Visual Word Recognition Without Central Attention: Evidence for

Psychology and Aging
2006, Vol. 21, No. 3, 431– 447
Copyright 2006 by the American Psychological Association
0882-7974/06/$12.00 DOI: 10.1037/0882-7974.21.3.431
Visual Word Recognition Without Central Attention: Evidence for Greater
Automaticity With Advancing Age
Mei-Ching Lien
Philip A. Allen
Oregon State University
University of Akron
Eric Ruthruff
Jeremy Grabbe
University of New Mexico
University of Akron
Robert S. McCann
Roger W. Remington
National Aeronautics and Space Administration
Ames Research Center
Johns Hopkins University
The present experiments examined the automaticity of word recognition. The authors examined whether
people can recognize words while central attention is devoted to another task and how this ability changes
across the life span. In Experiment 1, a lexical decision Task 2 was combined with either an auditory or
a visual Task 1. Regardless of the Task 1 modality, Task 2 word recognition proceeded in parallel with
Task 1 central operations for older adults but not for younger adults. This is a rare example of improved
cognitive processing with advancing age. When Task 2 was nonlexical (Experiment 2), however, there
was no evidence for greater parallel processing for older adults. Thus, the processing advantage appears
to be restricted to lexical processes. The authors conclude that greater cumulative experience with lexical
processing leads to greater automaticity, allowing older adults to more efficiently perform this stage in
parallel with another task.
Keywords: aging, dual-task interference, visual word recognition, divided attention
Because word reading plays a critical role in human cognition,
considerable effort has been devoted in recent years to understanding the underlying mechanisms. One important issue is the degree
to which word recognition (or lexical access) is automatic. Many
studies have shown that it is automatic in the sense that it does not
require the specific intention to read words. One example comes
from the well-known Stroop paradigm, whereby participants are
slow to name the ink color of a word that spells an incongruent
color name (e.g., the word red in the color green; see MacLeod,
1991, for a review). People cannot avoid reading the word even
when doing so strongly interferes with their assigned task.
Although word recognition does not require an intention to read,
there is evidence that it does require certain attentional resources.
Lachter, Forster, and Ruthruff (2004), for example, found that
words produced no repetition priming unless they received spatial
attention1 (see also Lachter, Ruthruff, Lien, & McCann, 2006;
McCann, Folk, & Johnston, 1992; but see Brown, Roos-Gilbert, &
Carr, 1995). There is also evidence that word recognition requires
central attention; that is, word recognition on one task cannot take
place while central attention is devoted to selecting a response to
another task (McCann, Remington, & Van Selst, 2000). However,
another dual-task study used somewhat different methods (different age groups and a different input modality for the primary task)
and obtained a different outcome (Allen et al., 2002). Although no
firm conclusions can yet be drawn, as we discuss later in detail,
these studies suggest two interesting hypotheses. One is that older
adults are better able than younger adults to perform word recognition without central attention. Another hypothesis is that visual
word recognition can proceed in parallel with another visual task
but not with an auditory task. The present study examines both of
these hypotheses.
Mei-Ching Lien, Department of Psychology, Oregon State University;
Philip A. Allen and Jeremy Grabbe, Department of Psychology, University
of Akron; Eric Ruthruff, Department of Psychology, University of New
Mexico; Robert S. McCann, National Aeronautics and Space Administration Ames Research Center, Moffett Field, California; Roger W. Remington, Applied Physics Laboratory, Johns Hopkins University.
This research was supported by funding from the Oregon State University Research Incentive Programs, the College of Liberal Arts at Oregon
State University, and National Aeronautics and Space Administration
Grant NCC 2-1325.
Correspondence concerning this article should be addressed to MeiChing Lien, Department of Psychology, Oregon State University, Corvallis, OR 97331. E-mail: [email protected]
Locus-of-Slack Logic
One direct way to establish whether a particular mental process
(e.g., word recognition) requires central attention is to determine
whether this process can be carried out while central attention is
devoted to another task. Before we describe the details of this
1
Johnston, McCann, and Remington (1995) provided evidence for two
dissociable forms of attention. Input attention, which is identical to what
we call spatial attention, limits parallel perceptual processing of multiple
stimuli, whereas central attention limits parallel processing in higher
mental functions, such as response selection.
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LIEN ET AL.
approach, however, it is necessary to provide background on
dual-task methodology and findings.
Probably the most widely used dual-task paradigm is the psychological refractory period (PRP) paradigm, in which two tasks
are separated by a variable time interval (called the stimulus onset
asynchrony [SOA]). The task presented first is called Task 1, and
the task presented second is called Task 2. The typical PRP finding
is that the response time (RT) for Task 1 (RT1) is roughly constant
across SOAs, but the RT for Task 2 (RT2) increases sharply as the
SOA decreases (i.e., when the tasks are demanded at nearly the
same time). This robust form of dual-task interference, known as
the PRP effect (Telford, 1931), has been found even when tasks
have no input conflicts or output conflicts.
Many studies have found evidence that the PRP effect occurs
largely because central stages (e.g., response selection, decision
making) for Task 1 and Task 2 do not operate in parallel (for
reviews, see Lien & Proctor, 2002; Pashler, 1994; Pashler &
Johnston, 1989; see also Meyer & Kieras, 1997, for a different
point of view2). This central bottleneck, shown in Figure 1, has
been reported to occur even with exceptionally easy tasks (e.g.,
Lien, McCann, Ruthruff, & Proctor, 2005; Lien, Proctor, & Allen,
2002). Because central stages of Task 2 are postponed until central
stages of Task 1 are completed, this central bottleneck creates a
period of cognitive slack between the perceptual and central stages
in Task 2 at short SOAs (Pashler, 1984; Schweickert, 1978;
Welford, 1952). At long SOAs, however, the tasks are performed
more or less independently, so there is no period of cognitive
slack.
According to this central bottleneck model, variables that primarily affect the duration of Task 2 central processing should
produce additive effects with SOA. However, any variable affecting earlier Task 2 stages should produce effects that are underadditive with SOA. In brief, the reason is that any lengthening of
prebottleneck stages of Task 2 (Stage 2A in Figure 1) can be
absorbed into the cognitive slack at short SOAs but not at long
SOAs (see Pashler, 1994; Schweickert, 1978). For ease of discussion, we refer to this as a slack effect. By observing whether
manipulations of a certain stage interact additively or underaddi-
Figure 1. The temporal relations between central processing stages of
Task 1 and Task 2 at short stimulus onset asynchrony (SOA) in the
psychological refractory period paradigm, as suggested by the central
bottleneck model. This model assumes that perceptual and response initiation/execution stages of Task 2 can operate in parallel with any stage of
Task 1 but that central stages of Task 2 cannot start until central stages of
Task 1 have been completed. 1A, 1B, and 1C are the perceptual, central,
and response initiation/execution stages of Task 1, respectively. 2A, 2B,
and 2C are the corresponding stages for Task 2. S1 ⫽ stimulus for Task 1;
S2 ⫽ stimulus for Task 2; R1 ⫽ response for Task 1; R2 ⫽ response for
Task 2.
tively with SOA, one can determine whether that stage is subject
to the central bottleneck (i.e., whether it requires central attention).
This logic, used in a large number of dual-task studies, has become
known as locus-of-slack logic (see McCann & Johnston, 1992;
Pashler, 1984; Schweickert, 1978).
Does Word Recognition Require Central Attention?
Two recent PRP studies used locus-of-slack logic—within the
framework of the central bottleneck model—to determine whether
word recognition requires central attention, but they reached seemingly opposite conclusions (Allen et al., 2002; McCann et al.,
2000). In both studies, Task 2 required participants to determine
whether a letter string formed a word or nonword, also known as
a lexical decision task. To manipulate the duration of Task 2 word
recognition, the authors in both studies selected a set of lowfrequency words and a set of high-frequency words, with frequency defined in terms of occurrences in the English language
(Kučera & Francis, 1967). If word recognition requires central
attention, then the effect of word frequency on RT2 should be
additive with the effects of SOA. However, if word recognition
does not require central attention, then the word frequency effect
on RT2 should be underadditive with the effects of SOA (i.e.,
producing a slack effect for word frequency).
McCann et al. (2000) investigated the reliance of word processing on central attention in a series of experiments involving
younger adults. In Experiments 1 and 2, participants made manual
keypresses to a high- or low-pitched tone for Task 1 and a
word/nonword judgment (lexical decision) for Task 2. The key
finding was that word frequency effects were roughly additive
with the effects of SOA. Experiments 3 to 6 replicated the roughly
additive effects of word frequency and SOA when Task 2 was a
speeded naming task rather than a lexical decision task. McCann et
al. therefore concluded that Task 2 word recognition was postponed until central attention switched from Task 1 to Task 2. In
other words, they concluded that word recognition requires central
attention.
Allen et al. (2002) used a similar paradigm to look for age
differences in the ability to perform tasks in parallel. Given one
widely held theory that older adults exhibit a decrement in processing resources (e.g., Craik & Salthouse, 2000), the authors
hypothesized that older adults should consistently show less efficient parallel processing than younger adults across a wide variety
of tasks and processing stages, including memory retrieval and
response selection. That is, older adults should have more difficulty than younger adults in performing Task 2 (a lexical decision
task) while central attention is devoted to Task 1. Whereas McCann et al. (2000) used an auditory discrimination (high- vs.
low-pitched tones) for Task 1, Allen et al. (2002) used a visual
2
These authors pointed out that the central bottleneck might reflect a
strategic choice rather than a structural limitation. On the one hand,
attempts to induce participants to choose to bypass the central bottleneck
have generally failed (e.g., Ruthruff, Pashler, & Klaassen, 2001). On the
other hand, there is some evidence that bypassing is possible with relatively
easy tasks after multiple practice sessions (Hazeltine, Ruthruff, & Remington, 2006; Hazeltine, Teague, & Ivry, 2002; Ruthruff, Hazeltine, &
Remington, in press; Ruthruff, Van Selst, Johnston, & Remington, 2006;
Schumacher et al., 2001). Note, however, that the present tasks were not
especially easy or highly practiced.
AGING AND WORD RECOGNITION
shape discrimination (triangle vs. rectangle). The word or nonword
for Task 2 was presented inside the shape, so that there was no
competition for spatial attention between tasks. Contrary to McCann et al., Allen et al. found an underadditive interaction between
word frequency effects and SOA in both of their experiments, for
both younger and older adults. On the basis of locus-of-slack logic,
this result suggests that word recognition can proceed without
central attention. Allen et al. argued that when a process is highly
overlearned (or automatized; e.g., Hasher & Zacks, 1979), as
might be the case for lexical processing, it can operate in parallel
with central stages on another task (see also Logan & Schulkind,
2000).
Although Allen et al. (2002) found an underadditive interaction
of word frequency and SOA (i.e., the slack effect) for both older
and younger adults, the effect was more pronounced for older
adults than for younger adults— especially in Experiment 2 (which
included more trials than Experiment 1). This finding suggests,
contrary to the general-resource decrement theory of cognitive
aging (Craik & Salthouse, 2000), that older adults actually show
more efficient parallel processing than younger adults, at least for
certain highly overlearned mental processes.
Given the potential importance of this finding for theories of
cognitive aging, Allen et al. (2002) attempted to provide converging evidence. In particular, they derived a measure of the degree of
parallel processing, which they called general savings. It is equal
to the time it should take participants to complete the tasks if
performed strictly sequentially (estimated as the sum of long-SOA
RT1 and long-SOA RT2) minus the time that it actually took
participants to complete both tasks at the shortest SOA (the time
between Task 1 stimulus onset and Task 2 response, which can be
expressed simply as SOA plus RT2).
General savings ⫽ 共RT1 Longest SOA
⫹ RT 2Longest SOA兲 ⫺ 共SOAShortest⫹RT 2Shortest SOA兲.
(1)
If there is no parallel processing, then general savings should be
equal to zero. To the degree that some parallel processing has
occurred, general savings should be positive. Allen et al. (2002)
argued that if older adults are better able than younger adults to
process the tasks in parallel, then they should show a larger general
savings score. Unlike the larger slack effects observed for older
adults (relative to younger adults), Allen et al. found no age
differences in general savings scores. They concluded that older
adults showed at least as much parallel processing, overall, as did
younger adults.
Nevertheless, there are three reasons why Allen et al.’s (2002)
findings regarding general savings are inconclusive. First, RT1
increased as SOA increased, and the increase was much stronger
for younger adults than for older adults. These results suggest that
participants often withheld the response to Task 1 so that it could
be initiated together with the response to Task 2 (a phenomenon
known as response grouping; Borger, 1963; Pashler & Johnston,
1989). Consequently, the observed long-SOA RT1 does not necessarily reflect the actual time required to complete Task 1 processing. Second, Allen et al. used a relatively long SOA (250 ms)
as their shortest SOA, limiting the opportunity for parallel processing and the opportunity to observe savings. Finally, Allen et al.
measured general savings averaged across high- and lowfrequency words, which might not have provided the most sensitive test for age differences. Given that lexical access (the stage
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that older adults are hypothesized to perform in parallel with Task
1) is longer for low-frequency words than for high-frequency
words, the best opportunity to observe the increase in general
savings is for low-frequency words in isolation. As we discuss
later, the present study addresses each of these three issues and
provides a more sensitive test of the hypothesis that older adults
are better able than younger adults to carry out word recognition in
parallel with Task 1.
The Present Study
McCann et al. (2000) and Allen et al. (2002) used a PRP
paradigm to study the automaticity of word recognition but arrived
at seemingly conflicting conclusions. There are two possible explanations for the discrepancy between these two studies. One
hypothesis, which we call the input modality hypothesis, is that
visual word recognition can proceed in parallel with a visual Task
1 (as in Allen et al.) but not with an auditory Task 1 (as in McCann
et al.). When both Task 1 and Task 2 are visual (which we call the
visual–visual [VV] condition) and the Task 1 stimulus is in the
same location as the word/nonword of Task 2 (as in Allen et al.),
spatial attention to the visual Task 1 stimulus would also cover the
word/nonword of Task 2. In contrast, when an auditory Task 1 is
combined with the visual Task 2 (which we call the auditory–
visual [AV] condition), participants have more leeway to direct
spatial attention away from the location of the word/nonword. The
motivation to divert spatial attention is that it would temporarily
prevent the Task 2 word from being identified (Lachter et al.,
2004) and thus reduce the interfering effects of Task 2 processing
on Task 1 processing. According to this hypothesis, the lack of
spatial attention, rather than the lack of central attention, caused
the failure of McCann et al.’s participants to recognize the Task 2
word/nonword in parallel with an auditory Task 1.
To evaluate this input modality hypothesis, we had participants
in the present Experiment 1 perform both the AV and the VV
conditions in separate experimental sessions. In both the AV and
the VV conditions, an unfilled visual shape was presented as an
auditory stimulus was played. However, only the visual shape was
relevant to Task 1 in the VV condition, and only the auditory
stimulus was relevant to Task 1 in the AV condition. The advantage of this approach is that the stimulus conditions are identical in
the AV and VV conditions. If lexical processing of Task 2 cannot
proceed in parallel with central processing of the auditory Task 1,
then additive effects of word frequency and SOA should be obtained. If lexical processing on Task 2 can proceed in parallel with
central processing of the visual Task 1, then an underadditive
effect should be observed.
Another hypothesis, which we call the age hypothesis, is that the
degree of parallelism of word recognition with the performance of
another task increases with age. Because word reading is a skill
that develops over time, the ability to perform word recognition in
parallel with another task might improve as the cumulative experience with words increases (Hasher & Zacks, 1979; Logan &
Schulkind, 2000). Therefore, older adults might show more efficient parallel processing of Task 2 word recognition with Task 1
than younger adults. That is, older adults might show an underadditive interaction between the effects of word frequency and SOA,
as found by Allen et al. (2002), whereas younger adults might
show a more additive interaction, as found by McCann et al.
(2000).
LIEN ET AL.
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To evaluate this age hypothesis, we examined slack effects for
both younger adults and older adults (who performed both the AV
and the VV conditions). To look for converging evidence that
older adults are better able than younger adults to perform word
recognition in parallel with Task 1, we also estimated the general
savings (see Equation 1) for both age groups. As we show, Experiment 1 reveals parallel processing for older adults in both AV
and VV conditions but not for younger adults. Thus, Experiment 2
was designed to test our hypothesis that the increase in parallel
processing for older adults is restricted to lexical processes.
Experiment 1
The purpose of Experiment 1 was to evaluate (a) whether visual
word recognition can proceed in parallel with a visual Task 1 (as
in Allen et al., 2002) but not with an auditory Task 1 (as in
McCann et al., 2000) and (b) whether older adults show more
efficient parallel processing of Task 2 word recognition with Task
1 than younger adults.
Method
Participants. A total of 48 participants (24 younger adults and 24 older
adults) were tested. Younger adults were undergraduate students at the
University of Akron who participated in partial fulfillment of a course
requirement. Their mean age was 25 years, with a range of 19 to 44 years.
Older adults were community-dwelling individuals and were paid $20 per
hour for their participation. Their mean age was 71 years, with a range of
59 to 83 years. All participants had normal or corrected-to-normal vision.
Each participant performed two sessions, one for the AV condition and one
for the VV condition. Half of the participants performed the AV condition
first, whereas the other half performed the VV condition first. Both
sessions were conducted during a single visit to the laboratory, although
participants were given a break between sessions. The entire experiment
lasted less than 2 hr.
All participants were tested on the Wechsler Adult Intelligence Scale—
Revised (WAIS–R; Wechsler, 1981) Vocabulary and Digit Symbol Substitution Task subscales. For the Digit Symbol task, younger adults (mean
score ⫽ 67.3) scored significantly higher than older adults (mean score ⫽
50.8), t(46) ⫽ 3.73, p ⬍ .001. For the WAIS–R Vocabulary test, older
adults showed higher scores (mean score ⫽ 53.3) than younger adults
(mean score ⫽ 45.7), t(46) ⫽ 2.03, p ⬍ .05.
Apparatus and stimuli. Stimulus presentation, timing, and data collection were controlled via IBM-compatible microcomputers driven by
E-Prime software (Schneider, Eschman, & Zuccolotto, 2002). For Task 1,
a visual shape appeared on the screen at the same time that an auditory
stimulus was sounded. The shape was an unfilled circle or square. The
circle was 6 cm in diameter, and the square was 6 cm long on each side.
At a viewing distance of 55 cm, both shapes subtended horizontal and
vertical visual angles of 6.23°. The auditory stimulus was either a pure tone
or white noise (similar to a hissing sound). For the AV condition, Task 1
was to respond to the sound and ignore the shape. For the VV condition,
Task 1 was to respond to the shape and ignore the sound.
In both the AV and the VV conditions, the Task 2 stimulus was a word
or a nonword presented inside the circle or square. Each letter was
presented in lowercase in Courier New font, size 18, and was approximately 0.8 cm in height and 0.6 cm in width. At a viewing distance of 55
cm, each letter subtended a visual angle of 0.83° ⫻ 0.63°. The word stimuli
were taken from the Kučera and Francis (1967) norms to form two
different stimulus lists. Because each participant completed two sessions
(one for the AV condition and one for the VV condition), we generated two
different word lists (see Appendixes A and B). One word list (List 1),
essentially the same as in Allen et al. (2002), included low-frequency
words ranging from 10 to 30 occurrences and high-frequency words
ranging from 240 to 1,016 occurrences. The other word list (List 2) also
included low-frequency words ranging from 10 to 30 occurrences but
included high-frequency words ranging from 151 to 236 occurrences
(taken from Allen, Wallace, & Weber’s, 1995; medium high-frequency
category).3 We formed nonwords by changing one of the letters of a word
stimulus. Each word or nonword appeared only once during the experimental trials for an individual participant. The presentation of the stimulus
lists in the AV and VV conditions was counterbalanced. That is, half of the
participants received List 1 in the AV condition and List 2 in the VV
condition, whereas the other half of the participants received List 1 in the
VV condition and List 2 in the AV condition. Thus, although the two lists
were not identical, each was used equally often in each condition for both
younger and older adults.
Design and procedure. To begin the session, each participant performed two practice blocks. The first block contained 32 trials with a
constant 1,500-ms SOA. The purpose of this block was to provide an
opportunity for participants to learn the tasks without having to deal with
both tasks at the same time and to encourage participants to perform the
two tasks without grouping together the responses for Task 1 and Task 2.
The second practice block contained 72 trials with the same set of SOAs
used in the experimental blocks. Each participant was then given a total of
432 regular trials, divided into six blocks of 72 trials each. These trials
consisted of the 144 possible combinations of the following five variables:
Task 1 stimulus type (tone/noise for the AV condition or circle/square for
the VV condition), word type (word or nonword), letter-string length (four,
five, or six letters), word frequency (high or low), and SOA (50, 100, 300,
500, 700, or 900 ms). Therefore, there were three occurrences of each
combination of conditions (although with a different word each time) for
each modality condition (AV and VV). These conditions were selected
randomly within a session, with the restriction that each combination of
conditions must occur equally often during the regular trials.
The participant pressed the space bar of the keyboard to initiate the first
trial of each block. The fixation cross was then presented for 500 ms in the
center of the screen. One hundred ms after offset of the fixation cross, the
Task 1 stimulus (S1) was presented: The auditory stimulus was sounded
(for 100 ms), and the shape appeared in the screen center (until response).
The Task 2 stimulus (S2; a string of letters) followed S1 after one of six
SOAs (50, 100, 300, 500, 700, or 900 ms, randomly selected within blocks)
and remained on the screen until a response was recorded.
In the AV condition, participants were asked to respond to the auditory
S1 by pressing the z key with their left middle finger for the tone and the
x key with their left index finger for the noise. In the VV condition,
participants were asked to respond to the visual S1 by pressing the z key
with their left middle finger for the circle and the x key with their left index
finger for the square. For Task 2 (which was identical for the AV and VV
conditions), participants were asked to press the ⬎ key with their right
index finger if the letter string formed a word and to press the ? key with
their right middle finger if the letter string formed a nonword.
Participants were instructed to respond to S1 before S2 and to respond
as quickly and accurately as possible to both tasks. They were also asked
to maintain at least 90% accuracy and to respond to Task 1 within 3 s for
younger adults and within 5 s for older adults. The use of a time-out for
Task 1 discouraged response grouping. Feedback for incorrect responses
was presented on the screen for 1,200 ms.
3
The reason List 2 included a different range of high-frequency words
is that no other high-frequency words could be found in the same range as
those in List 1. Allen et al. (1995) found no RT difference between the
ranges of very high-frequency words and medium high-frequency words.
Similarly, we found no difference in performance between these ranges in
the present study. Therefore, the present data analyses were collapsed
across Word List 1 and List 2.
AGING AND WORD RECOGNITION
Results
Trials were excluded from the RT analyses if the response to
either task was incorrect. In addition, for younger adults, trials
were excluded if RT was either shorter than 100 ms or longer than
3,000 ms; approximately 0.8% of trials were eliminated because of
these RT cutoffs. For older adults, trials were excluded if RT was
either shorter than 100 ms or longer than 4,000 ms; approximately
0.9% of trials were eliminated because of these cutoffs. The
proportions of errors (PEs) for Task 1 (PE1) and Task 2 (PE2)
were determined without regard to whether the response for the
other task was correct. The independent variables included in the
data analyses were age group (younger vs. older), modality condition (AV vs. VV), S2 word frequency (high vs. low), S2 lexicality (word vs. nonword), SOA (100, 300, 500, 700, and 900
ms),4 and participants. S1 type (tone/noise in the AV condition and
circle/square in the VV condition) and session (first vs. second)
had little effect5 and therefore were not included as factors in the
final data analyses. An alpha level of .05 was used to determine
statistical significance.
Because word frequency and lexicality are not orthogonal, they
cannot be included in the same crossed analysis of variance
(ANOVA). Thus, we conducted two different ANOVAs. The
ANOVA of our primary interest, which included the S2 word
frequency variable, was conducted for words only.6 The secondary
ANOVA, which excluded the S2 word frequency variable, was
conducted to examine the lexicality effect (word vs. nonword). In
this particular data analysis, only significant main effects or interactions involving S2 lexicality and age group were reported. Note
that our tests for the automaticity of word recognition were based
on the interaction between word frequency and SOA, not the
interaction between lexicality (word vs. nonword) and SOA. In
brief, the reason is that the lexicality variable likely influenced not
only word recognition but also response selection and response
execution.
Word frequency effects. Mean RT1s and RT2s are shown in
Figure 2 for both the AV and the VV conditions. PE data for Task
1 are shown in Table 1, and PE data for Task 2 are shown in Table
2. For RT1, the main effect of age group was significant, F(1,
46) ⫽ 57.27, p ⬍ .0001, MSE ⫽ 505,731; mean RT1 was 634 ms
for younger adults and 982 ms for older adults. There were also
main effects of modality condition, F(1, 46) ⫽ 8.34, p ⬍ .01,
MSE ⫽ 155,107, and SOA, F(4, 184) ⫽ 13.84, p ⬍ .001, MSE ⫽
15,575. Mean RT1 was 74 ms longer in the AV condition (845 ms)
than in the VV condition (771 ms). Mean RT1s were 863, 797,
781, 790, and 810 ms at the 100-, 300-, 500-, 700-, and 900-ms
SOAs. The interaction of modality condition and SOA was significant, F(4, 184) ⫽ 3.90, p ⬍ .01, MSE ⫽ 8,371. For the AV
condition, mean RT1 was roughly constant across SOAs (RT1s ⫽
878, 842, 817, 829, and 858 ms at the 100-, 300-, 500-, 700-, and
900-ms SOAs). For the VV condition, mean RT1 was longer at the
shortest SOA than at the other SOAs (RT1s ⫽ 848, 751, 745, 751,
and 762 ms at the 100-, 300-, 500-, 700-, and 900-ms SOAs),
which might partly be because S2 laterally masked the visual S1.
Overall, the data suggest that response grouping rarely occurred at
long SOAs for both younger and older adults.
The PE1 data showed a significant main effect of SOA, F(4,
184) ⫽ 5.33, p ⬍ .001, MSE ⫽ 0.0012; PE1 was slightly higher at
the shortest SOA than at the other SOAs (PE1s were .03, .02, .02,
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.02, and .02, at 100-, 300-, 500-, 700-, and 900-ms SOAs, respectively). No other effects were significant.
For RT2, the main effect of age group was significant, F(1,
46) ⫽ 50.57, p ⬍ .001, MSE ⫽ 532,424; mean RT2 was 742 ms
for younger adults and 1,077 ms for older adults. The main effect
of SOA was also significant, F(4, 184) ⫽ 363.44, p ⬍ .0001,
MSE ⫽ 15,438; RT2 increased as SOA decreased (RT2s ⫽ 1,181,
968, 845, 788, and 765 ms at the 100-, 300-, 500-, 700-, and
900-ms SOAs). Thus, a sizeable PRP effect of 416 ms was obtained. The main effect of S2 word frequency was also significant,
F(1, 46) ⫽ 125.39, p ⬍ .001, MSE ⫽ 6,775. RT2 was 60 ms
shorter when S2 was a high-frequency word (879 ms) than when
it was a low-frequency word (939 ms). The interaction of age
group and SOA was also significant, F(4, 184) ⫽ 19.55, p ⬍
.0001, MSE ⫽ 15,438, reflecting that the PRP effect was smaller
for younger adults (321 ms) than for older adults (511 ms). Most
important, the Age Group ⫻ S2 Word Frequency ⫻ SOA interaction on RT2 was significant, F(4, 184) ⫽ 4.28, p ⬍ .01, MSE ⫽
6,436, reflecting that older adults showed underadditivity between
word frequency and SOA but younger adults did not (see Figure
2). For older adults, the word frequency effect was ⫺2, 59, 51, 64,
and 98 ms at 100-, 300-, 500-, 700- and 900-ms SOAs. For
younger adults, the word frequency effect was 92, 45, 48, 69, and
71 ms at the 100-, 300-, 500-, 700- and 900-ms SOAs. The
four-way interaction of age group, modality condition, S2 word
frequency, and SOA was not significant (F ⬍ 1.0).
For PE2, there were main effects of age group, F(1, 46) ⫽
30.33, p ⬍ .0001, MSE ⫽ 0.0119, and S2 word frequency, F(1,
46) ⫽ 57.28, p ⬍ .0001, MSE ⫽ 0.0080. PE2 was higher for
younger adults (.07) than for older adults (.03). PE2 was also
higher for low-frequency words (.07) than for high-frequency
words (.03). The interaction of age group and S2 word frequency
was also significant, F(1, 46) ⫽ 8.89, p ⬍ .001, MSE ⫽ 0.0080;
the word frequency effect on PE2 was .06 for younger adults but
was only .03 for older adults. No other effects were significant.
Lexicality effects. Mean RTs to Task 1 and Task 2 are shown
in Figure 3 for both the AV and the VV conditions. For RT1, the
only significant main effect or interaction involving S2 lexicality
was the main effect of S2 lexicality, F(1, 46) ⫽ 5.70, p ⬍ .05,
MSE ⫽ 4,500, and its interaction with age group, F(1, 46) ⫽ 5.28,
p ⬍ .05, MSE ⫽ 4,500. RT1 was 7 ms shorter when S2 was a word
(RT1 ⫽ 808 ms) than when it was a nonword (RT1 ⫽ 815 ms).
Younger adults showed no effect of lexicality on RT1 (RT1 ⫽ 634
ms for both words and nonwords), whereas older adults showed a
slightly shorter mean RT1 when S2 was a word (RT1 ⫽ 982 ms)
than when it was a nonword (RT1 ⫽ 996 ms). No effects involving
S2 lexicality on PE1 were significant.
4
Initially, Experiment 1 included six different SOAs (50, 100, 300, 500,
700, and 900 ms). Because of a technical difficulty, however, the software
did not present an SOA of less than 100 ms. Therefore, we did not analyze
data from the 50-ms trials, which left only five different SOAs (100, 300,
500, 700, and 900 ms) in the final data analyses.
5
The same pattern of results was obtained even when the data analysis
included the S1-type variable. The session variable also had little influence
on the data and did not modulate any interactions involving SOA and
frequency (Fs ⱕ 1.75).
6
The high- versus low-frequency distinction does not apply to nonword
stimuli. Consequently, the word frequency effect was examined only for
the word stimuli.
436
LIEN ET AL.
Figure 2. Mean response times (RTs) for Task 1 and Task 2 in Experiment 1 for younger adults and older
adults in the auditory–visual (AV) condition and the visual–visual (VV) condition as a function of stimulus onset
asynchrony (SOA; 100, 300, 500, 700, and 900 ms) and Stimulus 2 word frequency (high vs. low).
For RT2, there was a main effect of lexicality, F(1, 46) ⫽ 57.21,
p ⬍ .0001, MSE ⫽ 22,573; mean RT2 was shorter when S2 was
a word (RT2 ⫽ 909 ms) than when it was a nonword (RT2 ⫽ 961
ms). For PE2, there were significant main effects of group, F(1,
46) ⫽ 35.38, p ⬍ .0001, MSE ⫽ 0.0371, and lexicality, F(1, 46) ⫽
7.54, p ⬍ .01, MSE ⫽ 0.0141. PE2 was higher for younger adults
(PE2 ⫽ .087) than for older adults (PE2 ⫽ .034). Participants
made more errors when S2 was a nonword (PE2 ⫽ .068) than
when it was a word (PE2 ⫽ .053). The interaction between group
and lexicality was also significant, F(1, 46) ⫽ 6.18, p ⬍ .05,
MSE ⫽ 0.0141. The lexicality effect on PE2 was .029 for younger
adults and .001 for older adults. The three-way interaction of S2
lexicality, modality condition, and SOA was significant on PE2,
F(4, 184) ⫽ 2.68, p ⬍ .05, MSE ⫽ 0.0026. For the AV condition,
there was a trend for the lexicality effect on PE2 to decrease as
SOA increased (the effect on PE2 was .023, .023, .009, ⫺.008, and
.004 at the 100-, 300-, 500-, 700-, and 900-ms SOAs). For the VV
condition, there was no consistent trend across SOAs (the lexicality effect on PE2 was .031, .010, .018, .027, and .011 at the 100-,
300-, 500-, 700-, and 900-ms SOAs).
Discussion
In Experiment 1, older adults produced underadditive effects of
word frequency and SOA in both the AV and the VV conditions,
whereas younger adults produced additive effects in both conditions. Thus, age influenced the pattern of results, but Task 1
modality (auditory vs. visual) did not. On the basis of locus-ofslack logic and the central bottleneck model, these results indicate
that word recognition required central attention for younger adults
but not for older adults. Thus, these findings support the hypothesis that the efficiency of lexical access improves with age.
An alternative hypothesis that deserves consideration is that the
lack of slack effects for younger adults occurred simply because
these participants had insufficient slack time to absorb the effects
of word frequency. This hypothesis seems unlikely, however,
given that younger adults did show a substantial PRP effect of 321
ms, which should be more than long enough to absorb the 65-ms
word frequency effect. Nevertheless, it is conceivable that younger
adults would have shown more underadditivity had they produced
even longer slack times. To address this possibility, we rank
ordered younger adults on the basis of their mean RT1 (which
AGING AND WORD RECOGNITION
437
Table 1
Proportion of Errors on Task 1 for Younger Adults and Older Adults in Experiment 1 as a
Function of Stimulus Onset Asynchrony (SOA), Modality, Stimulus 2 Lexicality, and Stimulus 2
Word Frequency
SOA
Condition and word type
100
300
500
700
900
Younger adults
Auditory–visual condition
Nonword
High-frequency word
Low-frequency word
Visual–visual condition
Nonword
High-frequency word
Low-frequency word
.027
.032
.025
.022
.021
.021
.024
.019
.019
.026
.014
.028
.019
.014
.026
.035
.028
.037
.026
.023
.032
.017
.028
.007
.017
.007
.009
.019
.023
.028
Older adults
Auditory–visual condition
Nonword
High-frequency word
Low-frequency word
Visual–visual condition
Nonword
High-frequency word
Low-frequency word
.038
.039
.041
.030
.030
.029
.027
.023
.030
.027
.032
.019
.026
.023
.028
.024
.021
.021
.019
.014
.012
.012
.009
.009
.010
.009
.005
.010
.007
.007
should be positively correlated with the amount of slack time; see
Figure 1). We then examined the RT2 data for the 12 younger
participants who exhibited the longest RT1 and hence the longest
slack times. Even these younger adults with the longest slack times
failed to show an interaction of S2 word frequency and SOA, F(4,
44) ⫽ 1.08, p ⬎ .05, MSE ⫽ 3,603; the word frequency effect was
98, 60, 50, 66, and 66 ms at the 100-, 300-, 500-, 700- and 900-ms
SOAs. Another method of examining the effect of slack duration
for younger adults is to analyze just the half of the trials for each
participant in which RT1 was the longest. Even the longer half of
Table 2
Proportion of Errors on Task 2 for Younger Adults and Older Adults in Experiment 1 as a
Function of Stimulus Onset Asynchrony (SOA), Modality, Stimulus 2 Lexicality, and Stimulus 2
Word Frequency
SOA
Condition and word type
100
300
500
700
900
Younger adults
Auditory–visual condition
Nonword
High-frequency word
Low-frequency word
Visual–visual condition
Nonword
High-frequency word
Low-frequency word
.086
.049
.079
.088
.035
.098
.092
.052
.119
.092
.060
.143
.072
.037
.096
.092
.046
.079
.086
.037
.113
.81
.031
.088
.93
.039
.100
.085
.035
.113
Older adults
Auditory–visual condition
Nonword
High-frequency word
Low-frequency word
Visual–visual condition
Nonword
High-frequency word
Low-frequency word
.036
.023
.048
.031
.019
.040
.038
.027
.045
.030
.014
.043
.033
.021
.047
.040
.025
.050
.036
.019
.054
.036
.021
.058
.032
.012
.045
.031
.023
.039
438
LIEN ET AL.
Figure 3. Mean response times (RTs) for Task 1 and Task 2 in Experiment 1 for younger adults and older
adults in the auditory–visual (AV) condition and the visual–visual (VV) condition as a function of stimulus onset
asynchrony (SOA; 100, 300, 500, 700, and 900 ms) and Stimulus 2 lexicality (word vs. nonword).
younger adults’ RT data failed to show an interaction of S2 word
frequency and SOA, F(4, 92) ⫽ 2.44, p ⬎ .05, MSE ⫽ 9,574; the
word frequency effect was 109, 34, 34, 63, and 69 ms at the 100-,
300-, 500-, 700-, and 900-ms SOAs. Consequently, there is no
evidence that the failure of younger adults to produce an underadditive interaction between word frequency effects and SOA was
due to insufficient slack time.
For a converging measure of the amount of parallel processing
(in addition to slack effects), we also computed the amount of
general savings for each participant (see Equation 1). Again,
general savings reflects the degree to which actual dual-task performance was faster than strictly serial processing of the two tasks.
For this analysis we used data from the low-frequency words only,
because they should show the largest benefit of performing lexical
access in parallel with Task 1 central operations. There was a
significant age difference in general savings, F(1, 46) ⫽ 12.67,
p ⬍ .001, MSE ⫽ 110,697; younger adults showed general savings
of 193 ms, whereas older adults showed general savings of 434 ms.
Given that responses were slower overall for older adults than
for younger adults, the larger general savings for older adults than
for younger adults could be due to a generalized slowing of all
mental processes with age (e.g., Cerella, 1990; Salthouse, 1996). If
we assume equal parallelism for both age groups, generalized
slowing of all processing stages by the same multiplicative factor
k would increase general savings by the same factor k (see Appendix C). Therefore, to evaluate whether the increase in general
savings for older adults exceeded that predicted by generalized
slowing, we also used a more conservative test. That is, we
computed the proportional savings for both younger adults and
older adults as follows:
Proportional savings
⫽
共RT1Longest SOA ⫹ RT2Longest SOA) ⫺ (SOAShortest ⫹ RT2Shortest SOA)
. (2)
(RT1Longest SOA ⫹ RT2Longest SOA)
When we used this more conservative measure, there was still a
trend for older adults to show larger savings than younger adults
(.20 vs. .14), F(1, 46) ⫽ 3.43, p ⫽ .07, MSE ⫽ 0.0207. In
summary, the general and proportional savings scores suggest that
older adults showed more overall parallel processing. Thus, they
provide converging evidence that older adults were better able than
AGING AND WORD RECOGNITION
younger adults to perform the word recognition Task 2 in parallel
with Task 1.
Experiment 2
We have hypothesized that older adults show greater slack
effects because they are better able to overlap Task 2 lexical
processing with Task 1 central operations. An alternative hypothesis, however, is that older adults are less able to block out Task 2
processing while performing Task 1. A related hypothesis is that
older adults simply chose a strategy of processing more of Task 2
in parallel with Task 1.
To determine whether the increased parallel processing in older
adults is due specifically to superior lexical processing (as opposed
to a general inability to block out Task 2 or a processing strategy),
we conducted a conceptual replication of Experiment 1 using a
nonlexical Task 2. Because word frequency influences the stimulus categorization stage, our goal was to find a nonlexical task that
would allow a similar manipulation of stimulus categorization. The
task we chose was based on an experiment reported by Johnston
and McCann (2006), in which participants decided whether a box
was narrow or wide. We manipulated the difficulty of this categorization by using two different narrow boxes and two different
wide boxes, one of which was close to the arbitrary boundary
between narrow and wide (the difficult condition) and one of
which was far from the boundary (the easy condition). Thus, we
manipulated the difficulty of a stimulus categorization stage in
both Experiment 1 (lexical task) and Experiment 2 (nonlexical
task), and this manipulation was followed by a response selection
stage.
Johnston and McCann (2006) found additive effects between
this box-width manipulation and SOA in a sample of younger
adults, which suggests that this categorization (like lexical access)
did not proceed in parallel with Task 1 central operations. The key
question in the present experiment is whether the same findings
will be obtained in a sample of older adults (i.e., additive effects of
box-width difficulty and SOA). If older adults have an advantage
specific to lexical processing, as we have proposed, then there is
no reason to expect older adults to produce especially large slack
effects with a nonlexical Task 2. However, if older adults
produce larger slack effects because they are generally less able
to block out Task 2 processing, then one might expect results
similar to those of Experiment 1 (i.e., larger slack effects for
older adults). Likewise, if older adults are simply more likely to
choose not to block out Task 2 processing in general, then one
might expect results similar to those of Experiment 1. For
younger adults, we expect to replicate Johnston and McCann’s
(2006) results.
Method
Participants. A total of 48 participants (24 younger adults and 24 older
adults) were tested. All younger adults were undergraduate psychology
students at Oregon State University who participated in exchange for
course credit. Their mean age was 20.58 years, with a range of 18 to 32
years. Thirteen older adults were recruited from the community surrounding Oregon State University, and 11 older adults were drawn from the same
participant pool as in Experiment 1 (i.e., from the University of Akron
community). Older adults were paid $20 per hour for their participation.
Their mean age was 68 years, with a range of 61 to 78 years. None had
participated in Experiment 1.
439
As in Experiment 1, all participants were tested on the WAIS–R Vocabulary and Digit Symbol Substitution Task subscales. The participants’
performance was similar to performance in Experiment 1. For the Digit
Symbol task, younger adults (mean score ⫽ 65.3) scored significantly
higher than older adults (mean score ⫽ 54.5), t(46) ⫽ 3.63, p ⬍ .001. For
the WAIS–R Vocabulary test, older adults showed higher scores (mean
score ⫽ 59.8) than younger adults (mean score ⫽ 50.6), t(46) ⫽ 5.59, p ⬍
.001.
Apparatus, stimuli, and procedure. The apparatus, stimuli, and procedure were similar to those in Experiment 1, except as noted in the
following. Each participant received only one session. Task 1 involved a
tone/noise discrimination task, like the AV condition of Experiment 1,
except that there was no irrelevant shape. Task 2 was to decide whether
boxes (1.4 cm in height, subtending a visual angle 0.20°) were narrow or
wide. Two different narrow and wide boxes were used to form an easy and
a difficult discrimination condition. For the easy condition, the narrow box
was approximately 1 cm in width (subtending a visual angle of 0.17°), and
the wide box was about 3.8 cm in width (subtending a visual angle of
0.66°). For the difficult condition, the narrow box was approximately 1.8
cm in width (subtending a visual angle of 0.29°), and the wide box was
about 2.6 cm in width (subtending a visual angle of 0.435°). Participants
were asked to press the ⬎ key with their right index finger for a narrow box
and to press the ? key with their right middle finger for a wide box.
Results
The data analysis was similar to that of Experiment 1. Application of the RT cutoff values eliminated 1.33% of trials for
younger adults and 1.18% of trials for older adults. Data were
analyzed as a function of age group (younger vs. older), Task 2
difficulty (easy vs. difficult), SOA (50, 100, 300, 500, 700, and
900 ms), and participants. RT data for Task 1 and Task 2 are
shown in Figure 4, and PE data are shown in Table 3.
For RT1, the main effect of age group was significant, F(1,
46) ⫽ 24.85, p ⬍ .001, MSE ⫽ 1,215,571; mean RT1 was 584 ms
for younger adults and 813 ms for older adults. There was also a
main effect of SOA, F(5, 230) ⫽ 18.74, p ⬍ .0001, MSE ⫽
21,535, reflecting a slight increase in RT1 at short SOAs. This
effect was more pronounced for older adults (see Figure 4), leading
to a significant interaction between age group and SOA, F(5,
230) ⫽ 4.45, p ⬍ .001, MSE ⫽ 21,535. Age group also interacted
with Task 2 difficulty, F(1, 46) ⫽ 4.83, p ⬍ .05, MSE ⫽ 17,187;
RT1 was 8 ms longer in the easy condition (588 ms) than in the
difficult condition (580 ms) for younger adults but was 16 ms
shorter in the easy condition (805 ms) than in the difficult condition (821 ms) for older adults.
The PE1 data showed a significant main effect of SOA, F(5,
230) ⫽ 13.38, p ⬍ .0001, MSE ⫽ 0.0027, with smaller PE1s at
long SOAs (PE1s were .04, .03, .02, .02, .02, and .01, at the 50-,
100-, 300-, 500-, 700-, and 900-ms SOAs, respectively). No other
effects were significant.
For RT2, the main effect of age group was significant, F(1,
46) ⫽ 44.52, p ⬍ .0001, MSE ⫽ 1,311,322; mean RT2 was 674 ms
for younger adults and 992 ms for older adults. There was also a
main effect of SOA, F(5, 230) ⫽ 475.78, p ⬍ .0001, MSE ⫽
32,866; the overall PRP effect was 474 ms. The interaction of age
group and SOA was significant, F(5, 230) ⫽ 20.07, p ⬍ .0001,
MSE ⫽ 32,866; the PRP effect was 375 ms for younger adults and
573 ms for older adults. Age group also interacted significantly
with Task 2 difficulty, F(1, 46) ⫽ 10.00, p ⬍ .01, MSE ⫽ 36,981;
the Task 2 difficulty effect on RT2 was larger for older adults (138
ms) than for younger adults (87 ms).
LIEN ET AL.
440
Figure 4. Mean response times (RTs) for Task 1 and Task 2 in Experiment 2 for younger adults and older
adults as a function of stimulus onset asynchrony (SOA; 50, 100, 300, 500, 700, and 900 ms) and Task 2
difficulty (easy vs. difficult).
Although the Task 2 difficulty effects on RT2 were roughly
additive with SOA (see Figure 4), the interaction of SOA and Task
2 difficulty was statistically significant, F(5, 230) ⫽ 2.58, p ⬍ .05,
MSE ⫽ 11,643. The Task 2 difficulty effects were 89, 114, 106,
104, 121, and 141 ms at the 50-, 100-, 300-, 500-, 700-, and
900-ms SOAs, respectively. The three-way interaction of these
variables with age group was not significant, F(5, 230) ⬍ 1.0.
Separate data analyses for each age group revealed that the interaction of Task 2 difficulty and SOA failed to reach significance
both for younger adults, F(5, 115) ⫽ 1.38, p ⫽ .24, MSE ⫽
10,213, and older adults, F(5, 115) ⫽ 1.81, p ⫽ .12, MSE ⫽
13,074. For younger adults, the effects of Task 2 difficulty were
80, 84, 78, 69, 94, and 118 ms at the 50-, 100-, 300-, 500-, 700-,
and 900-ms SOAs. For older adults, the effects of Task 2 difficulty
were 98, 144, 134, 138, 148, and 164 ms at the 50-, 100-, 300-,
500-, 700-, and 900-ms SOAs.
Although the Task 2 Difficulty ⫻ SOA interaction (i.e., the
slack effect) was not significantly modulated by age, it is important
to ask whether there is a trend toward larger slack effects for older
adults than for younger adults. To provide a stable measure of
slack effects, we combined the two shortest SOAs (50 and 100 ms)
and combined the two longest SOAs (700 and 900 ms). The
percentage decrease in the Task 2 difficulty effect from the two
longest SOAs to the two shortest SOAs was 22.46% for younger
Table 3
Proportion of Errors on Task 1 and Task 2 for Younger Adults and Older Adults in Experiment
2 as a Function of Stimulus Onset Asynchrony (SOA) and Task 2 Difficulty
SOA
Task and difficulty
50
100
300
500
700
900
Younger adults
Task 1
Easy
Difficult
Task 2
Easy
Difficult
.042
.045
.038
.039
.024
.025
.020
.022
.021
.024
.012
.020
.031
.118
.029
.111
.019
.107
.020
.084
.028
.107
.020
.084
Older adults
Task 1
Easy
Difficult
Task 2
Easy
Difficult
Note.
.033
.028
.029
.027
.012
.017
.009
.014
.0141
.014
.012
.012
.011
.040
.011
.053
.013
.041
.014
.049
.013
.042
.019
.041
For the Task 1 data, the easy and difficult conditions refer to the difficulty of Task 2.
AGING AND WORD RECOGNITION
adults and 22.51% for older adults. Thus, the slack effect was
nearly identical for both age groups.
The PE2 data revealed a main effect of age group, F(1, 46) ⫽
18.77, p ⬍ .0001, MSE ⫽ 0.0363, indicating that PE2 was .03
higher for younger adults (.06) than for older adults (.03). Age
group interacted significantly with SOA, F(5, 230) ⫽ 2.81, p ⬍
.05, MSE ⫽ 0.0043. Separate data analyses for each group on PE2
showed no PRP effect for older adults, F(1, 23) ⬍ 1.0, but a
significant PRP effect of .023 for younger adults, F(1, 23) ⫽ 2.73,
p ⬍ .05, MSE ⫽ 0.0065. Age group also interacted significantly
with Task 2 difficulty, F(1, 46) ⫽ 22.79, p ⬍ .0001, MSE ⫽
0.0137; the effect of Task 2 difficulty on PE2 was higher for
younger adults (.08) than for older adults (.03).
Discussion
Unlike Experiment 1, both younger and older adults showed a
roughly additive interaction between Task 2 box-width difficulty
and SOA. The percentage decrease in the Task 2 difficulty effect
from the two longest SOAs to the two shortest SOAs was about
22.5% for both younger and older adults. This finding is consistent
with our hypothesis that age-related differences in parallel processing (like those observed in Experiment 1) are restricted to
lexical processes (and perhaps other processes for which older
adults have an experience advantage).
For a converging measure of parallel processing, we calculated
the general savings scores in the same manner as in Experiment 1.
For this analysis we used data from the difficult condition only,
just as we did in Experiment 1. The age difference in the general
savings scores was not significant, F(1, 46) ⬍ 1.0; the general
savings was 162 ms for younger adults and 199 ms for older adults.
We also computed the proportional savings (general savings divided by the overall RT; Equation 2) to correct for the fact that
older adults— by virtue of having longer overall RTs— had more
opportunity to produce savings. Analyzed this way, the trend was
actually for younger adults to show more savings (.13) than older
adults (.11), although the difference did not reach significance,
F(1, 46) ⬍ 1.0. In summary, the savings data provide converging
evidence that older adults have no special advantage in parallel
processing when Task 2 is nonlexical.
General Discussion
In the present study, we have examined age-related differences
in parallel processing using a PRP design. Both experiments revealed larger PRP effects for older adults than for younger adults,
replicating earlier aging studies (e.g., Allen, Smith, Vires-Collins,
& Sperry, 1998; Glass et al., 2000; Hartley, 2001; Hartley & Little,
1999). Although this finding might appear to suggest that dual-task
ability declines with age, a closer analysis suggests otherwise.
According to the central bottleneck model, older adults’ longer
RT1 should produce larger PRP effects even if older adults have
no dual-task processing deficits. Indeed, the observed increase in
PRP effects for older adults relative to younger adults was no
larger than expected on the basis of the increase in RT1. Thus,
there is no evidence in the overall data from the present experiments for a dual-task processing deficit in older adults. Furthermore, a finer grained analysis of the data suggests that there were
isolated processes (e.g., word recognition) for which older adults
actually showed improved dual-task processing.
441
To determine whether people can recognize a Task 2 word while
central attention is devoted to Task 1, in Experiment 1 we factorially manipulated word recognition difficulty (by using low- and
high-frequency words) and SOA. For younger adults, these variables produced additive effects in both the AV condition, replicating McCann et al. (2000), and in the VV condition. On the basis
of locus-of-slack logic and the central bottleneck model, these
results indicate that word recognition did not occur in parallel with
Task 1 central stages. For older adults, however, there was an
underadditive interaction between word frequency and SOA in
both the AV and the VV conditions. This result replicates Allen et
al.’s (2002) aging study using the VV condition and extends their
finding to the AV condition. These results indicate that older adults
are able to carry out word recognition in parallel with Task 1 but
that younger adults are not.
The Effect of Input Modality and Spatial Attention
In the introduction, we discussed the hypothesis that parallel
processing of word recognition with another task depends critically on the input modality of that task. When Task 1 is presented
visually in the same general location as the Task 2 word/nonword
(as in Allen et al., 2002), spatial attention to the Task 1 stimulus
might be directed to the Task 2 word/nonword as well. When the
Task 1 stimulus is auditory (as in McCann et al., 2000), however,
participants might intentionally direct spatial attention away from
the location of the word/nonword of Task 2 to minimize potential
interference from Task 2 processing. Diversion of spatial attention
is a critical issue, because previous studies have provided evidence
that words cannot be recognized without spatial attention (see
Lachter et al., 2004; McCann et al., 1992). Thus, failures to
recognize words without central attention in the AV condition of
McCann et al. (2000) could have been due to the lack of spatial
attention rather than the lack of central attention.
In the present study, we have found no evidence for this hypothesis. For younger adults, the effects of word frequency and
SOA were additive in the VV condition, even though spatial
attention was presumably directed to the Task 2 word/nonword.
Furthermore, older adults showed an underadditive interaction in
the AV condition, even though spatial attention could have been
directed away from the Task 2 word/nonword. Although spatial
attention might be required for word recognition, we conclude that
it was not a critical factor in our study, presumably because the
words were spatially attended in both the AV and the VV
conditions.
The Effect of Cognitive Aging
The other hypothesis we have considered in the present study is
that the ability to perform word recognition without central attention improves with age. Allen et al. (2002) found that older adults
produced a stronger underadditive interaction between word frequency and SOA than did younger adults. The results were not
entirely conclusive, however, because the authors failed to find a
difference between older and younger adults in general savings
from parallel processing. Furthermore, Allen et al. examined only
the VV condition. In the present study, we have replicated Allen et
al.’s (2002) finding of a stronger underadditive interaction between
the word frequency effect and SOA for older adults than for
younger adults and have shown that this finding does not depend
442
LIEN ET AL.
on Task 1 input modality. These findings provide further evidence
that older adults are able to carry out word recognition without
central attention, whereas younger adults are not.
To provide converging evidence for this conclusion, we examined general savings (a measure of the overall degree of parallel
processing) in Experiment 1 for both younger and older adults (see
Equation 1). This analysis confirmed that older adults showed
larger savings (434 ms) than younger adults (193 ms). The proportional general savings (Equation 2) also showed a similar trend
(.20 for older adults and .14 for younger adults). The reasons we
found an age-related difference in savings, whereas Allen et al.
(2002) did not, might be that (a) we successfully deterred response
grouping, which allowed us to obtain a truer measure of the time
needed to complete Task 1 and Task 2 at long SOAs; (b) we
included a shorter SOA, providing more opportunity for parallel
processing and more opportunity to observe savings; and (c) we
focused on low-frequency words, which should benefit the most
from parallelism. In summary, we have obtained converging evidence that although older adults exhibit a longer bottleneck delay
than younger adults (i.e., a larger PRP effect), older adults are
better able to use this time to perform Task 2 word recognition
(producing larger proportional savings). This conclusion is surprising, because it is rare for cognitive processing to actually
improve with age.
Our claim that older adults are better able than younger adults to
perform word recognition in parallel with Task 1 might appear to
conflict with the finding that older adults produced larger PRP
effects. However, we are not claiming that older adults necessarily
have a greater ability, in general, to perform tasks in parallel or that
they have eliminated the central bottleneck. The large overall PRP
effects suggest that there was still a central bottleneck—Task 2
response selection still must wait for Task 1 response selection to
finish. Because older adults select responses to Task 1 more
slowly, they would be expected to produce longer bottleneck
delays and, hence, larger PRP effects. The hypothesized ability of
older adults (but not younger adults) to perform Task 2 word
recognition in parallel with Task 1 should reduce these age-related
differences in the PRP effect but not entirely eliminate them. This
analysis can explain why, for low-frequency words in Experiment
1, the difference in PRP effects (130 ms) between older adults and
younger adults was much smaller than one would have expected
given the large difference in mean RT1 (348 ms). Consequently,
the big picture of cognitive aging in visual word recognition
appears to reflect a complex interplay of stage-specific advantages
and disadvantages for older adults compared with younger adults.
Source of Age-Related Differences in Parallel Processing
Experiment 1 provides evidence that (a) it is possible to carry
out word recognition without central attention and (b) whether
word recognition requires central attention depends on age, not on
Task 1 input modality. One logical follow-up question is why older
adults typically can carry out word recognition for Task 2 in
parallel with Task 1 but younger adults typically cannot. In the
following sections, we discuss three possible explanations for this
finding.
Blocking. To minimize interference from Task 2 processing
into Task 1 processing, participants might attempt to prevent word
recognition from occurring during cognitive slack (see McCann et
al., 2000). If the blocking is successful, then the interaction be-
tween word frequency and SOA on Task 2 should be additive, as
evident in the younger adults’ data. Older adults, however, might
have difficulty imposing a complete block on word recognition
during cognitive slack and thus might produce an underadditive
interaction between word frequency and SOA. According to this
view, the increased parallel processing for older adults in Experiment 1 was due not to a rare processing advantage but to yet
another cognitive deficit (reducing blocking ability).
This blocking hypothesis is consistent with the findings of
previous aging studies that older adults are less able than younger
adults to inhibit or suppress irrelevant stimuli (e.g., older adults
show a larger Stroop effect than younger adults; Hasher & Zacks,
1988; Zacks, Hasher, & Li, 2000). In particular, several aging
studies explicitly suggested that inhibitory mechanisms for older
adults fail to limit the presence of irrelevant information in working memory during encoding and retrieval of target information
(e.g., Spieler, Balota, & Faust, 1996). In our study, word recognition was relevant to Task 2 but was irrelevant to Task 1. Consequently, older adults might have had difficulty preventing Task 2
word recognition from occurring while Task 1 was being carried
out. If so, then word recognition could occur in parallel with Task
1 for older adults, producing an underadditive interaction between
word frequency and SOA.
Although this blocking explanation might account for many of
our findings, there are several lines of evidence against it. First, the
theory that older adults have a general inhibitory deficit is not
always supported (for a summary, see McDowd & Shaw, 2000, pp.
268 –272). Second, if older adults have blocking problems, in
general, then they should show underadditive interactions between
SOA and other manipulations of Task 2 difficulty as well, even
when younger adults show additive interactions between the same
factors. The present Experiment 2, however, shows that is not
always the case. This experiment used a nonlexical Task 2 involving a box-width judgment. To manipulate categorization time, we
varied the width of the boxes. Although both groups showed a
modest amount of underadditivity, which suggests some parallel
processing, the amount was roughly equal for younger and older
adults (22.5%). Furthermore, younger and older adults showed
similar amounts of general savings. These findings are also supported by Maquestiaux, Hartley, and Bertsch (2004), who found an
additive interaction between Task 2 stimulus–response compatibility (compatible vs. incompatible mapping) and SOA for both
younger and older adults. These authors also found a strong
underadditive interaction between letter contrast and SOA for
younger and older adults, which suggests that neither group
blocked letter categorization. Although it is impossible to rule out
differential amounts of blocking specifically for lexical processing,
there is no evidence for a general inability of older adults to block
out Task 2 processing.
Task coordination strategies. Another possible explanation
for the findings of Experiment 1 is that older adults adopted
different task coordination strategies (Meyer & Kieras, 1997).
Whereas younger adults might have chosen to strategically defer
word recognition, older adults might have allowed it take place in
parallel with Task 1 (deferring at some later stage, e.g., response
selection). This account is similar in many respects to the blocking
account and thus has some of the same deficiencies. In particular,
if older adults had adopted an aggressive task coordination strategy
in Experiment 1, one might have expected them to also adopt an
aggressive strategy in Experiment 2. Furthermore, Glass et al.
AGING AND WORD RECOGNITION
(2000) studied age differences in dual-task processing and actually
reached the opposite (and more plausible) conclusion—that older
adults adopted more cautious task coordination strategies than
younger adults.
Reading ability. Perhaps the most parsimonious interpretation
of the present results is that visual word recognition and reading
are skills that develop over time (i.e., as the cumulative experience
with words increases). As word recognition skill reaches a certain
point (obtainable by many older adults but not by many younger
adults), individuals are capable of performing word recognition in
parallel with other tasks. That is, older adults are able to begin
lexical access for Task 2 even before central processing for Task
1 has been completed. For younger adults, conversely, lexical
access still requires limited central resources, and thus Task 2
lexical access cannot take place before Task 1 central processing is
complete.
As a follow-up test of this hypothesis, we computed the correlation between each participant’s general savings score (a measure
of parallel processing) and his or her WAIS–R Vocabulary score in
Experiment 1. Consistent with the reading ability hypothesis, the
correlation was strong for older adults (.516 for general savings
and .534 for proportional savings; ps ⬍ .05); the best readers
produced the largest savings. For younger adults, there was essentially no relation between savings and vocabulary scores (.005 for
general savings and .014 for proportional savings; ps ⬎ .90). It
may be that a great amount of cumulative experience with words
is necessary before word recognition is truly automatic, even for
good readers.
On the basis of this reading ability hypothesis, one would also
predict little correlation between general savings scores and
WAIS–R scores in Experiment 2, in which a nonlexical Task 2 was
used. As expected, the analyses revealed no significant correlations between general savings scores and WAIS–R scores for both
older adults (.117 for general savings and .089 for proportional
savings; ps ⬎ .60) and younger adults (⫺.228 for general savings
and ⫺.303 for proportional savings; ps ⬎ .15). Although these
correlational data from Experiments 1 and 2 are consistent with
our reading ability hypothesis, it is premature to reach firm conclusions on the basis of these data alone. Further work is needed
with larger samples of younger adults and a wider range of
vocabulary scores.
Relations to Stroop Studies
Our claim that lexical access requires central attention for
younger adults appears to conflict with the conclusions from
Stroop studies (see MacLeod, 1991, for a review). In the typical
single-task version of the Stroop paradigm, younger adults cannot
avoid reading the irrelevant word while they are naming the color
in which the word is printed. Thus, contrary to our findings, Stroop
data suggest that younger adults can recognize words while attention is devoted to another central operation.
There are two ways to reconcile these seemingly discrepant
findings. First, note that the studies of the Stroop effect typically
use three or four relatively high-frequency color words (e.g., red,
green, blue, and yellow) that are repeated many times during the
experiment. It is therefore possible that lexical access can take
place without central attention (even for younger adults) for words
that have been repeatedly accessed in the recent past (and thus are
highly activated) but not for less activated words in the person’s
443
lexicon. That is, we are suggesting that word recognition may
occur without central attention in the Stroop task (in which each
word is repeated many times), but not in lexical decision tasks such
as ours (in which each word was presented only once).
Second, when central attention is devoted to the color-naming
task in the Stroop paradigm, it might accidentally slip to the
irrelevant word name. That is, it might be difficult for central
attention to name colors without also naming color words, because
these operations are so closely related (see Lien, Ruthruff, Hsieh,
& Yu, in press). When the central operations are more distinct, as
in the present study (shape or tone classification for Task 1 vs.
lexical decision for Task 2), central attention may be devoted
exclusively to one operation or the other (e.g., to Task 1 but not
Task 2). Further work is needed to test these two possible
reconciliations.
Conclusion
The present study examined under what conditions, if any, word
recognition can proceed without central attention. We found evidence that, regardless of Task 1 input modality, word recognition
on Task 2 can proceed while central attention is devoted to Task 1
for older adults but not for younger adults. One line of evidence
was based on locus-of-slack logic: Older adults showed a strong
underadditive interaction between word frequency and SOA,
whereas younger adults did not. The second line of evidence was
based on the fact that older adults showed larger general savings,
a measure of the overall degree of parallel processing. These
findings challenge the idea that older adults slow down because
they suffer from a general resource decrement. Experiment 2, in
which the lexical Task 2 was replaced by a nonlexical one (a
box-width judgment), shows no evidence for improved dual-task
abilities in older adults. Superior dual-task processing for older
adults, therefore, appears to be restricted to processes for which
older adults have much greater cumulative experience, such as
lexical processes.
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AGING AND WORD RECOGNITION
445
Appendix A
Word/Nonword List 1
Four letters
Words
No. occurrences
Five letters
Nonwords
Words
No. occurrences
Six letters
Nonwords
Words
No. occurrences
Nonwords
thase
never
houne
foung
woter
thonk
naght
goint
luter
poirt
groip
givun
whote
lorge
leest
paweq
thung
lighe
bigar
sunse
whule
timas
humen
hends
todey
tuken
deeth
wirds
fielt
shilh
miney
whise
majoy
hearg
stody
knawn
before
should
during
school
number
course
always
though
public
system
better
called
toward
social
rather
second
things
looked
become
within
church
seemed
family
turned
matter
having
really
period
cannot
behind
making
became
street
result
reason
change
1,016
888
585
492
472
465
458
442
438
416
414
401
386
380
377
373
368
367
361
359
348
332
331
320
308
279
275
265
258
258
255
246
244
244
241
240
befare
stould
doring
schoon
namber
coulse
alweys
thoigh
pablic
systam
botter
callen
towerd
sociar
rathen
secand
thengs
looken
bacome
wathin
charch
seeted
fomily
turnel
motter
hoving
rearly
perios
cannol
behind
meking
becime
streel
resilt
realon
chenge
bried
splin
serit
pourd
gried
scole
beam
pount
baint
rigil
draft
troce
chast
panil
demay
newer
lebby
lavel
twest
chass
runch
reveal
reform
shorts
dining
colony
combat
cellar
mutual
lonely
phases
barrel
select
motive
nerves
merger
jungle
vacuum
filling
submit
denial
basket
30
30
29
28
28
27
26
26
25
24
24
23
22
22
21
20
20
19
18
18
17
remeal
reford
sharts
bining
calony
combal
cellan
mutuad
monely
phasen
burrel
selece
rotive
derves
ferger
jengle
wacuum
liling
submid
denian
lasket
High frequency
must
know
last
year
come
take
went
part
left
less
find
next
give
days
room
face
case
need
four
best
mind
done
kind
help
name
past
feet
body
half
word
tell
held
sure
keep
free
miss
1,013
683
676
660
630
611
507
500
490
438
399
394
391
384
383
371
362
360
359
351
325
320
313
311
294
291
283
276
275
274
268
264
264
264
260
258
mest
knaw
lasc
yeal
coms
teke
wunt
pirt
laft
liss
fint
naxt
guve
deys
rool
foce
cuse
neel
foun
bost
mond
dobe
kond
halp
nime
pust
feen
bidy
hald
werd
telt
helt
sare
keed
fren
misk
those
never
house
found
water
think
night
going
later
point
group
given
white
large
least
power
thing
light
began
sense
whole
times
human
hands
today
taken
death
words
field
shall
money
whose
major
heard
study
known
850
698
591
536
442
433
411
399
397
395
390
377
365
361
343
342
333
333
312
311
309
300
299
289
284
281
277
274
274
267
265
252
247
247
246
245
Low frequency
cuts
meal
barn
sand
cure
chin
gear
wars
pack
jump
bend
lock
tire
herd
beam
trim
slim
span
bell
fame
fuel
30
30
29
28
28
27
26
26
25
24
24
23
22
22
21
20
20
19
18
18
17
culs
meaf
barl
sant
bure
chib
geaf
warb
kack
jume
benk
loce
tirt
hird
leam
trid
slib
spen
beld
fime
muel
cried
split
merit
pound
dried
scope
beard
mount
faint
rigid
draft
trace
chart
panic
delay
newer
lobby
label
twist
chase
bunch
30
30
29
28
28
27
26
26
25
24
24
23
22
22
21
20
20
19
18
18
17
(Appendixes continue)
LIEN ET AL.
446
Appendix A (continued)
Four letters
Words
No. occurrences
Five letters
Nonwords
Words
No. occurrences
Six letters
Nonwords
Words
No. occurrences
Nonwords
refuse
locate
client
valued
superb
gossip
nuclei
ballot
cavity
herald
retain
cement
reject
mister
boiled
16
16
15
14
14
13
13
12
12
11
11
11
10
10
10
refust
locade
plient
vanued
superd
gossil
nucler
hallot
lavity
hurald
retair
lement
roject
misten
goiled
Low frequency (continued)
damp
kick
rope
shoe
weep
lime
grin
cane
boil
mill
tide
dash
rust
knit
bolt
Note.
16
16
15
14
14
13
13
12
12
11
11
11
10
10
10
domp
kict
rone
shog
welf
lims
gran
cune
doil
cill
mide
dast
hust
knat
solt
liver
lined
sweep
gloom
stare
tower
media
bloom
dimly
haven
wired
blond
theft
lunar
bacon
16
16
15
14
14
13
13
12
12
11
11
11
10
10
10
civer
linet
sween
gloop
stabe
towen
medil
bloot
gimly
haren
wiren
flond
thaft
lunor
sacon
No. occurrences refers to the occurrences in the Kučera and Francis (1967) frequency norms.
Appendix B
Word/Nonword List 2
Four letters
Words
No. occurrences
Five letters
Nonwords
Words
No. occurrences
Six letters
Nonwords
Words
closk
voick
frong
cleab
musit
parth
clasm
norto
leavn
soung
blace
valum
linev
peack
womet
thirn
basiv
spaco
moven
wrotd
browl
costh
hourg
hearf
staga
milew
makex
trieo
showe
rivey
doinp
terme
rangx
brinf
flooq
finaz
future
wanted
center
common
policy
figure
strong
modern
living
longer
nature
months
needed
ground
values
father
spirit
return
recent
beyong
forces
person
taking
report
coming
single
simply
trying
higher
walked
passed
county
growth
market
police
likely
No. occurrences
Nonwords
High frequency
west
turn
cost
seem
wife
girl
town
rate
plan
hard
play
near
road
gone
book
call
fire
kept
view
dark
late
hope
live
data
read
lost
move
hold
sort
rest
care
fine
wall
cent
talk
hall
235
233
229
229
228
220
212
209
205
202
200
198
197
195
193
188
187
186
186
185
179
178
177
173
173
171
171
169
164
163
162
161
160
158
154
152
wesp
turb
cosk
seef
wifs
girb
towb
ratz
plab
harb
plar
neac
roaj
gonk
bool
calt
firg
kepd
vieb
darp
latk
hoce
livn
datu
reaa
losi
movs
holp
sorn
resb
carv
finu
wals
cenw
tald
halm
close
voice
front
clear
music
party
class
north
leave
sound
black
value
lines
peace
women
third
basis
space
moved
wrote
brown
costs
hours
heart
stage
miles
makes
tried
shown
river
doing
terms
range
bring
floor
final
236
226
221
219
216
216
207
206
205
204
203
200
198
198
192
190
184
184
181
181
176
176
175
174
174
173
172
170
166
165
163
163
160
158
158
156
227
226
224
223
222
209
202
198
194
193
191
189
187
186
186
183
182
180
179
175
175
175
175
174
174
172
170
163
161
159
157
155
155
155
155
151
futurn
wantel
centen
commor
polict
figurk
strond
moderl
livink
longel
naturm
monthy
needeh
grounp
valuez
fathei
spiric
returk
recenk
beyont
forceq
persoy
takint
reporr
comina
markej
simplo
tryinr
highew
walkex
passel
countj
singlg
growti
polics
likelz
AGING AND WORD RECOGNITION
447
Appendix B (continued)
Four letters
Words
No. occurrences
Five letters
Nonwords
Words
No. occurrences
Six letters
Nonwords
Words
No. occurrences
Nonwords
fance
strig
filse
laigh
nowly
fiben
storg
trean
deval
brove
swint
nober
deult
fauld
glort
cheel
slode
crawn
brict
squar
grast
spran
selar
cubec
prise
grive
steeg
glabe
rivan
loisy
glize
joice
moind
creet
foral
fally
secure
virtue
guilty
paused
profit
gentle
repeat
paying
critic
sitter
wholly
genius
thrust
wealth
linear
gather
pursue
timber
buried
ranged
hunger
closet
finest
picnic
custom
breeze
sprang
derive
saloon
deduct
tender
census
shaken
detect
button
poison
30
30
29
28
28
27
26
26
25
24
24
23
22
22
21
20
20
19
18
18
17
16
16
15
14
14
13
13
12
12
11
11
11
10
10
10
securt
virtun
gailty
pausal
profin
gantle
repead
poying
critil
sitten
whelly
ganius
thrusp
weilth
lineam
gathed
pursur
tember
baried
renged
honger
closel
finost
pacnic
castom
breate
sprant
derave
salood
dedict
tenden
censul
shiken
ditect
buttan
poisor
Low frequency
lane
flux
stem
dawn
fled
dull
card
fist
harm
bore
rank
plug
palm
soap
neat
cape
nest
fury
colt
pole
seal
grab
toll
drag
bark
hawk
cone
pint
tank
deaf
cult
plea
rake
fake
vent
slug
Note.
30
30
29
28
28
27
26
26
25
24
24
23
22
22
21
20
20
19
18
18
17
16
16
15
14
14
13
13
12
12
11
11
11
10
10
10
lene
flix
stam
dawl
fleg
dall
cerd
fost
horm
bort
renk
plut
pelm
soal
nead
cipe
nast
furt
calt
polt
sead
grap
tolt
drad
birk
hawe
cene
pind
tant
deam
culp
prea
roke
fike
vont
slun
fence
strip
false
laugh
newly
fiber
storm
treat
devil
brave
swing
nobel
dealt
fault
glory
cheek
slide
crown
brick
squad
grasp
spray
solar
cubic
prose
grove
steep
globe
rival
lousy
glaze
juice
mound
creep
forum
folly
30
30
29
28
28
27
26
26
25
24
24
23
22
22
21
20
20
19
18
18
17
16
16
15
14
14
13
13
12
12
11
11
11
10
10
10
No. occurrences refers to the occurrences in the Kučera and Francis (1967) frequency norms.
Appendix C
Generalized Slowing and General Savings
General savings
⫽ 共RT1 Longest SOA ⫹ RT 2Longest SOA兲 ⫺ 共SOAShortest ⫹ RT 2Shortest SOA兲.
According to the central bottleneck model, Equation 1 can be rewritten as
follows:
General savings ⫽ 关共1A ⫹ 1B ⫹ 1C兲 ⫹ 共2A ⫹ 2B ⫹ 2C兲兴
⫺ 关共SOAShortest兲 ⫹ 共1A ⫹ 1B ⫺ SOAShortest ⫹ 2B ⫹ 2C兲兴.
In this equation, 1A, 1B, and 1C correspond to the prebottleneck (e.g.,
perceptual), bottleneck (e.g., response selection), and postbottleneck (e.g.,
response initiation) stages of Task 1, respectively, and 2A, 2B, and 2C
correspond to the same processes for Task 2. This equation simplifies to
General savings ⫽ 1C ⫹ 2A.
Given a generalized slowing of all stages for older adults (e.g., Stages A,
B, and C) by a multiplicative factor k, the general savings for older adults
will be k times larger than the general savings for younger adults.
Received February 17, 2004
Revision received April 26, 2006
Accepted May 15, 2006 䡲