Individual differences in working memory capacity and temporal discrimination.

Abstract

Temporal judgment in the milliseconds-to-seconds range depends on consistent attention to time and robust working memory representation. Individual differences in working memory capacity (WMC) predict a wide range of higher-order and lower-order cognitive abilities. In the present work we examined whether WMC would predict temporal discrimination. High-WMC individuals were more sensitive than low-WMC at discriminating the longer of two temporal intervals across a range of temporal differences. WMC-related individual differences in temporal discrimination were not eliminated by including a measure of fluid intelligence as a covariate. Results are discussed in terms of attention, working memory and other psychological constructs.

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Individual Differences in Working Memory Capacity and
Temporal Discrimination
James M. Broadway*, Randall W. Engle
Georgia Institute of Technology, Atlanta, Georgia, United States of America
Abstract
Temporal judgment in the milliseconds-to-seconds range depends on consistent attention to time and robust working
memory representation. Individual differences in working memory capacity (WMC) predict a wide range of higher-order and
lower-order cognitive abilities. In the present work we examined whether WMC would predict temporal discrimination.
High-WMC individuals were more sensitive than low-WMC at discriminating the longer of two temporal intervals across a
range of temporal differences. WMC-related individual differences in temporal discrimination were not eliminated by
including a measure of fluid intelligence as a covariate. Results are discussed in terms of attention, working memory and
other psychological constructs.
Citation: Broadway JM, Engle RW (2011) Individual Differences in Working Memory Capacity and Temporal Discrimination. PLoS ONE 6(10): e25422. doi:10.1371/
journal.pone.0025422
Editor: Warren H. Meck, Duke University, United States of America
Received March 14, 2011; Accepted September 5, 2011; Published October 7, 2011
Copyright: ? 2011 Broadway, Engle. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits
unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Funding: These authors have no support or funding to report.
Competing Interests: The authors have declared that no competing interests exist.
* E-mail: jbroadway@gatech.edu
Introduction
Working memory capacity (WMC) refers to an ability to
maintain, manipulate, and access mental representations as
needed to support complex cognition [1,2]. WMC varies widely
across individuals and reliably predicts higher-order cognitive
abilities such as novel problem solving or general fluid intelligence
(gF) [1,3–5]. WMC also predicts lower-order abilities reflected in the
accuracy and/or latency of simple decisions, especially under
strongly interfering conditions such as: looking away from a
peripheral sudden-onset stimulus (antisaccade task) [6], or naming
the ink-color of an ‘‘incongruent’’ color-word (Stroop task) [7]. Such
tasks as these require cognitive control to over-ride the more
automatic but incorrect response. In contrast, individual differences
in WMC are not often associated with performance in tasks where
the more automatic response is instead the correct one: such as
looking toward a sudden-onset stimulus in a prosaccade task or
naming the ink-color of a ‘‘congruent’’ color-word in a Stroop task
[1,6,7].
The ‘‘executive attention view’’ of WMC [1,8] emphasizes the
supervisory role(s) of the ‘‘central executive’’ construct in
Baddeley’s influential multiple-component model of working
memory [9] more than the ‘‘phonological loop,’’ ‘‘visuospatial
sketchpad,’’or various buffers that have been much the focus of
much other research into individual differences in WMC (see
[10]). According to this perspective, WMC is not directly about
remembering per se, but instead reflects a more general ability to
control attention and exert top-down control over cognition. The
domain-general ability to combat interference through the control
of attention is also proposed to account for strong relationships
between WMC and other important abilities like gF [1,3,8]. There
is a consensus that WMC depends on a ubiquitous frontal-parietal
brain network implicated across a range of experimental tasks
requiring cognitive control [11–13].
However, strongly interfering conditions are not always sufficient
to observe WMC-related individual differences, as when searching
for a ‘‘conjunction target’’ among highly similar distractors [14].
And strongly interfering conditions are not always necessary to
observe WMC-related individual differences, as when counting a
small number of objects [15,16], or maintaining psychomotor
vigilance [17]. Recently we have reported that individual
differences in WMC predict yet another core mental ability
important for the control of behavior, time estimation [18],
assessed by the method of temporal reproduction.
This outcome was consistent with recent theories of short-term
memory [19–21], and of individual differences in WMC [22], that
have likened recall and recognition to acts of perceptual
discrimination, but made on the basis of multiple dimensions
represented in memory- among the most salient of which is
temporal. Theoretical connections between time perception and
WMC are considered next in more detail.
Timing and WMC
Dual-component WMC theory.
Engle [22] introduced a ‘‘dual-component framework’’ for
understanding individual differences in WMC that has much in
common with general theories of short-term memory; in particular
with those proposing that recall and recognition depend much on
discriminating temporal relations among events [19–21]. According
to the WMC theory of Unsworth and Engle [22], WMC reflects the
interaction of two components, ‘‘primary memory’’ (likened to the
‘‘focus of attention’’ in other theories [23,24] and ‘‘secondary
memory’’ (associative memory [25] outside the focus of attention),
functioning together to support active maintenance and selective
retrieval. Selective retrieval depends in large part on the specificity
of ‘‘search sets’’ in secondary memory, which are delimited in large
part by temporal-contextual cues [22]. Unsworth and Engle
proposed that individuals differ in performance across a wide
Recently Unsworth and
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range of memory tasks (e.g., serial order recall as well as free recall)
in large part because low-WMC individuals are less able than high-
WMC to use ‘‘temporal-contextual cues’’ that support efficient
search of secondary memory [22].
According to this account, a complete session of memory testing
(e.g., for letter strings) forms a hierarchy of nested temporal
contexts. Temporal-contextual elements associated with each level
undergo change at different rates. For example the experimental
session is the highest, the global-level context. Contextual elements
associated with the global-level context change relatively slowly.
Below this level in the hierarchy, a complete list of items to be
recalled in a single trial is intermediate, the list-level context.
Contextual elements associated with the list-context change more
rapidly: within a single global-context, the participant is exposed to
a number of different lists. Below this level, individual items in a
particular list constitute the lowest, the item-context. Contextual
elements associated with the item-context change most rapidly:
within a single list-context, the participant is exposed to a number
of different items. The dual-component WMC theory proposes
that low-WMC individuals are less able to use information that
distinguishes these temporal contexts with sufficient precision to
prevent confusion of search-sets, which leads to greater forgetting
and erroneous recall.
Confusion of information within a contextual level is common, as
seen for example in transposition gradients for items swapped during
recall output for a particular list. Notably, adjacent items are most
likely to be swapped [19–22]. Confusion of information across
contextual levels is also common, and shows a systematic property
giving additional insight into similarity-based mechanisms of
forgetting. For example, previous-list intrusions occur in serial and
free recall tasks when the participant incorrectly recalls an item
that appeared in the list previous to the one currently tested.
Importantly, it is most often the case that the incorrectly reported
item had appeared in the same within-list position as the item from
the current list for which it is swapped [19–22].
Like the OSCAR model of short-term memory [21], the dual-
component WMC theory explains previous list intrusions by the
confusability, or similarity, of the temporal contexts in which the
two swapped items had appeared during list learning [22].
Notably, low-WMC individuals are more likely to commit
previous list intrusions in serial order and free recall tasks [26];
suggesting that for low-WMC, memory search sets are not well-
constrained to include only representations of items from the
current list being tested. This provides evidence, albeit somewhat
indirectly, for greater confusion of temporal contexts by low-
WMC individuals. This is also consistent with predictions that
could be generated from the OSCAR model [21].
Notably, recent fMRI experiments have shown common
activation in prefrontal cortex when retrieving temporal context
information across diverse stimulus domains [27]. This is overall
consistent with assumptions that WMC depends on (a) prefrontal
cortex [13] and (b) retrieving temporal context information [22].
The dual-component framework proposed by Unsworth and
Engle would seem to directly predict that individual differences in
WMC are associated with individual differences in temporal
discrimination. The main goal of the present work was to address
this question.
Timing theories.
From the literature on time perception
there are a number of theoretical links to attention and memory,
as well as proposed neural substrates for these cognitive systems.
There are a staggering number of time perception theories [28],
but the modal frameworks broadly conform to ‘‘clock-counter’’
models (or pacemaker-accumulator models, e.g., [29–33]; see e.g.,
[34–37] for discussion of major alternatives). Most prominent
among these is the scalar expectancy theory [29], an information-
processing model originally developed to account for animal
conditioning by temporal regularities in the environment.
Clock-counter models assume that event timing is accomplished
through the cooperation of internal clock, memory, and decision-
making components. The clock emits pulses that are transmitted to
a counter (or accumulator). In the attentional-gate theory [31,32]
a gate between the clock and counter is opened and pulses are
allowed to accumulate when attention is directed to judging time.
More elapsed time is represented by more pulses in the
accumulator. The current pulse count is continuously integrated
and transferred to working memory as a single value, to be
compared to the value of a sampled duration represented in
‘‘reference memory’’ (long-term memory). A temporal decision is
made when comparison between the current pulse-count to the
remembered one exceeds a threshold ratio.
Scalar expectancy theory accounts for a wide range of
behavioral findings [30], including the Weber’s Law property of
time estimation; in which temporal judgment error increases
proportionally with the length of the interval to be timed (this is
often called the ‘‘scalar property’’ in the timing literature).
However, recently there has been a major push to incorporate
somewhat greater ‘‘biological plausibility’’ into timing models
[30,34,37]. In a connectionist implementation of scalar expectancy
theory proposed by Church and Broadbent [38,39] durations are
coded by the phase relations among signals generated by banks of
multiple oscillators. Notably, the same multiple-oscillator mecha-
nisms are proposed by the OSCAR model to underlay short-term
memory [21].
Lustig, Matell, and Meck [40] traced several striking corre-
spondences between recent computational models for timing [37]
and working memory [41]; each theoretically driven by dopamine
and by the activity of circuits connecting fronto-parietal cortex
with subcortical basal ganglia and striatum. In broad outlines,
Lustig and colleagues suggested that the identities and temporal
properties of to-be-remembered events could be coded simulta-
neously by the same brain networks. Identity information is
determined by which cortical neuron population fires in an
oscillatory manner to encode and maintain working memory for
an event. Temporal information is determined by the phase
relations between such oscillatory activity, as determined by a
‘‘coincidence detection’’ mechanism of the striatum [37,40] (see
also [35]).
All together, theories of working memory and time perception
reviewed above provide strong reasons to expect an association
between individual differences in WMC and temporal judgment.
Next we consider some of the existing evidence for such an
association.
Individual Differences in WMC and Timing
There have been many experiments examining effects on time
estimation from imposing additional non-temporal loads on
working memory and/or attention in dual-task procedures,
generally finding that directing attention away from time leads
to shortened time estimates and/or more variable time estimates
[42]. Loads placed on verbal or visual working memory resources
have shown analogous effects, independently of stimulus modality
[43]. Such manipulation of available attentional or working
memory resources can be ‘‘mimicked’’ by naturally occurring
variation among individuals [1]. Systematic inter-individual
variation may then become an object of measurement for
psychology, in order to better understand the operation of the
underlying system(s).
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There have been relatively few studies that have examined
relationships between individual differences in WMC and timing
within the population of healthy younger adults [18,44–46]. This
question has been addressed to a greater extent in developmental
and neuropsychological research. The picture is not always clear,
but there seems to be evidence for changes temporal judgment
throughout the lifespan, comparing children or older adults to
younger adults [47–52]. Notably, tend to differ in WMC as well
[51,53], and some research appears to show associations among
WMC, timing, and aging [51,52].
Additionally, temporal processing deficits have been shown in a
wide variety of neurological disorders [54]; most notably among
patients with dopaminergic disorders like schizophrenia [55,56]
and Parkinson’s disease [57–60]. These groups are known for
WMC deficits as well, and some research has shown associations
among timing, WMC, and schizophrenia [55] or Parkinson’s
disease [57,58]; while other research has not [56].
The variegated picture that emerges for relationships among
timing, WMC, and individual differences in developmental or
neurological state, is likely due to the diversity of tasks and time
scales used to measure temporal judgment [28,33]. Another
reason may be our general lack of knowledge about the
relationship between individual differences in WMC and timing
within the typical control group, i.e., healthy younger adults.
General fluid intelligence.
extensively examined temporal processing as a predictor of gF
[46,61–62]. As noted earlier, WMC is also widely recognized as a
major predictor of gF [1,5]. According to the temporal resolution power
hypothesis of Rammsayer and colleagues, faster rates of neural
oscillation lead to faster information processing (see also [5,63]);
and also to better coordination of information processing. Higher
temporal resolution is thus proposed to lead to better performance
on WMC and gF tests because critical information is less likely to
be lost or degraded during elementary processes supporting e.g.,
serial order recall or abstract problem solving [46]. Troche and
Rammsayer [46] showed through structural equation modeling
that WMC, temporal discrimination, and gF are strongly inter-
related. Indeed, WMC fully mediated relationships between time
perception and gF [46]. We sought to further examine
relationships among WMC, timing, and gF using a temporal
discrimination task designed from a signal detection theory
approach [64].
Rammsayer and colleagues have
Present Research
With relatively little prior evidence in this area, an extreme-
groups design can be justified for the goals of the present research
[65]. Participants were identified as either high-WMC or low-
WMC in a pre-screening session in which two valid measures of
WMC were administered. The present method of forming
extreme-groups (described in more detail below) is not unlike
methods commonly used when studying cognitive effects of aging
or neuropathology. We additionally obtained gF measures for
participants (from their participation in other studies in the lab), in
order to assess contributions from gF to relations between WMC
and temporal judgment.
We predicted generally that high-WMC observers would be
more sensitive to differences between temporal durations.
Following the report by Troche and Rammsayer [46], in which
WMC completely mediated relationships between temporal
discrimination and gF in structural equation modeling, we
predicted that WMC and gF would both account for variance in
temporal discrimination– but if WMC-related differences in
temporal discrimination were to be attenuated by including gF
as a covariate, they would still not be completely removed.
Methods
Ethics Statement
The present research was conducted with approval by the
Institutional Review Board of the Georgia Institute of Technology.
Participants gave written informed consent.
Participants
A total of 52 individuals (27 high-WMC, 15 women; 25 low-
WMC, 16 women) participated in the present experiment.
Participants were the same as in a recent study of WMC and
temporal reproduction [18]; Experiment 2]. Temporal discrimi-
nation results in the present article were not reported therein.
Participants were recruited from the Atlanta community or
undergraduate research pool, were between the ages of 18 and
35 years (M=23.6, SD=3.9), and were compensated with a check
or partial course credit.
We had measures of gF for 44 participants (high-WMC, n=22;
low-WMC, n=22) from their participation in other studies in the
lab. The following results include data from only these 44
participants so that gF could be included as a covariate in
ANCOVA (ANOVA results from the full sample were similar to
those from the reduced sample). WMC groups in this sample were
not statistically different in age, t (42)=1.65, p=.106 (Low-WMC
M=24.36 years,
SD=3.81;
SD=3.23). WMC measurement and participant recruitment
procedures are described below.
High-WMC
M=22.59years,
Procedure
Participants in the experiment were recruited after first visiting
the lab for WMC measurement in a session lasting approximately
60 minutes. Participants performed computer-administered tasks
seated at a comfortable distance from the monitor, alone in a
sound-attenuated room. Participants were made aware they would
be monitored for compliance with general instructions via closed-
circuit cameras when the research assistant was absent from the
room. All tasks in the present studies were programmed in e-prime
experimental software, with presentation timing accurate to 1
millisecond [66]. The WMC tasks administered in the pre-
screening session have been extensively validated as measures of
domain-general WMC and executive control of cognition [67].
Operation Span is a test of WMC for verbal material. Participants
solved simple math equations, in between encoding to-be-
remembered letters presented sequentially in the center of the
screen (from the set: F, H, J, K, L, N, P, Q, R, S, T, Y).
Participants were prompted to report the presented letters in order
after 3–7 of these equation-letter events (set-size; randomly
determined on each trial), by clicking with the mouse on their
choices from a 463 grid presenting the complete set of 12 letters
that could be shown. In order to maintain correct serial position in
the response sequence for recalled letters, participants were
instructed to click a ‘‘blank’’ option for any letters they could
not recall [68].
Symmetry Span is a test of WMC for visual-spatial material.
Participants judged whether black-and-white images were sym-
metrical, in between encoding the location in which a red square
sequentially appeared in a 464 grid. Participants were prompted
to report the square locations in order after 2-5 of these symmetry-
square events, by clicking on their choices in the cells of a 464
grid. In order to maintain correct serial position in the response
sequence for recalled square locations, participants were instructed
to click a ‘‘blank’’ option for any square locations they could not
recall [69].
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There were three trials for each set-size in each WMC task.
Scoring was done automatically by the computer program. One
point was assigned for each item correctly reported in correct serial
position. ‘‘Strict’’ serial position scoring was applied, i.e., if the
letters JRKT were to be reported, the response ‘‘JRK’’ would be
assigned 3 points, the response ‘‘blank RKT’’ would be assigned 3
points, but the response ‘‘RKT’’ would be assigned 0 points. This
scoring method has been shown to yield WMC scores with good
reliability and validity (Conway et al., 2005). The ranges of
possible scores were (0, 75) for Operation Span and (0, 42) for
Symmetry Span.
Scores for each WMC task were converted to z-scores in
reference to distributions of scores obtained over a period of
several years of testing student and community volunteers (ages 18
to 35 years). At the time the present studies were conducted there
were approximately 2,000 scores in the reference distributions for
the two WMC tasks. The z- scores for the two WMC tasks were
averaged to form a composite WMC z-score. Individuals were
classified as high-WMC (or low-WMC) if their composite z-score
fell within the upper (or lower) quartile of a reference distribution
of composite z-scores. Raw score reference distribution summary
statistics at the time the study was conducted were: Operation
Span:
M=57.87, SD=13.27,
SD=8.67. The correlation between WMC measures was statisti-
cally reliable in the normative sample, r=.56, p,.001.
It is necessarily the case that differences in measured WMC
between high- and low-WMC groups in the present experiments
were statistically significant because participants were classified as
high-WMC or low-WMC based on extreme composite z-scores,
located in either the upper or lower tails (respectively) of a
reference distribution of composite z-scores. For the sake of
completeness, we report that measured-WMC was statistically
different between high- and low-WMC groups, t (42)=211.63,
p,.001 (high-WMC M=.895, SD=.394; low-WMC M=21.064,
SD=.707; WMC scores are reported in z-score units). Recruited
participants returned to the lab to perform the temporal
discrimination task in the first half of a follow-up session lasting
approximately 60 minutes.
Temporal discrimination
discrimination task conformed to a so-called ‘‘roving’’ 2-
alternative forced-choice task (2-AFC) [64]; see also [33] for a
discussion of this design applied to temporal discrimination. In
roving 2-AFC designs the ‘‘standard’’ interval is not necessarily a
fixed duration nor is it always presented first—here, the
‘‘standard’’ and comparison intervals can both vary trial-to-trial
[33]. Also in roving 2-AFC designs the difference between
comparison intervals can be held constant while their absolute
magnitudes can vary over a relatively wide range [64].
Absolute durations of paired comparison intervals and their
corresponding duration differences in the present discrimination
task are presented in Table 1. The difference between comparison
intervals (duration difference) in the present task was 250 ms,
500 ms, or 750 ms on each trial, randomly determined. Absolute
durations of comparison intervals were multiples of the shortest
comparison intervals (250 ms); the longest absolute duration was
2750 ms. These time scales were chosen to assess temporal
judgment over a range thought to be within the so-called
‘‘psychological present’’ [50,70]. Furthermore this range covers
much of the time scale at which working memory processes are
thought to be critical to ongoing cognition and action [2].
Participants were exposed to two comparison intervals in
sequence and were prompted on each trial to press the ‘b’ key if
the comparison interval presented first was the longer one or the
‘n’ key if the comparison interval presented second was the longer
Symmetry Span:
M=27.89,
task.
Thetemporal
one. The word ‘‘interval’’ in capital letters appeared on the screen
during each comparison interval. The longer comparison interval
was presented first on half of the trials, randomly determined. The
stimulus defining the first comparison interval was preceded by a
fixation cross for 250 ms. After the first comparison interval
terminated, participants were prompted to press ‘Enter’ to view
the stimulus defining the second comparison interval, which
appeared after an unfilled blank-screen delay of 500 ms and a
second fixation cross for 250 ms. Thus, a minimum delay of
750 ms separated the first and second comparison intervals. After
the second comparison interval terminated, participants pressed
‘Enter’ to immediately view the next screen prompting their
response to indicate which of the two comparison intervals had
been the longer one. No feedback was provided. Temporal
discrimination responses were followed by an inter-trial interval of
1000 ms. Giving participants self-paced control over the onsets of
trials (and comparison intervals within trials) was intended to
ensure that participants were paying full attention to the task at the
onsets of stimuli defining the comparison intervals. There were 80
trials for duration difference=250 ms, 72 trials for duration
difference=500 ms, and64
ce=750 ms. Trial types were randomly intermixed so that any
duration difference and any pair of comparison intervals listed in
Table 1 could be experienced on a given trial.
trialsfor durationdifferen-
Table 1. Paired comparison intervals and duration
differences in the temporal discrimination task.
Duration Difference (ms)Comparison Intervals (ms)
250250500
500750
7501000
10001250
12501500
15001750
17502000
20002250
22502500
25002750
500250750
5001000
7501250
10001500
12501750
15002000
17502250
20002500
22502750
750 2501000
5001250
7501500
10001750
12502000
15002250
17502500
20002750
doi:10.1371/journal.pone.0025422.t001
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Ravens Matrices.
in the lab,weobtained ina post-hocmannerscoresfromtwo closely
related measures of gF for different sub-sets of the participants in the
present study. For one sub-set of participants (high-WMC n=11;
low-WMC n=12), we had scores from a 12-item set of Raven’s
Matrices problems [71]. Participants in this task had 5 minutes to
complete 12 items. Participants selected by mouse click, from an
array of choices shown at the bottom of the computer screen, the
figure that would best complete an incomplete abstract pattern. For
a different sub-set of participants (high-WMC n=11; low-WMC
n=10), we had scores from an 18-item set of Raven’s Matrices
problems. Participants in this task had 10 minutes to complete 18
problems. Stimulus presentation, response collection, and scoring
procedures were the same as in the 12-item test. One point was
assigned for each correct response, making the possible range of
scores (0, 18).
To facilitate combining data across test versions, raw scores
from the 12-item and 18-item Raven’s Matrices tests were
converted to proportion-correct scores. The two Raven’s measures
have been shown to strongly correlate to the same measures of
WMC used in the present work, in previous large-sample studies
[69,72]; and with overlapping ranges of magnitude (For the 12-
item test [69]: Operation Span r=.49, Symmetry Span r=.51.
With two separate samples [72], for the 18-item test: Operation
Span rs=.42 and .50, Symmetry Span rs=.56 and .62).
From their participation in other studies
Results
Sensitivity
Correct responses increased, and errors decreased, monotoni-
cally for both WMC groups, as duration differences increased
(Table 2). Correct responses were treated as ‘‘hits’’ and errors as
‘‘false alarms’’ (FA) in order to express discrimination sensitivity as
d’, which is a dependent measure from signal detection theory
[64]. This measure expresses in standard deviation units, how
distant was a person’s sensitivity to differences between stimuli,
from the point of perfect indifference (represented by zero); after
controlling for ‘‘guesses’’ or ‘‘response bias’’ (a predisposition to
say e.g., ‘‘second one longer’’). Higher d’ means that there was
greater sensitivity to differences between stimuli. Furthermore, d’
allows sensitivity across a range of stimulus differences to be
expressed in a common metric [64]. Proportion-correct (p (Hit))
and proportion-error (p (FA)) scores for each individual were
converted to probabilities according to Table A5.1 in [64],
changing ‘‘p (Hit)’’ and ‘‘p (FA)’’ into ‘‘z-Hit’’ and ‘‘z-FA’’
respectively [64]. Then d’ was calculated according to equation 7.2
for 2-AFC designs in [64]: d’=(1! 2) * (z-Hit–z-FA).
Discrimination sensitivity increased monotonically for both
WMC groups as duration differences increased. High-WMC
observers were better able to discriminate the longer of two
temporal intervals than low-WMC across the range of duration
differences. See Figure 1 (A; not starred). A 3 (Duration
Difference: 250 ms, 500 ms, 750 ms) 62 (WMC: High, Low)
mixed-model ANOVA was applied to mean d’. (All ANOVA
statistics were Huynh-Feldt corrected as necessary for any
violations of sphericity). The main effect of duration difference
was statistically significant, F (2, 41)=147.79, p,.001, gp2=.779.
The main effect of WMC was significant, F (1, 42)=26.26,
p,.001, gp2=.385. These effects were qualified by the significant
interaction of duration difference with WMC, F (2, 41)=4.94,
p=.009, gp2=.105.
Inspecting the means for d’ suggests the interaction was due to
the smaller difference between WMC groups for the 250 ms
duration difference (Mean Difference=.56, SD=.12) compared to
the larger differences between WMC groups for the 500 ms and
750 ms duration differences (respectively Mean Difference=.92,
SD=.19; and Mean Difference=.92, SD=.19); although high-WMC
individuals were more accurate overall.
Correlations.
Spearman’s rank-order correlations between d’
and response time (RT) across levels of duration difference were
consistently negative (Table 3), suggesting there were no speed-
accuracy tradeoffs. Spearman’s rank-order correlation coefficients
were examined due to the extreme-groups nature of the sample.
WMC was binary coded (low-WMC=0, high-WMC=1). Faster
responses were generally associated with more accurate temporal
discrimination (and also with higher WMC). Additionally, given
the relatively wide range of time scales tested, we sought also to
evaluate whether measured levels of performance could be
considered to reflect the same construct of temporal sensitivity
across conditions. Spearman’s rank-order correlations for d’
among the three duration difference conditions were consistently
high and statistically significant (Table 3). These results show that
the rank ordering of individuals by discrimination sensitivity was
very consistent across different levels of absolute duration and
duration difference, suggesting that the same construct of temporal
sensitivity was measured across the ranges of duration differences
andcomparisonintervals.Furthermore,
reliability was computed for the task, defining ‘‘test item’’ by
either the first or second comparison interval of each pair (e.g.,
1250 ms). When test item was defined by the first comparison
interval, r=.923, p,.001; and when defined by the second
comparison interval, r=.926, p,.001. These results show a high
degree of ‘‘internal consistency,’’ i.e., systematic variance shared
among all responses to all comparison interval pairings in the task,
irrespective of absolute duration or order of comparison intervals.
Cronbach’salpha
Bias
One of the proposed virtues of d’ as a measure of discrimination
sensitivity is that it controls for any bias in favor of one response
versus the other (a predisposition to say e.g., ‘‘second one longer’’)
Table 2. Means (Standard Deviations) for proportions of
correct responses (hits) and errors (false alarms) by high-WMC
and low-WMC in temporal discrimination across duration
differences.
250 ms
p (Hit)p (FA)
High.806 (.076).195 (.079)
Low.687 (.085).313 (.085)
500 ms
p (Hit) p (FA)
High.919 (.074) .081 (.074)
Low.805 (.098).197 (.098)
750 ms
p (Hit)p (FA)
High .949(.049).051 (.049)
Low .850(.109).150 (.109)
Note. N=44.
doi:10.1371/journal.pone.0025422.t002
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[64]. Still, it is customary to estimate response bias for the sake of
completeness. Bias was calculated here as c (for criterion; [64]),
because unlike other measures of response bias such as b, estimates
of c are not affected by estimates of d’, and vice-versa [20]. C was
calculated according to equation 2.1 in [64]: c=21/2 * (z-Hit + z-
FA). C expresses in standard deviation units how far a participant’s
response criterion was located from the point of perfect indifference
(represented by zero). Macmillan and Creelman [64] note that in
simple detection tasks in which a participant must simply report
whether a target is present or absent, higher c generally indicates a
more conservative setting (less willingness to say ‘‘yes, target
present’’). However, they observe that c has no reasonable
interpretation in a 2-AFC design like the present task. Therefore,
we will confine interpretation to the measure of sensitivity, d’.
While zero response bias might be ‘‘ideal,’’ it is not reasonable
to expect it in practice. The following results show that the
response criterion was indeed not located at zero for most
participants for discriminating the 250 ms duration difference, and
moved farther from zero with increasing duration difference; and
was farther from zero overall for high-WMC individuals compared
to low-WMC. A 3 (Duration Difference: 250 ms, 500 ms, 750 ms)
62 (WMC: High, Low) mixed-model ANOVA on mean c showed
that the main effect of duration difference was significant, F (2,
41)=15.50, p,.001, gp2=.431, as was the main effect of WMC, F
(1, 42)=8.37, p,.001, gp2=.261. The interaction of duration
difference and WMC did not reach statistical significance, F (2,
41)=3.12, p=.058, gp2=.069. See Figure 1 (B; not starred).
gF as Covariate
Sensitivity.
WMC groups was statistically significant, t (42)=23.897,
p=.001 (high-WMC M=.718, SD=.177; low-WMC M=.489,
SD=.210), and gF was correlated with d’ (Table 3), justifying the
following ANCOVAs (gF was evaluated in the following models as
Raven’s proportion-correct=.604). (Correlations between gF and
temporal discrimination variables were of somewhat larger
magnitude for the 18-item version of Raven’s Matrices than for
the 12-item version, unsurprisingly. However, because the
correlationsinvolving datafrom
statistically significant and in the same direction, we do not
believe this harms the overall validity of the analyses.)
Unsurprisingly, the difference in gF between
thetwoversionswere
Figure 1. Temporal discrimination by WMC groups. Left panel: Temporal discrimination sensitivity (d’) at three duration differences (not
starred) and with gF as covariate (starred). Right panel: Response bias (c) at three duration differences (not starred) and with gF as covariate (starred).
Error bars represent 95% confidence intervals. Legends refer to WMC groups.
doi:10.1371/journal.pone.0025422.g001
Table 3. Rank-order correlations among gF, WMC, and temporal discrimination variables.
1. 2. 3.4.5. 6.7.8.9.10. 11.
1. Raven-
2. WMC.541**-
3.d’ 250 .413** .610**-
4.d’ 500.490** .592** .904**-
5.d’ 750 .418**.597** .873** .864**-
6.c 250 .225.486**.793** .761** .724**-
7.c 500.250 .364*.549** .619**.531**.398**-
8. c 750.303*.375* .348*.431**.418** .399*.533**-
9. RT 250.025
2.279
2.302*
2.240
2.213
2.356**
2.119
2.127-
10. RT 500
2.111
2.369*
2.353*
2.347*
2.289
2.522**
2.182
2.253 .789**-
11.RT 750.037
2.365*
2.423**
2.389**
2.347*
2.540**
2.303*
2.348* .706** .866**-
Note. N=44. Spearman’s rank-order correlation coefficients were examined due to the extreme-groups nature of the sample. WMC was binary coded here (low-
WMC=0, high-WMC=1). Raven represents proportion-correct scores for Raven’s Matrices tests.
**p,.01.
*p,.05.
doi:10.1371/journal.pone.0025422.t003
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As in the ANOVA, the main effect of duration difference was
statistically significant, F (2, 40)=8.37, p,.001, gp2=.170. See
Figure 1 (A; starred). As in the ANOVA, the main effect of WMC
was significant, F (1, 41)=12.72, p=.001, gp2=.237. Unlike in
the ANOVA, the interaction of duration difference with WMC
was not significant, F (2, 40)=1.85, p=.164, gp2=.043. The main
effect of gF did not reach statistical significance, F (1, 41)=3.38,
p=.073, gp2=.385; neither did the interaction of duration
difference with gF, F (2, 40)=1.55, p=.220, gp2=.036. However,
gF was positively and significantly correlated with d’ for all three
duration differences (Table 3).
Bias.
Unlike in the ANOVA, the main effect of duration
difference was not significant, F,1. See Figure 1 (B; starred). As in
the ANOVA, the interaction of duration difference and WMC was
not significant, F (2, 40)=1.40, p=.243, gp2=.033. As in the
ANOVA, the main effect of WMC was significant, F (1, 41)=8.41,
p=.006, gp2=.170. The main effect of gF was not significant,
F,1; neither was the interaction of duration difference with gF,
F,1. However, gF was positively correlated with c, and
significantly so for the largest duration difference (Table 3).
Discussion
The present work adds to a small number of studies so far to
examine relationships among individual differences in WMC, gF,
and temporal judgment, within the population of healthy younger
adults. Low-WMC individuals were less sensitive than high-WMC
at identifying the longer of two comparison intervals across a range
of absolute durations and duration differences. WMC-related
effects on temporal discrimination were not eliminated by
including gF as a covariate. There was an interaction between
duration difference and WMC in ANOVA, but this was removed
by including gF as covariate in ANCOVA. Therefore we conclude
the interaction between WMC and duration difference was due to
variance shared between WMC and gF and only apparently
related to WMC. Overall, results support the idea of close relations
between WMC and time perception over and above any shared
relations with gF, consistent with a limited amount of previous
related work [11,18]. Overall, results are consistent with
predictions from a recent theory proposing that individual
differences in WMC are closely related to the ability to
discriminate events by their temporal relations [32,33]; and with
predictions from general theories of short-term memory that
attribute recall and recognition to mechanisms of temporal
discrimination [30] and/or temporal context-reinstatement [31].
The present work raises questions concerning the degree to
which the relationship between WMC and timing depends on
executive control of attention versus the ability to robustly encode,
maintain, and access representations in working memory. This is a
difficult problem to tease apart, given the shared dependence of
attention and working memory on a ubiquitous, dopamine-driven
fronto-parietal network [11-13,30,37,39,59,60]. Also Engle and
colleagues have argued elsewhere that these functions might not be
strictly separable [1, 8. 22]. For example Unsworth and Engle [22]
proposed that WMC emerges from ongoing interactions between
a flexible focus of attention [23,24] or ‘‘primary memory’’ that
provides direct access to a limited number of representations for
immediately past events, and an associative memory or ‘‘second-
ary memory’’ that is the substrate of controlled retrieval of
representations that have been displaced from primary memory
[25].
In the present work the timing task required a comparison
between a currently elapsing time interval and a memory
representation of an interval that just finished elapsing. We
propose that low-WMC individuals would be more likely to
experience lapses of attention to currently elapsing time; and
where multiple durations are tested as in the present task, would
experience greater confusion among representations for time
already elapsed. Teasing apart these contributions to overall
performance is an important direction for future research.
Matters are complicated somewhat by the unresolved general
question of which way the causal arrow should point between the
constructs of time perception and memory. Some timing theories
invoke a comparison to remembered duration to explain interval
timing, e.g., [29]. Other timing theories propose that the
experience of time arises due to time-varying decay of memories
[35,36]. And as noted earlier, some memory theories explain recall
and forgetting by discrimination of temporal and other attributes
[19,20] or re-instatement of temporal-contextual cues [21].
Given that memory and time are intrinsically confounded (i.e.,
all events that are remembered or forgotten are by definition
events that occurred in the past), it has remained a difficult
problem for the researchers to determine empirically whether
memory ‘‘causes’’ the experience of time or vice-versa. Most often,
the direction of the causal arrow is decided by assumption. The
present study shows that individual differences in WMC and
temporal discrimination are associated but much additional work
is needed, perhaps using structural equation modeling or finer-
tuned experimentation, to disambiguate the causal direction of this
relationship.
The present work adds to the few studies that have shown that
WMC, gF, and timing are strongly associated abilities in the
population of healthy younger adults [18,46]. But the separable
contributions of WMC and gF to timing remain unclear. Indeed
the question might be more tractable if posed otherwise: treating
timing instead as one of the ‘‘primitives,’’ along with WMC, for
explaining gF (see, e.g., [5]). The goal of including a measure of gF
as a covariate in the present work was mainly to examine whether
the relationship between WMC and timing could be explained by
a third variable that is correlated with each of them. Because
WMC and timing each share much of their systematic variance
with gF [46], gF appeared to be the strongest candidate for this
purpose. Correlations indeed showed strong relationships among
the three variables, but still ANCOVA demonstrated a strong
relationship between WMC and timing, over and above any
variance shared with gF. However, the ANCOVA did remove the
interaction between WMC and duration difference that had been
significant in the ANOVA. For reasons that are discussed below,
this interaction is difficult to interpret but apparently it was
associated with variance in gF not WMC. That said, we might
speculate within clock-counter terms that WMC contributes to
temporal judgment via the control of attention directed to elapsing
time, and the controlled retrieval of memory representations for
elapsing time; while gF contributes to timing through the decision
process that compares the currently elapsing interval to the elapsed
interval represented in memory. A prominent alternative to this
suggestion is discussed next.
Troche and Rammsayer [46] proposed that temporal resolution
power is fundamental to both WMC and gF. According to this view,
faster rates of neural oscillation (reflected in finer temporal
discrimination) lead to better performance on WMC and gF tests
because critical information is less likely to be lost or degraded
during elementary cognitive processes supporting e.g., serial order
recall or abstract problem solving (see also, e.g., [5,63]). Their
best-fitting structural equation model showed that WMC com-
pletely mediated the relationship between timing and gF– meaning
that whatever variance in gF that was explained by temporal
judgment, that same variance and more was explained by WMC.
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The authors interpreted this result as consistent with the theory
that timing is the causal primitive for WMC, which then ‘‘causes’’
gF. However, the result is also consistent with the alternative view
that WMC is the more fundamental variable for both temporal
processing and gF. The authors did not test an alternative
structural equation model to evaluate the fit of this alternative
perspective. This would be clear direction for future research.
It should also be noted that the present work does not show that
WMC-related differences in discrimination are specific to
temporal processing per se. Future work in this area is much
needed that would include also tests of discriminating non-
temporal stimulus attributes such as brightness or line-length. This
would help evaluate whether WMC-related differences observed
here do not arise from a general ability to form and maintain
representations, and/or to discriminate them. Indeed it appears
that temporal and non-temporal discrimination are also strongly
associated with each other and with gF [73]. Parceling out the
shared and unique relationships to WMC among these constructs
should be a focus of future research.
An important limitation of the present design is that the
duration differences were not proportionally scaled to the absolute
durations of the comparison intervals, to respect Weber’s Law for
timing. Thus in the set of durations used here, the smaller duration
differences were more often a smaller proportion of the
comparison intervals. This confound could have contributed to
increases in discrimination sensitivity across increasing duration
differences; however, this would not appear to compromise the
overall difference in sensitivity between WMC groups. Likewise
the interaction of duration difference with WMC is difficult to
interpret on account of this problem, but again this would not
appear to compromise the overall difference in sensitivity between
WMC groups– especially since this interaction was removed in the
ANCOVA and therefore seems to have been related more
specifically to gF.
A related consequence of the design is that many of the
durations were probably long enough to support a strategy of
chronometric counting. This is of concern here because individual
differences in WMC are also associated with differences in
enumeration [15,16]. However, given the wide range of durations
and unpredictability of their selection on each trial, we feel it is
unlikely that participants deployed an effective counting strategy
with any consistency. Still, relationships between individual
differences in WMC, counting, and temporal processing would
seem to be a ripe area for future research, especially given
relationships between counting and timing [74,75], WMC and
counting [15,16], WMC and timing [18,46]; and the general
importance of ordinal as well as temporal coding for working
memory [76,77].
Summary and Conclusions
In the present experiment, individual differences in WMC
predicted differences in temporal discrimination, following pre-
dictions from a recent theory of individual differences in WMC
[22] and general theories of short-term memory [19–21], which
propose that recall and recognition depend on discriminating
memory representations by multiple attributes, foremost among
which is temporal. Low-WMC individuals were less sensitive than
high-WMC at discriminating the longer of two comparison
intervals, across a range of duration differences and absolute
durations. WMC-related differences in timing were also related to
gF, but were not completely accounted for by it. These results are
predicted most specifically by the dual-component WMC
framework by Unsworth and Engle [22], but are also broadly
consistent with the ‘‘executive attention view’’ of WMC (e.g., [1];
although not necessarily predicted by it). Results are also predicted
by the temporal resolution power hypothesis by Troche and
Rammsayer [46], which also argues for strong relationships among
timing, WMC, and gF.
Author Contributions
Conceived and designed the experiments: JB. Performed the experiments:
JB. Analyzed the data: JB. Contributed reagents/materials/analysis tools:
RE. Wrote the paper: JB. Developed theoretical framework: RE.
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