTIONED
1
3
5
13
20
25
30
45
60
S1
1. 00
0.67
0.40
0.54
0.60
0.80
0.80
1. 00
0.83
S2
2.00
1. 00
0.40
1. 00
1. 05
0.28
0.90
0.68
0.52
S3
1.00
1. 00
0.60
0.19
0.28
0.24
0.50
0.27
0.67
S4
1. 50
0.67
0.60
0.46
0.80
2.00
1. 00
1. 33
0.83
ss
4.00
1. 67
0.80
1. 54
1.10
1. 20
1. 33
1. 22
1.17
S6
3.00
1. 00
1. 60
0.52
0.85
1. 65
0.90
0.89
1. 00
S7
1. 00
0.33
0.50
0.69
0.35
0.72
0.53
0.58
0.58
88
1. 00
1. 67
1. 00
0.38
0.75
0.60
2.00
1. 33
2.00
S9
4.00
2.00
1. 40
0.92
0.65
0.76
1. 00
0.78
0.67
SlO
2.00
1. 33
0.60
0.62
0.60
0.60
0.70
0.67
0.53
Sl1
1.00
1. 00
0.80
0.77
1. 25
1. 20
1. 67
0.95
0.83
Sl2
3.00
1. 00
0.70
0.38
0.75
0.52
0.30
0.36
0.33
Sl3
2.00
0.83
1. 00
1. 53
1. 25
1. 40
2.00
2.00
1. 50
S~.d
J. •
1. 00
0.67
1. 60
0.77
0.75
1. 00
0.83
1. 00
0.83
Sl5
3.00
2.00
1. 20
1.15
1. 00
0.60
0.67
0.67
0.42
816
2.00
1. 33
0.80
0.62
1. 00
0.68
0.50
0.56
0.58
Sl7
3.00
1. 67
1. 00
1. 08
0.60
0.94
1. 00
0.42
0.75
Sl8
2.00
1.·oo
1. 00
1. 00
0.70
0.60
0.50
0.56
2.00
Sl9
3.00
2.67
2.60
0.92
0.85
0.72
1. 33
1.11
1.10
820
2.00
1. 33
0.60
0.46
0.65
0.44
0.57
0.53
0.53
S21
3.00
2.00
1. 40
0.85
0.75
0.80
0.27
1. 44
1. 00
522
3.00
1. 67
0.90
0.54
0.65
0.92
0.73
0.89
0.67