Interference Within the Focus of Attention: Working Memory Tasks Reflect More Than Temporary Maintenance
One approach to understanding working memory (WM) holds that individual differences in WM capacity arise from the amount of information a person can store in WM over short periods of time. This view is especially prevalent in WM research conducted with the visual arrays task. Within this tradition, many researchers have concluded that the average person can maintain approximately 4 items in WM. The present study challenges this interpretation by demonstrating that performance on the visual arrays task is subject to time-related factors that are associated with retrieval from long-term memory. Experiment 1 demonstrates that memory for an array does not decay as a product of absolute time, which is consistent with both maintenance- and retrieval-based explanations of visual arrays performance. Experiment 2 introduced a manipulation of temporal discriminability by varying the relative spacing of trials in time. We found that memory for a target array was significantly influenced by its temporal compression with, or isolation from, a preceding trial. Subsequent experiments extend these effects to sub-capacity set sizes and demonstrate that changes in the size of k are meaningful to prediction of performance on other measures of WM capacity as well as general fluid intelligence. We conclude that performance on the visual arrays task does not reflect a multi-item storage system but instead measures a person's ability to accurately retrieve information in the face of proactive interference. (PsycINFO Database Record (c) 2012 APA, all rights reserved).
Interference Within the Focus of Attention: Working Memory Tasks
Reflect More Than Temporary Maintenance
Zach Shipstead and Randall W. Engle
Georgia Institute of Technology
One approach to understanding working memory (WM) holds that individual differences in WM capacity
arise from the amount of information a person can store in WM over short periods of time. This view is
especially prevalent in WM research conducted with the visual arrays task. Within this tradition, many
researchers have concluded that the average person can maintain approximately 4 items in WM. The
present study challenges this interpretation by demonstrating that performance on the visual arrays task
is subject to time-related factors that are associated with retrieval from long-term memory. Experiment
1 demonstrates that memory for an array does not decay as a product of absolute time, which is consistent
with both maintenance- and retrieval-based explanations of visual arrays performance. Experiment 2
introduced a manipulation of temporal discriminability by varying the relative spacing of trials in time.
We found that memory for a target array was significantly influenced by its temporal compression with,
or isolation from, a preceding trial. Subsequent experiments extend these effects to sub-capacity set sizes
and demonstrate that changes in the size of kare meaningful to prediction of performance on other
measures of WM capacity as well as general fluid intelligence. We conclude that performance on the
visual arrays task does not reflect a multi-item storage system but instead measures a person’s ability to
accurately retrieve information in the face of proactive interference.
Keywords: working memory, attention, visual arrays, temporal discriminability
Working memory (WM) is often conceptualized as a cognitive
system that provides dynamic storage and processing of informa-
tion in the service of ongoing cognition (Miyake & Shah, 1999).
For researchers who emphasize storage as the mechanism that
gives rise to individual differences in WM capacity (e.g., Awh,
Barton, & Vogel, 2007; Cowan et al., 2005; Vogel, Woodman, &
Luck, 2001), WM has at least two critical properties that differ-
entiate it from long-term memory (LTM). First, within WM, the
focus of attention
is used to maintain information in a fully
activated state (e.g., Cowan, 1999, 2001). Thus, information that is
stored in WM is protected from retrieval-based competition (i.e.,
proactive interference). Second, WM has a fixed capacity of about
four chunks of information (Cowan, 2001, 2010; Luck & Vogel,
1997). This estimate is assumed to vary among individuals (3–5
chunks) and to account for documented links between WM capac-
ity and novel reasoning ability (i.e., general fluid intelligence [Gf];
Cowan et al., 2005; Fukuda, Vogel, Mayr, & Awh, 2010).
Much of the evidence for maintenance-based perspectives of
WM has been collected via the visual arrays task (e.g., Luck &
Vogel, 1997). This simple, but effective, computer-based measure
of WM capacity begins with the brief presentation of an array of
randomly arranged objects (e.g., colored squares), which is fol-
lowed by a blank screen. After a short delay, the objects reappear.
On this second presentation, one is encircled (i.e., probe item). The
test-taker is required to decide whether this object has changed,
relative to its initial presentation (e.g., has the square’s color
Critical to storage-based accounts of WM capacity, accuracy is
stable when the displays contain up to 3– 4 items but steadily
decreases as additional items are added (Luck & Vogel, 1997).
Storage-based accounts of WM capacity interpret this trend as
evidence that when the number of objects contained in a display
exceeds the storage capacity of WM (referred to as k), it lowers the
likelihood that any one array-item will be stored. Once corrections
are made to account for array size (see the Design section in
Experiment 1), it can be shown that people are capable of accu-
We use the terms “focus of attention” or “storage in WM” to refer to
perspectives in either the tradition of Cowan (2001) or Luck and Vogel
(1997). The former is concerned with modality-free storage, whereas the
latter focuses on storage of visuo-spatial information. However, the present
experiments have similar implications for both views.
Zach Shipstead and Randall W. Engle, School of Psychology, Georgia
Institute of Technology.
This work was supported by Office of Naval Research Grant N00014-
09-1-0129. We thank Candice Morey for sharing her visual arrays tasks
with our lab. We additionally thank Kenny Hicks, Adam Moore, Tyler
Harrison, and Tom Redick for helpful comments on earlier versions of this
article, and Forough Azimi, Tyler Chappel, Dakota Lindsey, Kevin Strika,
Tamara Ware, and Robyn Marshall for assistance with data collection.
Correspondence concerning this article should be addressed to Zach
Shipstead, School of Psychology, J. S. Cook Building, Georgia Institute of
Technology, 654 Cherry Street, Atlanta, GA 30332-0170. E-mail:
Journal of Experimental Psychology: © 2012 American Psychological Association
Learning, Memory, and Cognition
2012, Vol. ●●, No. ●, 000– 000
0278-7393/12/$12.00 DOI: 10.1037/a0028467
rately responding to about four items, regardless of the total
number of items contained within an array (Cowan et al., 2005; see
also Pashler, 1988). The stability of this limit across array sizes has
been taken as an indication that the average person’s WM has four
discrete slots; each of which is capable of maintaining one chunk
of information in an interference-free state (Awh et al., 2007;
Cowan, 2001, 2010; Rouder, Morey, Moray, & Cowan, 2011).
While maintenance-based perspectives provide a reasonable ex-
planation of the visual arrays performance, basic issues remain
underexplored. In particular, the assumption that visual arrays
performance is strictly driven by stable maintenance in WM ne-
cessitates a further assumption that retrieval from LTM is not
involved. If a person can accurately respond to four items, it is
ostensibly because that person can maintain four items in WM.
However, within the broader scope of cognitive psychology,
multi-item storage is controversial. For instance, WM studies that
employ focus-switching (Garavan, 1998; Oberauer, 2002) and
n-back tasks (McElree, 2001; Verhaeghen, Cerella, & Basak,
2004) find that performance is slowed when a person responds to
anything other than the most recently presented item. These costs
have been interpreted as reflecting the time needed to reorient a
one-item attentional focus.
Carroll et al. (2010; see also Hanley & Scheirer, 1975) reported
that when participants are required to remember a series of three
item lists, recognition response times increase on a trial-by-trial
basis. That is, buildups of proactive interference occur even for
amounts of to-be-remembered information that should fit within a
four-slot focus of attention. Moreover, changing the type of stimuli
contained on each list was associated with a release from proactive
interference (cf. Wickens, Born, & Allen, 1963): When to-be-
remembered items were changed from digits to non-words (thus
reducing retrieval-based proactive interference), response times de-
Results such as these imply that WM is reliant on mechanisms
other than temporary storage. For instance, Oberauer’s (2002;
Oberauer, Su¨ß, Wilhelm, & Sander, 2007) concentric model of
WM assumes that focal attention is limited to one item. The 3–5
item capacity proposed by Cowan (1999, 2001) and Luck and
Vogel (1997) is reached via a “region of direct access” in which
activated elements of LTM are contextually bound to focal atten-
tion. Although all information outside of the one-item focus is
subject to interference (Oberauer & Kliegl, 2006; Oberauer &
Vockenberg, 2009), the bindings afford privileged access to atten-
tion and allow for integration of disparate information. Thus, a
critical determinant of individual differences in WM capacity is
not absolute storage but the ability to manage the region of direct
access through establishment and dissolution of contextual bind-
ings (e.g., WM updating; Miyake et al., 2000; Wiley, Jarosz,
Cushen, & Colflesh, 2011).
Unsworth and Engle’s (2006, 2007) temporal-contextual model of
WM assumes that the demands placed on WM often exceed 3–5
items, and thus individual difference in WM capacity also reflects
accurate retrieval of information from LTM. Relevant to the present
set of studies, Unsworth and Engle proposed that low WM capacity is
associated with difficulty constraining searches of LTM to specific
periods of time. This inaccurate cuing of time means that people with
low WM capacity contend with greater proactive interference and a
lower probability of retrieving critical information, relative to high
WM capacity individuals. From this view, visual arrays performance
is partially due to temporary storage but also reflects retrieval of
information that cannot be maintained in primary memory.
Visual Arrays and Proactive Interference
Increased response times associated with attention-shifting (e.g.,
Garavan, 1998; McElree, 2001; Oberauer, 2002; Verhaeghen et al.,
2004) and list retention (e.g., Carroll et al., 2010; Hanley &
Scheirer, 1975) tasks favor single-item accounts of WM storage.
However, these tasks feature serial order presentation and often
use verbal material. The visual arrays task, on the other hand,
presents visuo-spatial information in parallel. As such, single-item
accounts of the focus of attention may specifically pertain to
events that unfold over time (cf. McElree & Dosher, 2001) or
within a specific modality (Luck & Vogel, 1997). Cowan, Fristoe,
Elliot, Brunner, and Saults (2006) further resolved disparity by
assuming that delayed response times represent prioritization of
certain items above others within WM. Longer response times
are interpreted as lower prioritization, rather than the time
needed to shift the focus of attention.
It is therefore necessary to demonstrate the presence of proac-
tive interference using tasks that are in the tradition of Cowan’s
(2001) and Luck and Vogel’s (1997) theorizing. To date, a handful
of studies have directly examined the influence of proactive inter-
ference on visual arrays performance. The results are interesting,
but arguably equivocal.
Makovski and Jiang (2008) used a visual arrays task in which
colored circles were presented at five spatially fixed locations. On
some change-trials, the probe item’s color matched that of the item
that had been in that location on the preceding trial. That is, although
an item did change, it changed to something that was potentially
familiar. In these situations, participants were biased toward respond-
ing “no-change.” Thus, Makovski and Jiang argued that no-longer-
relevant information influences visual arrays performance.
While these results are intriguing (i.e., Makovski & Jiang,
2008), their generalizability is questionable (Lin & Luck, 2012).
Visual arrays tasks typically rely on random selection of object
characteristics and often present items in random patterns on a
trial-by-trial basis. While Makovski and Jiang (2008) show that
placing a familiar object in a critical location can influence re-
sponding, these situations are rarely encountered in practice and
are therefore unlikely to have a systematic impact in most studies.
Moreover, because Makovski and Jiang used displays with more
than four items, it is unknown whether familiarity influenced
information that participants were ostensibly maintaining in WM
or whether the feeling of familiarity arose from outside of WM.
Hartshorne (2008), however, found that when a single probe is
presented in the center of the screen (i.e., rather than its original
location), change detection accuracy is significantly influenced by
information from the last three trials (relative to a probe that was
presented eight trials back). Additionally, while Makovski and
Jiang (2008) used displays with five or more items, Hartshorne’s
arrays consisted of only three items. This amount of information
should be easily stored within WM. Thus, familiarity effects are
unlikely to have originated from outside of a traditional (e.g.,
Cowan, 2001) focus of attention.
2SHIPSTEAD AND ENGLE
A subsequent experiment (Hartshorne, 2008) demonstrated that
when the category of display objects (e.g., colors, shapes) is
switched, change detection accuracy increases (i.e., release from
proactive interference; Wickens et al., 1963). These performance
improvements then gradually disappear over the course of 10
subsequent trials and reoccur when the next category change is
Lin and Luck (2012) pointed out that the visual arrays tasks used
by Hartshorne (2008) differed from standard versions in a number
of ways. In particular, arrays were displayed for 1,000 ms, with a
1,000-ms delay between target and probe. Lin and Luck argued
that this 2-s interval provided time for LTM representations to be
formed and affect responding. These researchers thus halved the
length of each trial by reducing the array presentation to 100 ms
and the retention interval to 900 ms. Release from proactive
interference did not occur under these conditions.
Although this finding may prove informative, there are other
timing-related differences between the studies of Hartshorne
(2008) and Lin and Luck (2012). We consider their potential
impact following discussion of the present set of experiments.
The Present Study and Predictions
The present experiments employ a manipulation of temporal
discriminability (Baddeley, 1976; Brown, Neath, & Chater, 2007;
Crowder, 1976; Glenberg & Swanson, 1986; Neill, Valdes, Terry,
& Gorfein, 1992). The intent is to reveal retrieval-based processes
in visual arrays performance using a less explicit cue.
Figure 1 presents the two conditions used in Experiment 1. The
box labeled “Previous Response” represents the end of any given
trial. The participant’s response is immediately followed by an
inter-trial interval (ITI), after which a new array of colored squares
is presented. The offset of this “Target Array” is followed by an
inter-stimulus interval (ISI) of equal duration to the ITI. The
squares then reappear (i.e., Probe Array; see Figure 1), and the
participant must decide whether the encircled square has changed
color. The length of both the ISI and ITI were fixed between
subjects at either 900 ms or 3,900 ms. Either condition is consis-
tent with previous visual arrays studies, which have used fixed ISIs
of lengths similar to the ones presently employed (cf. Cowan et al.,
2005; Morey & Cowan, 2005; Vogel et al., 2001).
The intent of Experiment 1 was simply to demonstrate that a
participant’s memory for an array will not decay as a product of
the absolute length of the ISI (e.g., Vogel et al., 2001). This, of
course, is consistent with WM-based storage. For instance, Cow-
an’s (1999, 2001) embedded process model assumes that WM
contains a limited-capacity focus of attention, in which informa-
tion is protected from time-based decay. Outside of the focus of
attention, recently active units of LTM (referred to as short-term
memory) are continually decaying toward baseline activation lev-
els. Demonstration that visual arrays performance is not negatively
affected by absolute time would therefore be explained by assum-
ing that people respond based upon the contents of WM, without
reliance on decay-prone short-term memory.
However, a lack of time-based decay is not uniquely predicted
by storage in WM. Test-takers may also retrieve relevant infor-
mation from LTM. Critically, Experiment 1 has been designed
such that the absolute length of the ISI will not affect the proba-
bility of successful retrieval. This assertion is based upon the
principle of temporal discriminability (e.g., Baddeley, 1976;
Neath, 1993), in which the probability of successfully cuing a
specific episode in LTM is seen to be determined by that episode’s
distinctiveness in time. That is, along the dimension of time (cf.
Brown et al., 2007), an episode that is relatively isolated from
other events will be more readily cued than one that was relatively
compressed with other events.
Key to this concept is “relative” isolation. Examining Figure 1,
while the between-subjects ISIs and ITIs are different in terms of
absolute time, relative time is actually constant (Baddeley, 1976;
Capaldi & Neath, 1995; Neath, 1998). Regardless of the number of
milliseconds contained in either interval, the ratio of ITI to ISI is
fixed at 1. In both conditions, events are uniform. Thus, a lack of
time-based decay can also be understood as the result of neither
condition creating a situation in which target information is rela-
tively compressed with irrelevant information. So long as the ratio
of ITI to ISI is held constant within an experimental session,
relative distinctiveness of any given event should not be deter-
mined by the ISI (cf. Neill et al., 1992; Turvey, Brick, & Osborne,
Thus, maintenance and retrieval make the same prediction:
Relative to an ITI/ISI of 900 ms, an ITI/ISI of 3,900 ms will not
be associated with decayed memory of the critical array. Subse-
quent experiments were therefore designed to converge on a result
that is consistent with only one explanation. This was accom-
plished by manipulating temporal discriminability. Both ITI and
ISI were varied within-subjects and within-trial.
Figure 2 displays the combinations of ITI/ISI that were utilized
in the other three experiments. Under these circumstances, and
with regard to retrieval, two simple predictions can be made. First,
if retrieval processes are critical to visual arrays performance, then
the length of the ISI will influence memory for the most recent
array. Unlike Experiment 1, the relative spacing of events is no
longer uniform. Thus, if visual arrays performance involves rec-
ollection of information from the most recent array (rather than
strict maintenance), the effects of proactive interference will fluc-
tuate on a trial-by-trial basis. Compare (c)–(a) and (b)–(d)in
Figure 2. From the perspective of the box marked “Probe Array”
(i.e., attempting to look backward in time), decreasing the ISI
should facilitate recollection of the “Target Array” by improving
temporal proximity, thus allowing the relevant time period to be
cued with greater fidelity (e.g., Glenberg & Swanson, 1986). As
ISI decreases, the estimate of “WM capacity” (k) should increase.
The second prediction that pertains to retrieval from LTM
regards the effect of manipulating the ITI. Increasing the length of
the ITI should have an effect that is opposite of increasing the ISI.
That is, a long ITI will push the “Previous Probe” array farther
back in time, thus releasing the test-taker from proactive interfer-
ence (Kincaid & Wickens, 1970). In terms of relative time, this
effect is made apparent by viewing (a)–(d) and (c)–(b).
Therefore, as ITI increases, kshould also increase.
Critical to the present experiments, manipulations of temporal
discriminability specifically affect retrieval processes by increas-
ing or decreasing the intensity of proactive interference (Baddeley,
1976; Capaldi & Neath, 1995). Storage-based accounts of WM
Information regarding formal models of temporal distinctiveness can
be found in Brown et al. (2007) and Neath (1993, 1998).
INTERFERENCE WITHIN THE FOCUS OF ATTENTION
capacity (e.g., Awh et al., 2007; Cowan et al., 2005; Rouder et al.,
2011) would have difficulty explaining the predicted fluctuations.
In particular, these theories specifically assume WM is used to
maintain a fixed number of items in an interference-free state (e.g.,
Cowan, 2001; Cowan et al., 2005). Slot-based interpretations (e.g.,
Rouder et al., 2011) of the relationship between WM and visual
arrays performance thus predict a null effect of ISI and ITI. This
is because proactive interference is not assumed to affect perfor-
mance: The assumed role of WM-storage is to neutralize interfer-
ence. Therefore, maintenance-based accounts, which view visual
arrays performance as an indicator of a person’s capacity for
interference-free maintenance (e.g., Cowan et al., 2005), assume
that the relative lengths of ISI and ITI are irrelevant and, thus,
predict that subsequent experiments will replicate Experiment 1.
Participants. Sixty-one undergraduate students (40 females;
mean age ⫽20 years) were recruited from the Georgia Institute of
Technology subject pool. Participants were compensated with 1 hr
of credit toward course requirements. Data were excluded for one
participant who fell asleep during the session.
Materials. Participants sat roughly 45 cm from the monitor.
From this distance, each square subtends 0.76° of visual angle, left
to right and top to bottom (6 mm). Although square locations were
randomly assigned on a trial-by-trial basis, each square was pre-
sented at a distance of more than 2° (center to center) from the next
closest square. Squares locations were all at least 2° from fixation.
Each square was also randomly assigned (with replacement) one of
seven colors using standard E-prime color values (RGB): white
(255, 255, 255), black (0, 0, 0), red (255, 0, 0), yellow (255, 255,
0), green (0, 128, 0), blue (0, 0, 255), or purple (128, 0, 128).
Squares were presented within a centered silver (192, 192, 192)
background (19.1° ⫻14.3°).
Design. Experiment 1 was a 3 (array size: 4, 6, 8) ⫻2
(interval length: 900 ms or 3,900 ms) design. Array sizes were
manipulated within-subjects. Interval length was manipulated
between-subjects. The experimenter assigned participants to
interval-length condition according to a pre-randomized list.
The dependent variable was a participant’s kas described by
Equation A.6 of Cowan et al. (2005): k⫽N⫻(H ⫹CR ⫺1). “N”
Figure 1. Between-subjects conditions in Experiment 1. ITI ⫽inter-trial interval; ISI ⫽inter-stimulus interval.
Figure 2. Within-subjects conditions used in Experiments 2– 4. ITI ⫽inter-trial interval; ISI ⫽inter-stimulus
4SHIPSTEAD AND ENGLE
is the array size. “H” refers to hits, or accurately recognizing that
a block color has changed. “CR” refers to correct rejections, or
accurately noticing that a color-change has not occurred.
We controlled for the size of the array on the previous trial, such
that each array size (4, 6, 8) was preceded by each array size an
equal number of times. We also controlled for the number of times
a critical array size was preceded by a change or no-change trial.
These variables did not enter into our formal predictions but were
controlled out of concern for standardizing the histories of indi-
Procedure. Participants were run in a large room in groups of
1–5. Each worked at an individual computer. The experimenter
remained in the room throughout the session, which lasted less
than 1 hr. All studies were one session.
In order to control temporal factors, a new trial began immedi-
ately after a preceding trial response. Following an ITI (detailed
below), a set of randomly arranged color squares was presented for
250 ms. The offset of this array was followed by an ISI that was
of a duration equivalent to the ITI. Finally, the array reappeared
with one square encircled. The participant simply judged whether
this square was the same or a different color relative to its initial
presentation. Judgments were made via keys labeled “S” for same
and “D” for different (respectively, “f” and “j” on a standard
keyboard). Participants were allowed unlimited time to respond.
Thus, the critical temporal manipulation regarded (1) the space of
time between the offset of the previous array and onset of the
critical array and (2) the space of time between the offset of the
critical array and onset of the critical response set.
Each ITI began with a white screen that lasted for 300 ms or
3,300 ms, depending upon condition (i.e., short or long interval).
This was followed by a black fixation cross against a silver
background that lasted for 500 ms. After a 100-ms pause, the array set
was displayed. Thus, regardless of whether the total ITI was 900 ms
or 3,900 ms, the signal to prepare for an array was the same in both
conditions. A blank, silver screen was shown during the ISI.
In order to maintain control over events that preceded a critical
array, every other trial was actually a filler trial (“Previous Re-
sponse” in Figures 1 and 2). Performance on these trials was not
examined, as their purpose was to ensure that each array size was
preceded by an array of each size an equal number of times. Each
block therefore consisted of 36 pairs of filler/critical trials, in
which participants saw each potential combination of array size
and previous-array size four times. Within these trials, “change”
and “no change” arrays occurred an equal number of times for both
the critical and previous array. In the course of an experimental
session, participants completed three blocks, with self-paced rest
breaks in between. Sessions began with six practice trials.
Any violations of the sphericity assumption were corrected
using the Huynh–Feldt procedure. Table 1 presents karranged by
array size and interval length. Consistent with previous studies (cf.
Rouder et al., 2011), kincreased across set sizes. kdid not
statistically differ (p⫽.771) for array sizes 6 (k⫽4.32) and 8
(k⫽4.52), but both of these array sizes were different from array
size 4 (k⫽3.47; both ps⬍.001). Additionally, kwas larger for the
3,900-ms condition, relative to the 900-ms condition (respectively,
4.38 and 3.83).
These statements are supported by main effects of array size,
F(1.82, 105.73) ⫽25.86, MSE ⫽20.28, p⬍.001,
interval length, F(1, 58) ⫽7.61, MSE ⫽13.89, p⬍.01,
The interaction of array size and internal-length did not approach
significance, F(2, 116) ⫽0.96, MSE ⫽0.689, p⫽.39,
Experiment 1 was conducted with the explicit intention of
demonstrating that memory for an array does not decay over the
course of 4 s (e.g., Vogel et al., 2001). Consistent with our
predictions, kdid not shrink over time. In fact, the long-interval
group had a statistically larger kthan did the short-interval group.
One might assume that this difference is a byproduct of the
between-subjects design. That is, perhaps the 3,900-ms group had
a larger WM capacity than the 900-ms group. We note that due to
(1) the use of a large sample (n⫽60), along with (2) random
assignment and (3) a sample that was likely composed of a fairly
homogenous sample of people with higher than average WM
capacity (i.e., all Georgia Institute of Technology students; see
Redick et al., in press), this interpretation is unlikely. We explore
the potential meaningfulness of this finding in the General Dis-
Participants. Thirty-two undergraduate students (14 females,
mean age ⫽19.7 years) were recruited from the
Georgia Institute of Technology subject pool. None had partici-
pated in Experiment 1. Participants were compensated with 1 hr of
credit toward course requirements.
Design. All variables in Experiment 2 were manipulated
within-subjects. The design was 3 (array size: 4, 6, 8) ⫻2 (ITI
length: 900 ms vs. 3,900 ms) ⫻2 (ISI length: 900 ms vs. 3,900
ms). The dependent variable was not changed.
Procedure. Experiment 2 was similar to Experiment 1, with
the exception that ITI and ISI were no longer fixed. Four possible
combinations of ITI/ISI occurred within a single session (see
Figure 2). These combinations included 900/900; 3,900/3,900;
As with the first experiment, the “Previous Response” (see
Figure 2) was made in a filler trial that controlled previous array
Demographic information for one participant was lost.
k Values at Each ISI and Array Size
▫3▫3▫3.32 (0.10) 4.00 (0.20) 4.16 (0.24)
▫333▫333▫3.63 (0.10) 4.64 (0.20) 4.87 (0.24)
Note. Standard errors of the mean are in parentheses. ITI ⫽inter-trial
interval; ISI ⫽inter-stimulus interval.
INTERFERENCE WITHIN THE FOCUS OF ATTENTION
size and previous response. Due to time constraints, the ITI/ISI for
filler trials was always 900/900.
As with the first experiment,
participants received each combination of array size and previous
array size; however, these were also presented within each poten-
tial combination of ITI/ISI four times per block. Each block
included 144 trials. Participants completed two blocks in each
session, with a self-paced break in between each. Each session
began with eight practice trials in which participants encountered
each potential combination of ITI/ISI two times.
As predicted, the effects of manipulating the ISI and ITI were
both significant. Decreasing the ISI (thus making the to-be-
remembered array temporally proximate) was associated with a
significant increase in k(2.79 when ISI ⫽3,900 ms; 3.55 when
ISI ⫽900 ms). Conversely, increasing the ITI (and thus tempo-
rally separating the previous response screen and the critical array)
was associated with an increase in k(2.96 when ITI ⫽900 ms;
3.39 when ITI ⫽3,900 ms).
As with the first experiment, there was a main effect of array
size, such that participants had a larger kwhen array size was 6,
relative to when array size was 4 (respectively, 3.40 and 2.88; p⫽
.001). However, neither differed from array size 8 (3.22; respective
ps⫽.91 and .40).
Table 2 reveals that increased ISI was associated with decreased
kfor all array sizes. The effect was apparent at array size 4 (⌬k⫽
0.34; p⫽.003) and grew for array sizes 6 (⌬k⫽0.59; p⫽.005)
and8(⌬k⫽1.37; p⬍.001). This interpretation is supported by
within-subjects contrasts that revealed the interaction as linear,
F(1, 31) ⫽17.15, MSE ⫽50.53, p⬍.001.
The above statements are supported by main effects of ISI, F(1,
31) ⫽64.86, MSE ⫽55.89, p⬍.001,
⫽.68; ITI, F(1, 31) ⫽
15.28, MSE ⫽17.868, p⬍.001,
⫽.33; and array size, F(1.58,
48.84) ⫽4.39, MSE ⫽11.08, p⬍.03,
⫽.12. Additionally, the
interaction of ISI and array size was significant, F(2, 62) ⫽8.48,
MSE ⫽9.175, p⫽.001,
⫽.22. An interaction of array size by
ITI approached but did not reach significance, F(2, 62) ⫽2.60,
MSE ⫽2.05, p⬍.09,
⫽.08. No other interactions approached
significance (all ps⬎.12; all
The critical predictions regarding the influence of proactive
interference on visual arrays performance were confirmed. When
ISI was increased from 900 ms to 3,900 ms, participants’ kvalues
shrank. Taken in conjunction with Experiment 1, and consistent
with previous research (e.g., Neill et al., 1992; Turvey et al., 1970),
this effect cannot be attributed to time-based decay: It was only
present when the ratio of ITI to ISI varied on a trial-by-trial basis.
The results of the second experiment are inconsistent with the
hypothesis that performance on the visual arrays task purely re-
flects fixed-capacity storage. However, the array sizes used in
Experiment 2 were all at or above the supposed storage capacity of
WM. Thus, changes in kthat accompany fluctuations in retrieval
difficulty may reflect retrieval from outside of a 2–3 item storage
system. Experiment 3 addressed this issue by using array sizes of 2,
3, and 4. A 2–3 item account predicts that effects such as those found
in Experiment 2 will be apparent at array size 4, but completely absent
from array size 2, which should easily be stored in WM.
Participants. Thirty-one undergraduate students (16 females;
mean age ⫽19.7 years
) were recruited from the Georgia Institute
of Technology subject pool. None had participated in the previous
experiments. Participants were compensated with 1 hr of credit
toward course requirements.
Design and procedure. The only difference between Experi-
ments 2 and 3 is that Experiment 3 used array set sizes of 2, 3, and 4.
General analysis. The main effects of array size, F(1.75,
52.61) ⫽202.22, MSE ⫽72.69, p⬍.001,
⫽.87; ISI, F(1,
30) ⫽16.41, MSE ⫽5.40, p⬍.001,
⫽.35; ITI, F(1, 30) ⫽
8.18, MSE ⫽0.67, p⫽.008,
⫽.21; and the Array Size ⫻ISI
interaction, F(2, 60) ⫽3.22, MSE ⫽0.43, p⬍.05,
were found in Experiment 2 replicated in Experiment 3. The only
other interaction to approach significance was Array Size ⫻ISI ⫻
ITI, F(2, 60) ⫽2.96, MSE ⫽0.28, p⫽.06,
⫽.09 (all other
However, across conditions the average kvalue was 2.26 (see
Table 3), which is larger than possible kvalues in the smallest
array size condition (i.e., 2 items) and smaller than the kusually
found when array size is 4 (i.e., 3– 4 items). Therefore, the results
are presented as a series of 2 ⫻2 analyses of variance (ANOVAs)
at each set size.
Array size 2. The overall kvalue when array size was 2 was
1.56. kwas larger when the ISI was 900 ms (1.61) relative to when
it was 3,900 ms (1.50). Additionally, kwas smaller when the ITI
Our initial justification for using short intervals on buffer trials was based
on the argument that temporal distinctiveness is affected by all trials leading to
the present trial (Cowan et al., 2001). Thus, the effect of a long ISI would be
increased. However, Pierre Barrouillet (personal communication, June 1,
2011) noted that, because long ISIs were unusual, participants may have
engaged in encoding strategies that were amenable to short ISIs. We note that
the main effect of ISI replicates in Experiment 4, in which long and short
intervals were equally probable.
This is based on 30 participants, as one filled in her name rather than
Effects of ITI and ISI at Each Array Size
▫3▫3.06 (0.13) 3.70 (0.22) 3.91 (0.32)
▫333▫2.72 (0.15) 3.11 (0.22) 2.54 (0.33)
▫3▫2.80 (0.15) 3.18 (0.22) 2.89 (0.30)
▫333▫2.97 (0.13) 3.63 (0.22) 3.56 (0.35)
Note. Standard errors of the mean are in parentheses. ITI ⫽inter-trial
interval; ISI ⫽inter-stimulus interval.
6SHIPSTEAD AND ENGLE
was 900 ms (1.50) relative to when it was 3,900 ms (1.61).
Although these changes were numerically small, they were reli-
able, as revealed by main effects of both ISI, F(1, 30) ⫽7.65,
MSE ⫽0.40, p⫽.01,
⫽.20, and ITI, F(1, 30) ⫽7.51, MSE ⫽
⫽.20. These two variables did not interact (p⫽
Array size 3. When array size was 3, the overall kvalue was
2.23. Once again, kwas larger when ISI was 900 ms (2.36) relative
to when it was 3,900 ms (2.01), and kwas smaller when ITI was
900 ms (2.15) relative to when it was 3,900 ms (2.30). These
observations are supported by main effects of ISI, F(1, 30) ⫽
10.71, MSE ⫽2.20, p⫽.003,
⫽.26, and ITI, F(1, 30) ⫽4.80,
MSE ⫽0.728, p⫽.04,
These effects, however, are qualified by a significant ISI ⫻ITI
interaction, F(1, 30) ⫽7.12, MSE ⫽0.653, p⫽.01,
When ISI was 900 ms, the length of the ITI did not have a
numerical effect on k(2.36 in both cases). However, when ISI was
3,900 ms, ITI did have an effect on k(k⫽1.94 when ITI was 900
ms, k⫽2.24 when ITI was 3,900 ms; p⫽.004). From the
perspective of ITI, the effect of ISI was reliable when ITI was 900
ms (ISI ⫽900 ms, k⫽2.36; ISI ⫽3,900 ms, k⫽1.94; p⫽.001)
but was not reliable when ITI was 3,900 ms (ISI ⫽900 ms, k⫽
2.36; ISI ⫽3,900 ms, k⫽2.24; p⫽.12).
Array size 4. A main effect of ISI, F(1, 30) ⫽10.83, MSE ⫽
⫽.27, revealed that, as in the other conditions,
kwas larger when ISI was 900 ms (3.16) than it was when ISI was
3,900 ms (2.81). However, no effect of ITI was found, and ITI did
not interact with ISI (both ps⬎.88,
Experiment 3 demonstrates that the effects found in Experiment
2 are apparent even with array sizes as small as two items. The
effect of ITI weakened as set size increased from two to four items.
Although this is curious, we note that the direction of the trend is
opposite to what would be predicted by a WM storage model. That
is, the effect should have shrank as set size decreased.
It might be assumed that the smaller set sizes (i.e., two and three
items) created less proactive interference and thus increased the
relative distinctiveness of four item sets (e.g., Lustig, May, &
Hasher, 2001). We explored this possibility by conducting a post
hoc analysis of four-item arrays as a function of previous set size.
Neither an effect of previous array size nor an interaction of
previous array size with ITI was obtained (all ps⬎.5,
Experiment 3 is not a clean replication of Experiment 2, but this
is understandable. Whereas Experiment 2 focused on memory sets
that were larger than the average person’s k, Experiment 3 focused
memory sets that were sub-k. Thus, despite a disappearing effect of
ITI as set size increased, the important finding of Experiment 3 is
that ISI and ITI effects are apparent even for sets of items that
should readily be stored in WM.
Although the experiments have thus far demonstrated that kis
subject to retrieval-related effects, one may question whether these
effects are meaningful. Is kmore predictive of cognitive ability
under certain temporal conditions, or is its predictive power fixed
across all conditions?
Storage-based accounts of WM capacity assume that the rela-
tionship between visual arrays performance and Gf (i.e., novel
problem solving) is based on the number of units of information a
person can store in WM at any one point in time (Cowan, 2001;
Fukuda et al., 2010). Although the results of Experiments 3 are
incompatible with the assumption of fixed-capacity WM storage at
any size, the predictive power of kmay remain more-or-less
constant across manipulations of temporal discriminability. That
is, stable differences in the size of k, regardless of fluctuations of
proactive interference, may be the factor that links visual arrays
performance to cognitive ability, rather than the ability to manage
proactive interference within a given context.
This view contrasts Unsworth and Engle’s (2007) proposal that
low WM capacity is associated with difficulty constraining
searches of LTM to specific periods of time. By this account,
visual arrays performance will be most strongly related to WM
capacity when temporal discriminability is at its lowest (i.e., long
ISI and short ITI). In other words, WM capacity (as measured by
complex span tasks) will be most strongly correlated to visual
arrays under conditions that reduce the size of kand will be most
weakly correlated in situations that increase the size of k. Further,
Unsworth and Engle assumed that individual differences in
temporal-contextual retrieval are largely (but not entirely) respon-
sible for the relationship between Gf and measures of WM capac-
ity. Thus, this theory predicts that Gf will correlate to visual arrays
in a manner that replicates complex span.
To preview the results of Experiment 4, the predictions of
Unsworth and Engle (2007) were supported, but only as they relate
to WM capacity. To our surprise, kwas a better predictor of Gf
when the ITI was long, rather than short. We thus ultimately argue
that the results of Experiment 4 favor perspectives of WM capacity
that include a component of updating or forgetting of no-longer-
relevant information (i.e., Miyake et al., 2000; Oberauer et al.,
2007; Wiley et al., 2011).
Participants. In order to increase the cognitive diversity of
our sample, 54 participants (31 females; mean age ⫽23.8 years)
were recruited from our prescreened subject pool of college stu-
dents (e.g., Georgia Institute of Technology, Georgia State) and
members of the general Atlanta community. Participants were
reimbursed with $20 for their participation. Data for one partici-
pant, who did not follow instructions, were not examined.
Effects of ITI and ISI at Each Array Size
▫3▫1.61 (0.07) 2.36 (0.10) 3.16 (0.13)
▫333▫1.50 (0.09) 2.09 (0.12) 2.82 (0.18)
▫3▫1.50 (0.08) 2.15 (0.11) 3.00 (0.15)
▫333▫1.61 (0.08) 2.30 (0.11) 2.98 (0.16)
Note. Standard errors of the mean are in parentheses. ITI ⫽inter-trial
interval; ISI ⫽inter-stimulus interval.
INTERFERENCE WITHIN THE FOCUS OF ATTENTION
Design and procedure. The visual arrays task in Experiment
4 was similar to the one from Experiment 2. However, in an
attempt to create a less contrived context, buffer trials were re-
moved. This meant that “Previous Response” was now the re-
sponse from the previous probe array. As such, previous response
type, previous set size, and the ITI/ISI of the preceding trial were
free to vary. Thus, unlike Experiments 2 and 3, ITI/ISI of 900/900
was no longer the dominant trial type.
Experiment 4 included two blocks of trials separated by a
self-paced rest break. Within each block, participants responded to
each array size under each ITI/ISI combination twice as a change-trial
and twice as a no-change trial. The first trial of each block was not
preceded by an array and thus was dropped from further analysis.
Each session, therefore, included 98 trials and lasted approximately 45
min. Participants were run in groups of one to five.
All participants had been prescreened on two complex span
tasks and three Gf tasks. Scores on the complex span and Gf tasks
were combined into respective zscores referred to as “WM-span”
Complex span tasks. Complex span tasks require test-takers
to remember a series of items while performing interpolated pro-
cessing tasks. After 2–7 items are presented, the participant is
signaled to recreate the list in it proper serial order. The complex
span tasks used in this study may be downloaded at http://
The operation span (ospan; Unsworth, Heitz, Schrock, & Engle,
2005) requires test-takers to remember a list of letters. In between
the presentation of each letter, a simple mathematical equation
must be solved. Lists contained 3–7 items, and each list length
appeared three times.
The symmetry span (symmspan; Unsworth, Redick, Heitz,
Broadway, & Engle, 2009) task requires test-takers to remember a
series of spatial locations presented in a 4 ⫻4 grid served. In
between the presentation of each item, participants are shown a
black and white figure on an 8 ⫻8 grid. They were required to
indicate whether or not the figure was symmetrical. List contained
2–5 items, and each list length appeared three times.
General fluid intelligence. All fluid intelligence tasks were
administered via computer. Participants provided answers via
Raven’s Advanced Progressive Matrices (RAPM; Raven, 1990)
requires test-takers to choose which of several options completes a
series of eight abstract objects. The objects are arranged in a 3 ⫻
3 matrix with a blank space in the final location. Test-takers were
allowed 10 min to complete 18 problems (odd set).
Letter sets (Ekstrom, French, Harman, & Dermen, 1976) display
five groups of four letters and require test-takers to discover a rule
that is common to four the groups. Thus, the requirement of this
task is to indicate which set violates the rule. A total of 5 min was
given to complete 20 problems.
Number series (Thurstone, 1938) displays a series of numbers,
and test-takers select which of several options completed the
series. A total of 4.5 min was given to complete 15 problems.
Visual arrays. Mean kwas 3.53. Between array sizes, k
increased from 3.26 at set size 4 to 3.77 at set size 6 (p⬍.001).
kat set size 8 (3.56) did not differ from the other values (p⬎.25).
Table 4 indicates that kdecreased when ISI was extended from 900
ms (3.74) to 3,900 ms (3.33) and increased when ITI was extended
from 900 ms (3.37) to 3,900 ms (3.69). These observations are
supported by main effects of array size, F(1.76, 91.63) ⫽6.31,
MSE ⫽16.07, p⫽.004,
⫽.11; ISI, F(1, 52) ⫽15.13, MSE ⫽
⫽.23; and ITI, F(1, 52) ⫽9.74, MSE ⫽16.35,
The only interaction to approach significance was that of Array
Size ⫻ITI, F(2, 104) ⫽2.72, MSE ⫽4.64, p⬎.07,
This trend suggests that the effect of ITI increased from array sizes
4 – 8 (.11, .21, .67). This interpretation is supported by a significant
linear within-subjects contrast, F(1, 52) ⫽4.46, MSE ⫽8.28, p⬍
⫽.08. No other interactions approached significance (all
Correlation to WM-span and Gf. The correlations between
kand WM-span and kand Gf for each combination of ISI and ITI
are displayed in Table 5 (the full correlation matrix can be found in
the Appendix). First, examining the correlation between kand WM-
span, the overall effect of extending ISI numerically strengthened this
relationship from .33 to .46. However, a two-tailed dependent corre-
lation analysis (Cohen & Cohen, 1983) revealed that this change was
not reliable (t⫽1.53; p⫽.13). The overall effect of extending ITI
numerically weakened this relationship from .45 to .35. This change
was not reliable either (t⫽1.19; p⫽.24).
The individual combinations of ISI and ITI in Table 6 reveal
that the relationship between kand WM-span is not driven by the
absolute length of ISI or ITI but rather by overall temporal dis-
criminability. When ISI and ITI are of equal length, the correlation
to WM-span is similar regardless of whether that length is 900 ms
(r⫽.32) or 3,900 ms (r⫽.35; t⫽.27; p⫽.79). However, the
correlation weakens from .51 when temporal discriminability is
low (ITI ⫽900/ISI ⫽3,900) to .29 when temporal discriminability
is high (ITI ⫽3,900/ISI ⫽900; t⫽–2.07; p⬍.05).
Returning to Table 5, the correlation between kand Gf strength-
ened from .43 to .59 when ISI was increased (t⫽2.21; p⬍.04).
Similarly, the overall effect of extending the ITI strengthened this
relationship from .42 to .59 (t⫽2.25; p⫽.03).
As with WM-span, the relationship between kand Gf is not
straightforward. Table 6 reveals that, unlike WM-span, the rela-
tionship of kto Gf was stable across conditions of low (.45) and
high (.47) temporal discriminability (t⫽0.19; p⫽.85). On the
This was due to a programming oversight. Inclusion of these two trials
does not change the results.
Effects of ITI and ISI
▫3▫3.38 (0.10) 3.96 (0.19) 3.87 (0.25)
▫333▫3.15 (0.12) 3.59 (0.19) 3.25 (0.23)
▫3▫3.21 (0.11) 3.67 (0.19) 3.21 (0.24)
▫333▫3.31 (0.11) 3.88 (0.21) 3.88 (0.23)
Note. Standard errors of the mean are in parentheses. ITI ⫽inter-trial
interval; ISI ⫽inter-stimulus interval.
8SHIPSTEAD AND ENGLE
other hand, when ISI and ITI were of equal length, the correlation
between kand Gf strengthened as the interval length increased
from 900 ms (.33) to 3,900 ms (.61; t⫽2.94; p⫽.005).
Experiment 4 demonstrates that the manipulations thus far em-
ployed are meaningful to the prediction of WM-span and Gf. In
particular, the correlation between visual arrays and WM-span was
most affected by extreme manipulations of temporal discriminabil-
ity, which is consistent with Unsworth and Engle’s (2007) assump-
tion that WM capacity largely reflects individual differences in the
ability to conduct temporal-contextual searches of memory. In a
standard visual arrays task, this would be most apparent after
several trials have been run and proactive interference is in place
(e.g., Bunting, 2006; Lustig et al., 2001).
The relationship of Gf to visual arrays performance stands in
contrast to that of WM-span and visual arrays. Whereas the cor-
relation between WM-span and visual arrays was mainly influ-
enced by the overall temporal discriminability of a trial, the cor-
relation between Gf and visual arrays was more sensitive to the
individual lengths of the ISI and ITI. Surprisingly, the correlation
between Gf and visual arrays was stronger when the ITI was long,
rather than when it was short.
We interpret the latter phenomenon as an instance of individual
differences in memory “updating” (e.g., Miyake et al., 2000;
Oberauer et al., 2007; Wiley et al., 2011). This interpretation is
predicated upon two assumptions. First, individual differences in
updating are not always fully realized at short intervals, but they
can become apparent over time. Second, it is the context used for
retrieval (e.g., bindings) that is “updated,” rather than information
that is maintained within a WM store.
The first point is clarified by examining the data from the
perspective of ITI and Gf. Table 7 indicates that the longer ITI was
specifically beneficial to individuals with high Gf, as their kvalues
increased by about half an item. Low Gf individuals, on the other
hand, did not benefit from the increased ITI. This trend is consis-
tent with the proposal that people with low Gf are susceptible to
perseveration of no-longer-relevant information in WM (e.g., Wi-
ley et al., 2011), which ultimately prevents them from generating
novel solutions to problems. Conversely, though it may require
time, high Gf individuals are capable of disengaging from no-
longer-relevant information, thus allowing for better memory of
The second point states that updating is not performed on an
interference-free multi-item store. Although the concept of updat-
ing a WM store is intuitively concrete (and therefore appealing), it
must contend with the results of Experiment 3, which found
interference effects using array sizes of only two items. Thus,
while we are cautious in our endorsement of a concept as abstract
as “binding,” we note that the data imply that updating is per-
formed on the context used during a retrieval attempt, rather than
on stored information.
It may alternately be argued that high Gf individuals experience
a more rapid decay of no-longer-relevant information than do low
Gf individuals. Though Experiment 4 is not inconsistent with this
explanation, the concept of decay over absolute time has a rocky
past as a causal mechanism (e.g., Capaldi & Neath, 1995; Keppel
& Underwood, 1962; Lewandowsky, Oberauer, & Brown, 2009;
Nairne, 2002). Moreover, controlled processes are known to re-
quire absolute time to engage (e.g., Neely, 1977), and their ulti-
mate efficacy over time is subject to individual differences (e.g.,
Balota, Black, & Cheney, 1992; Heitz & Engle, 2007; Hutchison,
2007). Regardless of explanation (updating or decay of irrelevant
information), Experiment 4 demonstrates that (1) the predictive
power of kis not fixed and (2) not all people have the same
reaction to proactive interference that is generated during a visual
Trials in the visual arrays task are events along the continuum of
time (e.g., Brown et al., 2007; Crowder, 1976) and therefore
generate proactive interference. Traditional interpretations of vi-
sual array performance assume that this interference is counter-
acted by a fixed-capacity component of WM. However, across
Effects of ITI and ISI on the Correlations Between k and
WM-Span and Gf
ITI/ISI krWM-span rGf
▫3▫3.74 (0.16) .33 .43
▫333▫3.33 (0.15) .46 .59
▫3▫3.37 (0.15) .45 .42
▫333▫3.69 (0.16) .35 .59
Note. Standard errors of the mean are in parentheses. All correlations are
significant at p⬍.05. ITI ⫽inter-trial interval; ISI ⫽inter-stimulus
interval; WM-span ⫽working memory span; Gf ⫽general fluid intelli-
Correlation Between k and WM-Span and Gf at Separate Levels
ITI/ISI krWM-span rGf
▫3▫3▫3.58 (0.16) .32 .33
▫333▫333▫3.50 (0.18) .35 .61
▫3▫333▫3.16 (0.16) .51 .45
▫333▫3▫3.89 (0.18) .29 .47
Note. Standard errors of the mean are in parentheses. All correlations are
significant at p⬍.05. WM-span ⫽working memory span; Gf ⫽general
fluid intelligence; ITI ⫽inter-trial interval; ISI ⫽inter-stimulus interval.
Effect of ITI on k at Three Levels of Gf
Low (n⫽17) Mid (n⫽18) High (n⫽18)
900 3.10 p⫽.50 3.39 p⫽.13 3.60 p⫽.002
3,900 3.22 3.64 4.18
Note. Standard errors of the mean are in parentheses. All correlations are
significant at p⬍.05. ITI ⫽inter-trial interval; Gf ⫽general fluid
INTERFERENCE WITHIN THE FOCUS OF ATTENTION
four experiments, we found little evidence for such a storage
system. Rather, interference effects are apparent across a variety of
array sizes. Moreover, the relationship of kto WM-span and Gf
tasks is not driven by the absolute size of k(see Table 6) but rather
is driven by the ability of an individual to manage interference
within certain sets of conditions.
The finding of that high Gf individuals are particularly sensitive
to long ITIs (Experiment 4) suggests that the increased kover time
seen in Experiment 1 may represent an interaction of balanced
temporal circumstances along with a high-ability sample (e.g.,
Georgia Institute of Technology students; see Redick et al., in press).
That is, if high Gf individuals are indeed capable of using longer ITIs
to engage in intentional forgetting of no-longer-relevant information,
their memory will improve as absolute interval length increases,
provided the ratio of ITI to ISI remains at 1. It also suggests that this
effect is subject to individual differences.
We interpret our data as being most readily reconciled within
Oberauer’s (2002; Oberauer et al., 2007) concentric model of WM,
in which a region of direct access is formed through contextual
bindings between units of activated LTM and a single-item focus
of attention. However, this study does not provide evidence sup-
porting the existence a single-item focus of attention. Rather,
within the context of the visual arrays task, it provides evidence
against a multi-item focus of attention. This distinction is partic-
ularly relevant given the recent theoretical concession by Oberauer
and Bialkova (2011) that the single-item focus of attention is not
a structurally fixed feature of WM but rather is a type of process-
ing that is used to reduce cross-talk in novel situations.
Release From Proactive Interference
The present studies focus on time-based release from proactive
interference (Kincaid & Wickens, 1970), rather than release from
proactive interference in response to a change of category (Wickens et
al., 1963). Indeed, both are deemed to be important sources of context
around which memory is organized (e.g., Polyn, Norman, & Kahana,
2009a, 2009b). As such, one would expect visual arrays to be subject
to both types of release from proactive interference.
However, as referenced in the introduction, studies involving
categorical release from proactive interference have produced
equivocal results. Although Hartshorne (2008) found evidence for
such release, Lin and Luck (2012) did not when they used short
presentation times (100 ms) and short retention intervals (900 ms).
These researchers thus argued that LTM will only affect visual
arrays performance when longer time intervals are used.
Although Lin and Luck (2012) did not prescribe an interval at
which the influence of LTM becomes apparent, it might be argued
that our 250-ms array presentation allowed time for such processes
to engage. This interpretation is contradicted by the results of
Experiment 1, in which no evidence of increased interference over
longer intervals was found. Instead, we interpret an interesting
discrepancy between the methods of Hartshorne (2008) and Lin
and Luck (2012) within the context of the present results.
Hartshorne’s (2008) second experiment found release from pro-
active interference, using arrays that were presented for 1,000 ms
followed by a 1,000-ms retention interval. Lin and Luck (2012)
presented arrays for 100 ms, followed by a 900-ms retention
interval. This was not the only difference between these studies.
Hartshorne reported that each trial began with a 500-ms fixation.
Lin and Luck, on the other hand, ended each trial with an ITI of
1,000 ms, followed by a separate fixation period of 1,000 ms.
Thus, end-to-beginning, the trials in Hartshorne were compressed
in time, whereas the short trials of Lin and Luck were relatively
isolated. This provides an alternate explanation of the null effect
found by Lin and Luck: Rather than decreasing the role of LTM by
making the trials shorter, they may have reduced the meaningful-
ness of the category change by isolating each target array in time.
Alternate Accounts and Limitations
The effect of ITI. It has been suggested to us that the effect
of ITI may represent the effect of being given extra time to prepare
for the next trial. To the extent that this explanation can be
conflated with the individual differences variable that we have
termed “updating,” we are inclined to agree. However, the results
of Experiment 4 reveal that people are sensitive to ITI changes in
more than one way. Specifically, while Gf most strongly relates to
kwhen ITI-related discriminability is high, the correlation between
WM-span and kspecifically strengthens in response to low tem-
It would be parsimonious to argue that both of these effects are
preparation: WM-span representing rapid updating and Gf repre-
senting a slower process. However, this explanation must contend
with the finding that WM-span was not always sensitive to the
length of ITI. Instead, WM-span is most important when a short
ITI is paired with a long ISI (i.e., low temporal discriminability).
Verbal recoding. A second concern regards our lack of a
manipulation to discourage verbal recoding of visual material. This
may explain the inflated kscores in the long ISI condition of
Experiment 1: Participants knew that they would need to retain
information for an extended period and also knew that they had
ample time to recode the information into an articulatory format.
Although recoding provides a viable explanation of this partic-
ular effect (i.e., increased kwhen long intervals were fixed), it does
not endanger the next three experiments. In all subsequent exper-
iments, increases and decreases in kfollowed a pattern that is
consistent with temporal discriminability research (e.g., Neill et
al., 1992; Turvey et al., 1970) and theory (e.g., Baddeley, 1976;
Capaldi & Neath, 1995). Additionally, examination of Table 6
reveals that in Experiment 4 (in which long and short ISIs were
equally probable), kvalues were not time-sensitive on trials in
which the ISI and ITI were equal. Thus, while increased-k-over-
time can be explained as an artifact of the between-subjects design,
the lack-of-decay cannot.
Masked stimuli. None of our studies employed a post-
perceptual mask to reduce any effects of residual sensory infor-
mation (e.g., Sligate, Scholte, & Lamme, 2008) and ostensibly
obtain a cleaner estimate of fixed-capacity WM (e.g., Rouder et al.,
2008; Saults & Cowan, 2007). Although such an manipulation is
potentially informative, we argue that its absence does not threaten
the present results. Beyond the lack of absolute time-based decay
found in Experiment 1 (which would have been apparent if time-
limited sensory information was being used), the smaller array
sizes used in Experiment 3 should have been fully stored in WM.
However, even these small set sizes were subject to discriminabil-
Characteristics of the target and probe arrays. Finally, in
all experiments, colors were allowed to repeat within an array, and
10 SHIPSTEAD AND ENGLE
the probe included all items from the target array, rather than a
single probe. Thus, based on the work of Wheeler and Treisman
(2002), it might be argued that the color repetitions either in-
creased difficulty of maintaining binding between color and loca-
tion during the ISI, or they created interference when the whole-
display probe was presented.
We had initially considered the first possibility (i.e., inter-item
interference during retention) as an explanation of the Array
Size ⫻ISI interaction that was found in Experiments 2 and 3.
However, this explanation is contradicted by Experiments 1 and 4,
neither of which found such an effect. Thus, we attribute the Array
Size ⫻ISI interaction as evidence that larger set sizes are more
sensitive to the lower global temporal discriminability (e.g.,
Cowan, Saults, & Nugent, 2001) in Experiments 2 and 3 that was
created by the presence of 900-ms buffer trials.
It is possible that whole displays may increase interference by
providing a greater number of comparisons. However, inter-item
interference at response cannot explain all interference effects.
Hartshorne (2008) was able to find interference using single-item
probes. Moreover, our third experiment found significant effects
with probe displays of two items. These displays not only mini-
mize the potential for within-display color repetitions but also
minimize competition for representation in attention.
The history of psychology contains many examples of effects
that were once attributed to decay (e.g., Cowan, Saults, & Nugent,
1997; Neill & Westberry, 1987; Peterson & Peterson, 1959) but
were later reinterpreted as proactive interference in light of new
evidence (respectively: Cowan et al., 2001; Keppel & Underwood,
1962; Neill et al., 1992; see also Lewandowsky et al., 2009). The
present studies take a different angle by demonstrating that pro-
active interference influences performance in a paradigm that is
generally believed to reflect interference-free multi-item storage.
These effects are numerically small (see also Hartshorne, 2008),
yet we contend that their importance cannot be judged based on
absolute size: They are apparent at sub-karray sizes and produce
significant changes to the predictive nature of the task. In the end,
kprovides a simple and meaningful index of a person’s working
memory. However, the present results provide ample evidence that
the mechanisms underlying kare complex and multiply-
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Correlations Among Tasks and Conditions in Experiment 4
ISI2 .77 —
ITI1 .89 .88 —
ITI2 .90 .89 .78 —
ISI1_ITI1 .92 .73 .92 .75 —
ISI2_ITI2 .70 .92 .70 .91 .64 —
ISI2_ITI1 .70 .89 .92 .69 .69 .64 —
ISI1_ITI2 .93 .70 .73 .91 .72 .66 .62 —
WM-span .33 .46 .45 .35 .32 .35 .51 .29 —
Ospan .12 .18 .24 .08 .19 .09 .25 .05 .82 —
Symspan .42 .58 .50 .50 .34 .48 .58 .43 .82 .35 —
Gf .43 .59 .42 .59 .33 .61 .45 .47 .50 .23 .59 —
Raven .50 .51 .39 .62 .40 .60 .31 .52 .33 .10 .45 .76 —
LettS .24 .40 .27 .37 .14 .37 .36 .31 .37 .20 .41 .80 .34 —
NumbS .30 .52 .36 .45 .24 .52 .42 .30 .50 .27 .56 .87 .50 .60 —
M3.73 3.33 3.37 3.69 3.58 3.50 3.16 3.89 0 57.70 28.58 0 9.26 10.11 9.42
SEM 0.16 0.15 0.15 0.16 0.16 0.18 0.16 0.18 0.11 1.77 0.98 0.11 0.42 0.43 0.38
Note. All correlations above .28 are significant at the .05 level. ISI1 ⫽inter-stimulus interval of 900 ms; ISI2 ⫽
inter-stimulus interval of 3,900 ms; ITI1 ⫽inter-trial interval of 900 ms; ITI2 ⫽inter-trial interval of 3,900 ms; working
memory (WM)-span ⫽az-score composite of operation span (Ospan) and symmetry span (Symspan); general fluid
intelligence (Gf) ⫽az-score composite of Raven’s Advanced Progressive Matrices (Raven), Letter Sets (LettS), and
Number Series (NumbS).
Received April 17, 2011
Revision received March 5, 2012
Accepted March 21, 2012 䡲
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