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Journal of Experimental Psychology: General
The Visual Arrays Task: Visual Storage Capacity or Attention Control?
Jessie D. Martin, Jason S. Tsukahara, Christopher Draheim, Zach Shipstead, Cody A. Mashburn, Edward K. Vogel, and
Randall W. Engle
Online First Publication, September 30, 2021. http://dx.doi.org/10.1037/xge0001048
CITATION
Martin, J. D., Tsukahara, J. S., Draheim, C., Shipstead, Z., Mashburn, C. A., Vogel, E. K., & Engle, R. W. (2021, September
30). The Visual Arrays Task: Visual Storage Capacity or Attention Control?. Journal of Experimental Psychology: General.
Advance online publication. http://dx.doi.org/10.1037/xge0001048
The Visual Arrays Task: Visual Storage Capacity or Attention Control?
Jessie D. Martin
1
, Jason S. Tsukahara
2
, Christopher Draheim
2
, Zach Shipstead
3
, Cody A. Mashburn
2
,
Edward K. Vogel
4
, and Randall W. Engle
2
1
Battelle Memorial Institute, Arlington, Virginia, United States
2
School of Psychology, Georgia Institute of Technology
3
Department of Psychology, University of Illinois Urbana Champagne
4
Department of Psychology, University of Chicago
Extant literature suggests that performance on visual arrays tasks reflects limited-capacity storage of vis-
ual information. However, there is also evidence to suggest that visual arrays task performance reflects
individual differences in controlled processing. The purpose of this study is to empirically evaluate the
degree to which visual arrays tasks are more closely related to memory storage capacity or measures of
attention control. To this end, we conducted new analyses on a series of large data sets that incorporate
various versions of a visual arrays task. Based on these analyses, we suggest that the degree to which
the visual arrays is related to memory storage ability or effortful attention control may be task-depend-
ent. Specifically, when versions of the task require participants to ignore elements of the target display,
individual differences in controlled attention reliably provide unique predictive value. Therefore, at least
some versions of the visual arrays tasks can be used as valid indicators of individual differences in
attention control.
Keywords: attention control, change detection, visual arrays, working memory capacity
Supplemental materials: https://doi.org/10.1037/xge0001048.supp
The visual arrays task, also known as the change-detection task,
is one of the most commonly used tools to understand the cogni-
tive and neurophysiological nature of visual working memory
(Fukuda et al., 2010;Luck & Vogel, 1997). The task is typically
interpreted as a fairly pure measure of visual memory storage
capacity. However, the mechanisms reflected by these measures
have been questioned. Engle and colleagues (Draheim et al., 2021;
Shipstead et al., 2014) have suggested that the standard visual stor-
age interpretation may be incomplete. In particular, they have
shown a strong relationship between visual arrays tasks and atten-
tion control at the latent construct level that does not align with a
strict visual working memory explanation. Although this finding
does not preclude interpreting the visual arrays as a memory stor-
age (i.e., working memory capacity) task, it does warrant further
exploration of the nature of its relationship with constructs other
than visual storage. Additionally, there are various types of visual
arrays tasks that include differences in task design that may alter
which construct(s) causally contribute to change detection accu-
racy. Therefore, our question is: Which theoretical construct(s)
does the visual arrays task reflect and does this depend on the task
design?
We approach this question by reviewing a subset of the litera-
ture on the visual arrays task and, using data collected in our lab
over the last 10þyears, to empirically assess the extent to which
performance on visual arrays metrics is uniquely predicted by both
working memory capacity and attention control at the latent level.
Crucially, our review is selective and informed by a theoretical
approach which assumes that the working memory system comprises
of both mechanisms for memory storage and attentional control proc-
esses related to the active maintenance and manipulation of the con-
tents of working memory (Engle et al., 1999;Engle & Martin, 2018).
Our intent is not to create the impression that no viable theoretical
alternatives exist (e.g., Oberauer & Lin, 2017) but rather to narrow
the scope and focus of this project toward an evaluation of the pre-
vailing interpretation of visual arrays tasks as measures of visual stor-
age capacity. We do, however, discuss alternative interpretations of
our results based on multiple frameworks of attention and working
memory.
Visual Arrays Tasks: An Introduction
The general procedure of a visual arrays task is to briefly pres-
ent a target array of items (e.g., colored squares) on a computer
This work was supported by Grant N00014-12-1-1011 from the Office
of Naval Research to Randall W. Engle and Grant N00014-12-1-0972 to
Edward K. Vogel.
A preprint of this project is available on PsychArXiv using the following
link: https://psyarxiv.com/u92cm/. A selection of these data has also been
reported to the Office of Naval Research as part of our annual program
review on June 9, 2020. These data have been released on OSF at the
following link: https://doi.org/10.17605/OSF.IO/23NZU.
Correspondence concerning this article should be addressed to Jessie D.
Martin, Battelle Memorial Institute, 1550 Crystal Drive, Arlington, VA
22202, United States. Email: martinjd@battelle.org
1
Journal of Experimental Psychology: General
©2021 American Psychological Association
ISSN: 0096-3445 https://doi.org/10.1037/xge0001048
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monitor, typically for a duration of 100 ms. After a short interval,
a probe array appears and the test-taker must decide whether or
not one of the items has changed on some dimension (e.g., color)
relative to the target array. When the target array includes 3–4
items, accuracy tends to be nearly perfect. As items are added to
the display, performance declines in a linear manner (Luck &
Vogel, 1997). This trend is typically interpreted as an indication
that people can store a finite number of information chunks in
visuospatial memory (Cowan et al., 2005;Rouder et al., 2011; but
see Ma et al., 2014). Scores on these tasks are determined based
on an equation originally developed by Pashler (1988) by which
one can calculate a capacity score (denoted as k) for an individu-
al’s performance on the task. This kcapacity score is thought to
reflect the number of items one can store in visual working mem-
ory (Cowan, 2010). Moreover, kvalues reach asymptote around 3
or 4, suggesting that most individuals can maintain three to four
chunks in visual working memory at a time, a value that accords
well with estimates of memory storage capacity derived from other
measures (Cowan, 2010).
However, and critical to our empirical tests, there are different
versions of the visual arrays task that may change what cognitive
processes the resulting kcapacity score represents. In particular, in
visual arrays with a selection component, participants are cued to
focus on only a subset of the items presented in the target array.
Participants are asked to attend to only these cued items rather
than the entire array, and the cued dimension can vary on location,
color, size, shape, and so forth We will refer to the traditional vis-
ual arrays task as nonselective visual arrays and those that require
ignoring some elements of the target array as selective visual
arrays.
If the nonselective and selective visual arrays tasks are funda-
mentally the same (that is, they measure the same exact construct[s]
to the same degree), then kscores should be constant across the
two. In fact, mean kscores on selective visual arrays are typi-
cally lower, about half, compared with the typical three to four k
scores observed with nonselective visual arrays (Shipstead et al.,
2014;Shipstead & Yonehiro, 2016). To explain this dissociation,
task specific aspects must be considered. Specifically, nonselec-
tive visual arrays tasks have no explicit attentional filtering/
selection component and no distractors. By contrast, in the selec-
tive visual arrays tasks, ineffective selection/filtering would lead
to nontarget elements of the target array being represented in
working memory, effectively doubling the set-size of items
attended and resulting in a lower kscore (i.e., performance on a
set-size of three items becomes equivalent to performance on a
set-size of six items). Thus, the source of individual variability
may be different depending on the nature of the visual arrays
task in question (i.e., nonselective vs. selective tasks). Currently,
there are two proposed sources of variability: storage capacity,
which we have addressed (Cowan et al., 2005;Rouder et al.,
2011 )m and attention control (Draheim et al., 2021;Shipstead et
al., 2014), to which we now turn.
Attention Control
The ability to control and direct attention is necessary for the
successful execution of many tasks (Redick et al., 2016;Shipstead
et al., 2016). However, the degree to which a specific task reflects
this ability to control attention varies.
1
According to the executive
attention account of working memory capacity, the executive
attention system is responsible for maintaining and ignoring dis-
traction in the service of executing a given task (Engle et al.,
1999;Shipstead et al., 2016). In storage-based tasks, a principal
function of the executive attention system is to actively maintain
information in working memory and reduce interference by pre-
venting the storage of irrelevant information. More interference
diminishes available storage for relevant memory items, leading to
lower scores on capacity tasks (Oberauer, 2002).
A critical feature of this theoretical approach is that there may
be multiple sources of interference, some more obvious than
others. For instance, interference can occur while trying to actively
maintain items in memory by requiring the completion of a sec-
ondary task at the same time, such as in complex memory span
tasks (Conway et al., 2005). Interference can also occur proac-
tively, when memory items from previous trials interfere with
memory items on the current trial (Kane & Engle, 2000;Lustig
et al., 2001). Interference can even occur as a result of intrusive
and off-task thoughts (McVay & Kane, 2010). Given this execu-
tive attention account of working memory capacity, it would be
expected that even nonselective visual arrays would depend on the
executive attention system to reduce interference from previous
trials or from intrusive and off-task thoughts. We will now con-
sider evidence for the role of attention control in nonselective and
selective visual arrays tasks.
Attention Control in Nonselective Visual Arrays
First, most studies assessing individual variability in visual
arrays performance include set-sizes exceeding the average
capacity-limit of three to four items. From a pure storage capacity
interpretation, low and high-capacity individuals should be simi-
larly impacted by larger set-sizes. If kmerely represents storage
capacity independent of controlled processing, then kscores should
plateau at their maximum limit for all subjects. In a large sample
(N= 495), Fukuda et al. (2015) examined the change in kscores
from a set-size of 4 to a set-size of 8. Whereas the mean
kscore was slightly lower for a set-size of eight, the variability in
mean kscores nearly doubled. The main reason for this increased
variability was that low-capacity subjects performed much worse
on set-size eight compared with set-size four, whereas high-capacity
subjects showed only a small difference in performance on set-size
eight.
The variability in performance decrements at larger set-sizes is
more readily explained within an attentional control framework.
Fukuda et al. (2015) suggest that upon the initial presentation of a
target array, there is a global attentional capture to all of the ele-
ments comprising the array. This capture becomes overwhelming
at large set-sizes since not all items can be stored in working mem-
ory, and controlled processing is required to reorient attention to
1
Furthermore, researchers currently disagree on how best to
characterize and measure attention control as a psychometric construct,
with some researchers arguing that there is no such coherent latent
attention control ability (Frischkorn et al., 2019;Keye et al., 2009;Rey-
Mermet et al., 2019;Rouder et al., 2019;von Bastian et al., 2016;
Whitehead et al., 2019; but see Draheim et al., 2018,2021). Although this
is a contentious area warranting careful review, this is outside the scope of
the present project. However, we devote portions of the discussion section
to consideration of some of these issues.
2MARTIN ET AL.
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only a manageable subset of items. High-capacity individuals
engage these control processes more quickly and effectively,
leading to fairly stable performance across larger set-sizes. For
low-capacity individuals, however, the ineffective execution of
controlled processing causes a performance decrement at larger
set-sizes.
To explore this interpretation further, Fukuda et al. (2015)
increased the duration for which the target array was presented.
Consistent with their controlled processing explanation, only low-
capacity subjects benefited from the longer exposure. High-
capacity individuals already effectively reorient their attention dur-
ing the encoding phase, and therefore show no benefit from the
extra time. This suggests that low-capacity individuals are unable
to effectively engage controlled processing unless given more time
do so and therefore show lower kscores even on nonselective vis-
ual arrays tasks. These results corroborate those from Fukuda and
Vogel (2011), where low-capacity individuals were much slower
at disengaging from attention capture than high-capacity subjects
on a variant of a visual arrays task. Therefore, although these
results are difficult to reconcile from a pure storage capacity inter-
pretation of nonselective visual arrays performance, they do follow
naturally from an attention control explanation.
In addition, there may be other aspects of attention control at
play in visual arrays task besides dealing with larger set-sizes.
Shipstead and Engle (2013) manipulated the length of the intertrial
interval (ITI; the delay between the probe for trial n and the target
for trial nþ1) and interstimulus interval (ISI; the delay period
between target array and probe array for the same trial). They
assumed that shorter ITIs would create more proactive interfer-
ence. Consistent with this prediction, the correlation between
working memory capacity and nonselective visual arrays capacity,
k, was highest when the ITI was short and ISI was long. This
makes sense, given the executive attention view of working mem-
ory capacity. Nonselective visual arrays performance showed a
strikingly different relationship with fluid intelligence, which was
most strongly related to kcapacity scores with long ITIs and long
ISIs. This finding suggests that high fluid intelligence individuals
took advantage of the longer ITI to reduce proactive interference
from previous trials (cf., Shipstead et al., 2016). This study pro-
vides some evidence that even the nonselective visual arrays tasks
do not reflect a pure measure of storage capacity but also reflect
individual differences in reducing interference.
Finally, asserting that individual differences in attention control
are a determining factor in nonselective visual arrays capacity
scores is consistent with theoretical accounts of other working
memory capacity measures (see Shipstead et al., 2014). For
instance, in complex working memory span tasks there is a long
retention interval during which a secondary task is performed. In
the nonselective visual arrays tasks, the retention interval is very
short and there is no explicit interference or distractors. Given
these differences, it would be expected that nonselective visual
arrays would provide a more pure measure of storage capacity in
working memory and complex-span tasks would reflect more
active maintenance and interference reduction (i.e., controlled
processing). The differences between these measures of working
memory capacity have likely given face-validity to the interpreta-
tion of the nonselective visual arrays as a pure measure of visual
working memory capacity. If this were the case, then it would be
expected that complex-span measures of working memory capacity
would be more highly related to tasks that measure the control of
attention than would nonselective visual arrays. To the contrary,
Shipstead et al. (2015) found that a nonselective visual arrays factor
contributed unique variance to an attention control factor (i.e., anti-
saccade, Stroop, & flanker tasks) above and beyond complex-span
measures of working memory capacity. Therefore, despite the face-
validity of the visual arrays as a pure measure of storage capacity,
there is evidence which suggests that individual variability in visual
arrays performance reflects processes related to controlled process-
ing in nonmemory based attention tasks.
Attention Control in Selective Visual Arrays
Even though the selective visual arrays have more face-validity
to the involvement of attention control, these tasks are also typi-
cally considered as relatively pure measures of visual storage
capacity. However, there are physiological and behavioral evi-
dence that are more consistent with an attention control interpreta-
tion. A commonly used EEG signature in visual arrays tasks is the
contralateral delay activity. It is obtained in selective visual arrays
tasks in which participants are cued to only attend to either the left
or right side of the target array and is characterized by a negative
slow-wave event related potential (ERP) on the contralateral (op-
posite) side of the brain as attended items. As the number of mem-
ory items presented in the target array increases, so should arousal,
effort, or task difficulty; however contralateral delay activity
reaches a maximum at around three to four items, mirroring the
capacity indicated by behavioral indices such as the kscore (Vogel
& Machizawa, 2004). This provides evidence that contralateral
delay activity is sensitive to the number of items stored in visual
working memory (Feldmann-Wüstefeld et al., 2018). Fukuda et al.
(2015) observed a similar contralateral ERP response across larger
set-sizes for both low and high-capacity subjects (as indexed by k
score values). However, they also observed that low-capacity sub-
jects showed an increase in ipsilateral (corresponding to the side
with irrelevant items) ERP response with increasing set-size, but
high-capacity subjects did not. This suggests that low-capacity
individuals stored irrelevant items from the uncued side of the dis-
play, whereas high-capacity individuals effectively filtered out the
irrelevant items. Therefore, in selective visual arrays tasks, atten-
tion control may determine kscores because failing to sort the
irrelevant items would lead to a lower kscore.
Additionally, Vogel, McCollough, et al. (2005) assessed
whether high- and low-capacity individuals (as determined by k
scores) were equally capable of selectively attending elements of
a target array. To do so, they manipulated the set-size and num-
ber of irrelevant items in a selective visual arrays task in which
participants had to respond to the orientation of a probed rectangle,
but only in the target color (red (dark gray) or blue (light gray)). A
cue before the target array presentation indicated whether to attend
to red (dark gray) or blue (light gray) rectangles. There were three
conditions (a) a two-item array with no distractors (e.g., two red
(dark gray) rectangles), (b) a two-item array with two distractors
(e.g., two red (dark gray) rectangles and two blue (light gray) rectan-
gles), and (c) a four-item array with no distractors (e.g., four red
(dark gray) rectangles). To the extent that an individual effectively
ignores distractors, the contralateral delay activity for the first two
conditions should be equivalent, because both are of set-size two. To
the extent that an individual does not effectively ignore distractors
VISUAL ARRAYS AND ATTENTION CONTROL 3
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This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.
and stores them in working memory, the contralateral delay activity
for the second and third conditions should be equivalent, since both
have four total items in the display. High-capacity individuals exhib-
ited the former pattern, whereas low-capacity individuals exhibited
the latter.
These studies converge on the interpretation that, for selective
visual arrays tasks, high-capacity individuals are those who can
effectively ignore irrelevant items in the target array. Low-
capacity individuals cannot ignore irrelevant items and tend to
store the irrelevant items in working memory, diminishing avail-
able capacity. Based on the different pattern of contralateral
delay activity as a function of whether or not items were success-
fully selected, Vogel et al. (2005) concluded that control-led
processes were an important determinant of which items are
stored in visual working memory, and thereby one’s visual work-
ing memory capacity. Several other EEG investigations indicate
that filtering efficiency in selective visual arrays is sensitive to
the effects of sleep deprivation (Drummond et al., 2012), aging
(Jost et al., 2011), and Parkinson’s disease (Lee et al., 2010), fur-
ther supporting to the notion that selective visual arrays are
affected by attentional processes.
Finally, domain-generality is a core feature of how attention
control has been conceptualized (cf., Kane et al., 2004), and
therefore is an important benchmark for viewing the selective
visual arrays as reflecting attention control.
2
Shipstead and
Yonehiro (2016) found that selective visual arrays performance
reflects two factors, one domain-general and one visuospatial.
The domain-general factor correlated with reasoning ability,
regardless of whether reasoning occurred in the visual or verbal
domains. The visuospatial factor, meanwhile, was strictly related
to visual reasoning. Shipstead et al. (2014) also found that, de-
spite their heavily visuospatial nature, selective visual arrays per-
formance correlated with verbal retrieval (i.e., secondary
memory; see Unsworth & Engle, 2007). Moreover, this retrieval
ability also partially mediated the correlation between selective
visual arrays performance and fluid intelligence. Therefore, there
is evidence that selective visual arrays performance reflects a
unique domain-general resource beyond static visual storage
capacity.
3
The Current Study
The evidence reviewed so far calls into question the interpreta-
tion that visual arrays tasks only reflect individual differences in
visual storage capacity and is therefore a relatively pure measure
of capacity in visual working memory. With two diverging inter-
pretations of what abilities the visual arrays task reflects (visual
storage capacity and/or attention control), we find ourselves con-
fronted with two questions, both theoretical and practical in nature:
1. Are visual arrays tasks more closely related to storage-
based measures of working memory capacity or resist-
ance-to-interference aspects of attention control?
2. Does the nature of the visual arrays task (i.e., nonselective
or selective) influence which constructs that type of visual
arrays task primarily reflects?
Four potential answers follow these questions:
1. All visual arrays tasks primarily reflect visual storage
capacity related to working memory capacity measures.
2. All visual arrays tasks primarily reflect differences in con-
trolled attention independent of storage.
3. All visual arrays tasks reflect both visual storage capacity
and differences in controlled attention to the same degree.
4. The degree to which a visual array task primarily reflects
visual storage capacity or controlled attention is task-
(selection) dependent.
To answer these questions, we conducted three sets of analy-
ses on four entirely separate data sets collected over an 11-year
period by different groups of graduate students, postdoctoral
researchers, and undergraduate research personnel. Common to
all these data sets are measures of working memory capacity
(mainly but not exclusively defined by complex span tasks),
attention control (specifically the antisaccade, flanker, and Stroop
tasks), and at least one visual arrays task. Each set of analyses was
intended to identify whether various visual arrays tasks were more
closely related to working memory capacity or attention control.
These analyses were all novel; none of these results have been pre-
viously published in journals nor presented at conferences. The
same set of analyses was used on each of the four data sets.
1. We began with an exploratory factor analysis. Exploratory
factor analysis is a data-driven approach to defining the
latent factor structure in a set of tasks. If the visual arrays
task is more closely related to working memory capacity,
then they should load more with those tasks than measures
of attention control. Alternatively, if visual arrays measures
are more closely related to measures of attention control,
then they should load more consistently with measures
of attention control than measures of working memory
capacity.
2. Next, we conducted a structural equation model in which
working memory capacity and attention control latent fac-
tors uniquely predict individual differences in visual arrays
kcapacity scores. This allowed us to assess whether indi-
vidual differences in kcapacity scores from the visual
arrays tasks reflects primarily storage capacity, attention
control, or both.
3. Finally, we conducted additional structural equation mod-
els to further understand the processes underlying individ-
ual differences in visual arrays performance. In two
2
We should note that we regard domain-generality as a necessary but
not sufficient benchmark for demonstrating the importance of attention
control to visual arrays performance, as there are other plausible domain-
general processes that could come into play. For example, Lerche et al.
(2020) recently demonstrated that variability in drift rates (the diffusion
model parameter associated with information processing speed) derived
from many cognitive tasks has both domain-general and domain-specific
components.
3
We also note that there is some evidence for domain-generality in
nonselective visual arrays (see Morey & Cowan, 2004).
4MARTIN ET AL.
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separate models, we tested (a) whether visual arrays pre-
dicts attention control over and above of working memory
capacity and (b) whether visual arrays predicts working
memory capacity over and above attention control.
Method
We analyzed data from four different data sets collected over
11 years (the total number of subjects are listed for each set of
analyses, and the full population details for each data set are out-
lined in the Appendix A and Appendix B). In each data set, there
were three or more measures of working memory capacity, three
measures of attention control, and at least one visual arrays task.
Participants for each data set were recruited from the Georgia
Institute of Technology, surrounding universities, and the greater
Atlanta community. At minimum, half of our population was
recruited from outside of Georgia Tech to provide a sample
which reflected a diverse background of socioeconomic status,
race, gender, and education.
The studies from which the data are reported were all approved
by the Georgia Institute of Technology IRB. The data were col-
lected under four independent protocol numbers/titles. They are
listed from most recent to oldest. (a) Protocol #H17116 “Under-
standing the nature of attention control,”(b) #H16322 “Differenti-
ating between working memory capacity and fluid intelligence
(Part II),”(c) #H12234 “The relationships among working mem-
ory tasks and their relations to fluid intelligence and higher-order
cognition,”and (d) #H11309 “Relating the scope and control of
attention within working memory.”
Visual Arrays Tasks
Four variations of the visual arrays task were used (see Figure 1).
Two tasks explicitly involved a selection component (VA-color-S
and VA-orient-S) which required participants to ignore specific
distractor items (either those of a given color or those on one side
of the array). Two did not (VA-color and VA-orient). The cate-
gory listed after VA is the dimension on which individuals are
making a yes/no change evaluation (i.e., did a box change color,
or did a bar change orientation). In calculating the dependent vari-
able, k,Nwas always defined as the number of valid target-items
on a screen. Thus, if ten target/items are presented, but five are to-
be-ignored, then Nequaled 5. Two tasks required test-takers to
decide whether a relevant characteristic of any item in the display
had changed (VA-orient and VA-color-S). For these tasks, kwas
calculated using the whole display correction of Pashler (1988):
k=N3(%hits %false alarms/[1 %false alarms]). Two tasks
required test-takers to respond as to whether a relevant character-
istic of a probed item had changed (VA-color and VA-orient-S).
For these tasks, kwas calculated using the single probe correction
of Cowan et al. (2005):k=N3(%hits þ%correct rejections
1). In all cases, kwas first computed for each set size, and then the
set sizes were averaged. In all tasks, participants responded via
keypress. Change and no-change trials occurred with 50% proba-
bility and, along with set sizes, were randomly distributed. Items
were presented within a silver 19.1° 314.3° visual field at a dis-
tance of roughly 45 cm. Items were separated from one another by
at least 2° and were all at least 2° from a central fixation point.
VA-Color (Color Judgment Task)
Array sets were four, six, or eight colored blocks. Possible
colors included white, black, red (dark gray), yellow, green,
blue (light gray), and purple. Arrays were presented for 250 ms
followed by a 900 ms ISI. Participants responded as to whether
or not one circled item had changed color. Twenty-eight trials
of each set size were included; 14 were no-change, 14 were
change (see Figure 1a).
VA-Orient (Orientation Judgment Task)
The orientation judgment task was based on one of the conditions
used by Luck and Vogel (1997). Arrays consisted of five or seven col-
ored bars, each of which was either horizontal, vertical, or slanted 45°
to the right or left. Participants needed to judge whether any bar had
changed orientation. Colors included red (dark gray) and blue (light
gray) and did not change within a trial. Forty trials of each set size were
included; 20 were no-change and 20 were change (see Figure 1b).
Figure 1
Examples of Visual Arrays Tasks Used in the Present Study
Note. Visual arrays, with either a color change judgment or an orienta-
tion change judgment. The labeling of each task is based on the following
criteria: VA-[the category of the change-based judgment] - [is there a
selection component]. The two potential judgements for change are color
or orientation (i.e., has a square changed color, or has a bar changed ori-
entation. The selection components direct an individual to a pay attention
to half of the array (either one side [the right or left subset] or one subset
of stimuli [blue (light gray) or red (dark gray) bars only]). Going forward,
(a) and (b) will be referred to as nonselection versions as all array infor-
mation is needed for retrieval. In versions (c) and (d) the –S indicates a
selection component as evidenced by the cue in lieu of a fixation. (a) and
(b) begin with fixation, which is followed by a target array of to-be-
remembered items, then an interstimulus interval (ISI). For (a) the test-
taker must indicate whether the encircled box has changed colors. For (b)
the test-taker must indicate whether any box has changed its orientation. (c)
and (d) begin with a cue that indicates which information will be relevant.
This is followed by the array of to-be-remembered items, along with dis-
tractors. After the ISI, the probe array appears with only cued information
presented. For (c) the test-taker must indicate whether any box has changed
color. For (d) the test-taker must indicate whether the box with the white
dot has changed orientation. VA = visual arrays. See the online article for
the color version of this figure.
VISUAL ARRAYS AND ATTENTION CONTROL 5
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VA-Color-S (Selective Color Judgment Task)
This task was based on Experiment 2 from Vogel, Woodman,
et al. (2005) and was speeded relative to other tasks. Each trial
began with a left- or right-pointing arrow at the center of a com-
puter monitor indicating which side of the array participants
needed to focus on. This arrow was presented for 100 ms, fol-
lowed by a 100-ms interval. Next, two equally sized arrays of col-
ored blocks were presented on the right and left sides of the screen
for 100 ms. The array on each side contained either four, six, or
eight items. After a 900-ms delay, the boxes on the side indicated
by the arrow reappeared. Participants indicated whether any of
these relevant boxes had changed color. Twenty-eight trials of
each set size were included; 14 were no-change, 14 were change,
and they occurred equally often on the right and left sides of the
screen (see Figure 1c).
VA-Orient-S (Selective Orientation Judgment Task)
This task was based on the first experiment of Vogel, Wood-
man, et al. (2005). Single probe report was used. Each trial began
with presentation of a word, either RED (dark gray) or BLUE
(light gray) indicating the color of the items to be attended (the
selection instruction) for 200 ms, followed by a 100-ms interval.
Next, 10 or 14 bars were presented for 250 ms. Half of all bars
were printed in the to-be-attended color, that is set size was either
five or seven. Following a 900-ms delay, only the to-be-attended
bars returned. The critical item was identified at test by a white
dot superimposed on one of the bars. Test takers judged whether
the orientation of the item indicated by the dot had changed, rela-
tive to the initial presentation. No other changes could occur
within the display. Forty trials of each set size were included; 20
were change, and 20 were no-change (see Figure 1d).
Working Memory Capacity Tasks
Operation Span (OSpan; Kane et al., 2004;Turner &
Engle, 1989)
This task required subjects to remember a series of letters pre-
sented in alternation with simple math equations which they were
required to solve. On each trial, subjects first solved a simple math
equation where they decided whether a solution was correct (e.g.,
“[2 32] þ1 = 5) or not (e.g., “[3 34] 3=8”) followed by the
presentation of a single letter. After a variable set size, participants
attempted to recall the letters in their correct serial order. There
were a total of 14 trials (two blocks of seven trials), set-sizes
ranged from three to eight,
4
and each set-size occurred twice (once
in each block). The dependent variable was the partial span score,
which is the total number of letters recalled in proper serial posi-
tion (Conway et al., 2005).
Symmetry Span (SymSpan; Unsworth et al., 2009)
This task required subjects to judge whether remember a 16 3
16 matrix of black and white squares was symmetrical about the
vertical midline and while memorizing the locations of a red
(dark gray) square in a 4 34 matrix. Participants first made the
symmetry judgment and were then presented with the to-be-
remembered spatial location. This alternation continued until a
variable set-size of spatial locations had been presented. There
was a total of 12 trials (two blocks of six trials), set-sizes ranged
from two to seven, and each set-size occurred twice (once in
each block). The dependent variable was the partial span score,
which is the total number of square locations recalled in proper
serial position.
Rotation Span (RotSpan; Kane et al., 2004)
This task required subjects to solve a mental rotation task in
which they had to mentally rotate and decide whether a letter was
mirror reversed or not. Afterward, subjects were presented with a
to-be-remembered arrow with a specific direction (eight possible
directions; the four cardinal and four ordinal directions) and spe-
cific size (small or large).This alternation continued until a vari-
able set-size of arrows had been presented, at which point
participants attempted to recall the arrows in their correct serial
order. There as a total of 12 trials (two blocks of six trials), set-
sizes ranged from two to seven, and each set-size occurred twice
(once in each block). The dependent variable was the partial span
score, which is the total number of arrows recalled in proper serial
position.
Running Letter Span (Broadway & Engle, 2010)
The automated running letter span presented a series of five to
nine letters and required participants to remember the last three to
seven. Participants were informed of how many items they would
need to remember at the beginning of a block of three trials.
Blocks were randomly presented. There as a total of 15 trials.
Items were presented for 300 ms followed by a 200-ms pause.
Running Spatial Span (Harrison et al., 2013)
The running-spatial-span task was identical to the running-let-
ter-span task, except that matrix locations on a 4 34 matrix were
the to-be-remembered stimuli.
Rapid Running Digit Span (Cowan et al., 2005)
The automated running digit span presented a series of 12–20
digits and required participants to remember the last 6. Participants
performed 18 critical trials. Digits were presented at the rate of
four per second via headphones.
Attention Control Tasks
Antisaccade (Hallett, 1978;Hutchison, 2007;Kane et al.,
2001)
Subjects saw a central fixation cross lasting a random amount of
time between 2,000–3,000 ms followed by an alerting tone for 300
ms. After the alerting tone, an asterisk appeared for 300 ms at
12.3° visual angle to the left or the right of the central fixation fol-
lowed immediately by a target “Q”or an “O”for 100 ms on the
opposite side of the screen from the asterisk. The location of the
4
Owing to an error in programming of the advanced operation span
task, trials in which the set-size was supposed to be nine only displayed a
set-size of eight. This resulted in the set-size of eight occurring twice as
often as intended, a total of four trials compared with two trials for each
other set-size.
6MARTIN ET AL.
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asterisk and target letter were both masked for 500 ms by “##.”
The subject’s goal was to avoid looking at the asterisk and instead
look to the opposite side of the screen to catch the target “Q”or
“O.”Subjects had as much time as needed to respond to which let-
ter appeared by pressing the associated key on the keyboard. Sub-
jects completed 72 trials, with trial-by-trial feedback for 500 ms
following each response, and then a 1,000-ms waiting period until
the fixation cross appeared again to indicate a new trial was begin-
ning. The dependent variable was the number of correctly identi-
fied target letters.
Arrow Flanker (RT Flanker; Eriksen & Eriksen, 1974)
Subjects were presented with a target arrow in the center of the
screen pointing left or right along with two flanking arrows on
both sides. The flanking arrows were either all pointing in the
same direction as the central target (congruent trial; for example,
/////) or all in the opposite direction (incongruent trial; for
example, //!//)
5
. The subject was asked to indicate direc-
tion the central arrow was pointing by pressing the “z”(left) or
“/”(right) key. These keys had the words LEFT and RIGHT taped
onto them to assist with response mapping. A total of 144 trials
were administered; 96 congruent and 48 incongruent, with a
randomized 400- to 700-ms ITI. The dependent variable was the
flanker interference effect: the RT cost of the incongruent trials
calculated by subtracting each subject’s mean RT on congruent
trials from their mean RT on incongruent trials, excluding inaccu-
rate trials.
Color Stroop (RT Stroop; Stroop, 1935)
Subjects were shown the word “red (dark gray),”“green,”or
“blue (light gray)”in red (dark gray), green, or blue (light gray)
font. The words were either congruent with the color (for example,
red (dark gray)), or incongruent with the color (for example, blue
(light gray)). The subject’s task was to indicate which color the
word was printed by pressing the “1,”“2,”or “3”key on the num-
ber pad. To assist with response mapping, the keys had a piece of
paper of the corresponding color taped onto them. A total of 144
trials were administered; 96 congruent and 48 incongruent, with a
randomized 400- to 700-ms ITI and a 5,000-ms response deadline.
The dependent variable was the Stroop interference effect: the RT
cost of the incongruent trials calculated by subtracting each sub-
ject’s mean RT on congruent trials from their mean RT on incon-
gruent trials, excluding inaccurate trials.
Data Analysis
For each data set we ran the same general set of analyses.
Before analysis we removed subjects that had missing data on any
of the visual arrays tasks. We used the same criteria across all data
sets and each visual array task. See Appendix A Table A1 for task
reliabilities, and Appendix B Tables B1-B4 for correlation tables.
Exploratory Factor Analysis
For each data set we included all the working memory capacity,
attention control, and visual arrays tasks that were available from
that study. We used an oblimin rotation, and the number of factors
was determined by taking into account numerous methods; the
Kaiser criterion of eigenvalues greater than 1, scree plot, and par-
allel analysis.
Structural Equation Models
For our primary analyses we used structural equation model-
ing. For each data set we conducted four models to better
understand the processes related to individual differences in
visual arrays performance. (a) We conducted a structural equa-
tion model with both working memory capacity and attention
control latent factors as correlated predictors of each visual
arrays task. Rather than forming a latent visual arrays factor
(Data Sets 3 and 4 only) we used each visual arrays task as a
separate dependent variable. This model allowed us to assess
the unique contributions of working memory capacity and
attention control to individual differences in kcapacity scores
at the task level for each visual array task.
6
In Data Sets 3 and 4,
we essentially have an experimental manipulation where the only
difference between task versions (besides the judgment dimen-
sion) is whether there is a selective component or not. This
allowed us to evaluate whether the degree to which a visual arrays
task primarily reflects visual storage capacity or controlled atten-
tion is dependent on there being a selective component. (b) We
tested whether visual arrays performance can predict attention
control over and above working memory capacity and (c) whether
visual arrays performance can predict working memory capacity
over and above attention control. For these models, in Data Sets 3
and 4, we formed latent nonselective and selective visual arrays
factors. (d) Finally, we also conducted additional structural equa-
tion models testing whether working memory capacity and proc-
essing speed mediate the relationship between attention control
and visual arrays. For processing speed, we used the mean RT
from Flanker and Stroop congruent trials. This allowed us to assess
whether speed of processing is a viable explanation for any atten-
tion control and visual arrays relationship. This is important because
no task or latent factor is “process pure.”Therefore, we can rule out
potential confounding factors by establish incremental validity.
Analyses were conducted in R statistical software (R Core
Team, 2018). The R package psych (Revelle, 2018) was used to
conduct the exploratory factor analysis. The R package lavaan
5
Note that the arrow flanker task often has three trial types: congruent,
incongruent, and a neutral type in which dashes flank the central arrow.
Similarly, in the Stroop task a neutral trial type is often present in which the
word is not a color. Here we use only incongruent and congruent trials.
6
In addition to the structural model, we present pie charts representing
the contribution of unique attention control, unique working memory
capacity, and their common variance relative to the total variance explained
in visual arrays performance. The values in the pie chart were calculated
based on the path values in the structural equation models. The unique
working memory capacity contribution was calculated by squaring the path
value from working memory capacity to the visual arrays task divided by
the total proportion of variance explained in the visual arrays task. The
same was done for the unique attention control contribution. Although the
variance from common variance is not explicit in the structural model
diagram, it does contribute to the total variance explained in the visual
arrays task. To calculate the common variance, the three path values from
the model (the covariance between working memory capacity and attention
control, working memory capacity to visual arrays, and attention control to
visual arrays) are multiplied together and then doubled. It can also be
calculated indirectly by subtracting the total from the sum of the unique
contributions. In the pie charts, this common variance is then divided by
the total variance explained in the visual arrays task.
VISUAL ARRAYS AND ATTENTION CONTROL 7
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(Rosseel, 2012) was used for all structural equation models, treat-
ment of missing values was set to full-information maximum like-
lihood. Where necessary, we statistically compared models using
the Bayes Information Criteria (BIC) to provide an estimate of the
Bayes Factor value for the probability of one model over another
(Bollen et al., 2014;Wagenmakers, 2007).
Results
Data Set 1
Data Set 1 consisted of OSpan, SymSpan, and RotSpan for
working memory capacity; antisaccade, flanker, and Stroop for
attention control; and VA-orient-S for visual arrays. There was a
total of 397 subjects, with no more than 5% missing data for any
one task. The data analyzed in this study was part of a larger data
collection sample that occurred from 2017–2018. The following
link has a summary of the larger data collection procedure and a
reference list of all publications to come out of this data collection
sample with information on which tasks were used for each publi-
cation: https://osf.io/yc48s/.
Exploratory Factor Analysis
We conducted an exploratory factor analysis using principal
axis factoring with two factors and an oblimin rotation (Table 1).
Two factors were specified because two factors had eigenvalues
greater than 1, both scree plot and parallel analysis suggested that
the number of factors was two. The OSpan, SymSpan, and Rot-
Span loaded most strongly onto the first factor (a working memory
capacity factor). The VA-orient-S, antisaccade, flanker, and Stroop
all loaded most strongly onto the second factor (an attention con-
trol factor). However, the flanker loading was poor for both fac-
tors, each under .30. The two factors moderately correlated at r=
.6. The exploratory factor analysis supported the interpretation of
VA-orient-S as being more similar to attention control measures.
Structural Equation Models
Our primary question of interest is; are individual differences in
visual arrays kcapacity score explained more by differences in
working memory capacity, attention control, or both? To answer
this, we conducted a structural equation model with working mem-
ory capacity and attention control predicting kcapacity scores on
the VA-orient-S task (see Figure 2). Attention control, but no
working memory capacity, uniquely predicted kcapacity scores in
the VA-orient-S task. We compared this model with a “null”
model in which the working memory capacity –VA-orient-S path
was set to zero. The “null”model was 10.63 times more likely;
BF
01
= 10.63, P(H
0
jData) = .91. We also compared this model
with a model where the predictive paths for attention control and
working memory capacity were constrained to equality. This
model was also preferred, being 6.03 times more likely than the
freely estimated model, BF
01
= 6.03, P(H
0
jData) = .86. We thus
find evidence both for the hypothesis that the predictive path from
working memory capacity is statistically unnecessary and that it
does not reliably differ from the significant predictive path from
attention control. To gain clarity on this apparent contradiction,
we compared the Bayes Factors of the two constrained models.
This reveals that the null model is slightly preferred over the
model with equality constraints, BF
01
= 1.76, P(H
0
jData) = .64,
although the magnitude of the preference appears negligible.
Figure 3 visualizes the contributions of working memory capacity
and attention control relative to the 41% of explained variance in
VA-orient-S.
To better understand what individual variability in visual arrays
performance reflects, we tested the relationship of unique variance
in visual arrays with working memory capacity and attention con-
trol.
7
First, we tested whether visual arrays capacity can predict
attention control uniquely from working memory capacity. If var-
iance in visual arrays reflects nothing more than the capacity of
working memory, then visual arrays should not predict unique var-
iance in attention control. However, the model (see Figure 4) does
show that VA-orient-S uniquely predicts attention control above
and beyond working memory capacity, uniquely accounting for
21.2% of the variance in attention control (based on squaring the
path value of .46 between visual arrays and attention control). Fur-
thermore, this freely estimated model is strongly preferred over a
model where the selective visual arrays task and working memory
tasks are loaded on a single predictive factor, BF
01
= 119,593.70,
P(H
0
jData) ..999. This is consistent with the notion that indi-
vidual differences in selective visual arrays performance repre-
sents more than just the number of items stored in visual working
memory.
Next, we conducted a model with visual arrays and attention
control uniquely predicting working memory capacity. If storage
capacity, independent of attention control, is reflected in visual
arrays capacity score, then it would be expected to predict working
memory capacity uniquely from attention control. The model (see
Figure 5) suggests that this is not the case. The kcapacity score on
VA-orient-S did not predict working memory capacity above and
beyond attention control, and a model with a null predictive path
from the selective visual arrays factor was preferred over a model
where this path was estimated, BF
01
= 10.633, P(H
0
jData) =
.914.
8
However, a model with the two predictive paths were
Table 1
Data Set 1 –Exploratory Factor Analysis With Oblimin Rotation
Factor
Variable F1 F2
OSpan 0.74 0.13
SymSpan 0.76 0.06
RotSpan 0.62 0.24
VA-orient-S 0.12 0.57
Antisaccade 0.08 0.59
Flanker 0.02 0.29
Stroop 0.20 0.43
Note. VA = visual arrays.
7
Note that all models in this section are mathematically equivalent in
terms of how well they explain the underlying covariance structure (i.e.,
their fit indices are identical). Thus, these models should not be regarded as
independent pieces of evidence, as they all model exactly the same overall
covariance. However, apportioning this covariance in different ways is
useful for modeling and assessing the plausibility of alternative models and
the effects of placing constraints upon those (equally explanatory) models.
The same is true for similar models in our other data sets.
8
It should be noted that this test is equivalent to test in which the VA-
orient-S task is loaded directly onto the attention control factor.
8MARTIN ET AL.
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constrained to equality was also preferred to the freely estimated
model, BF
01
= 3.279, P(H
0
jData) = .766, indicating that the two
paths are not reliably different from one another.
We conducted a final structural equation model to rule out proc-
essing speed as a potential confounding factor. We tested whether
processing speed and working memory capacity can mediate the
attention control –VA-orient-S relationship (see Figure 6).
9
Work-
ing memory capacity only partially mediated the path from atten-
tion control to VA-orient-S; processing speed did not mediate the
path from attention control to VA-orient-S. Therefore, the direct
effect of attention control on individual differences in kcapacity
scores cannot be attributed to processing speed or working mem-
ory capacity.
In summary; the exploratory analysis revealed that the selective
visual arrays loaded more so with measures of attention control
than working memory capacity and the structural equation model
revealed that only attention control, not working memory capacity,
uniquely predicted variance in VA-orient-S. Likewise, after control-
ling for working memory capacity, VA-orient-S predicted additional
variance in attention control. Finally, processing speed was not able
to account for the attention control –VA-orient-S relationship.
Overall, the results from Data Set 1 suggest that the VA-orient-S
task shares substantial variance with attention control independently
from working memory capacity. These findings are consistent with
studies by Fukuda and Vogel (2009,2011) showing an important
role for attention control processes in visual arrays performance.
Data Set 2
The tasks used in Data Set 1 and Data Set 2 were very similar.
There were some differences in the number of trials in the flanker
and Stroop tasks. Also, the Stroop task in Data Set 2 included neu-
tral trials (though they were excluded from the present analysis).
Other than that, there were no major differences in the administra-
tion of the tasks. In Data Set 2 there were a total of 342 subjects
with no more than 7% missing values for any one task. These data
were collected from 2015–2017 and are associated with the fol-
lowing publications: Draheim et al. (2018) and Tsukahara et al.
(2016). The same set of analyses were conducted for this data as
in Data Set 1.
Figure 2
Structural Equation Model From Data Set 1 With the Unique Relationships of Working Memory
Capacity and Attention Control to VA-Orient-S
Note. Bold numbers indicate significant values based on p,.05. VA = visual arrays.
Figure 3
Pie Chart Representing the Contributions Uniquely From
Working Memory Capacity/Attention Control and Common
Variance in the 41% of Explained Variance in VA-Orient-S
Note. VA = visual arrays.
9
As specified, this model (and all such models we construct) assumes
that working memory capacity and processing speed share no residual
correlation beyond that explained by their mutual relationship with
attention control. To test this assumption, we specified a post hoc structural
equation model with attention control predicting both working memory
capacity and processing speed and estimated the residual correlation
between the latter factors (Figure S1). This revealed a large but
nonsignificant negative correlation (r=.67, p= .26) between the residual
nonattention control-related working memory capacity and processing
speed variance. Because this residual correlation was not significant, and
because this path would be tangential to the goal of explaining away the
direct effect relating attention control to VA-orient-S performance, we do
not estimate the correlation in our mediation analyses.
VISUAL ARRAYS AND ATTENTION CONTROL 9
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Exploratory Factor Analysis
We conducted an exploratory factor analysis using principal
axis factoring with two factors and an oblimin rotation (Table 2).
Two factors were specified because scree plot and parallel analysis
suggested that the number of factors was two, although only one
factor had an eigenvalue greater than 1. The OSpan, SymSpan,
and RotSpan loaded most strongly onto the first factor (a working
memory capacity factor). The antisaccade and flanker all loaded
most strongly onto the second factor (an attention control factor).
The Stroop task had poor loadings on both factors, each under .20.
The VA-orient-S, meanwhile, loaded very similarly on both
factors. The two factors correlated moderately at r= .6. The ex-
ploratory factor analysis supports the view that the VA-orient-S
task shares considerable variance with putative measures of atten-
tion control independent of working memory capacity but relates
to both constructs to a similar degree.
Structural Equation Models
We conducted a structural equation model with working mem-
ory capacity and attention control predicting kcapacity scores on
the VA-orient-S task (see Figure 7). Only attention control
uniquely predicted variance in the VA-orient-S task. We compared
this model to a “null”model in which the working memory
capacity –VA-orient-S path was set to zero. The “null”model
was 6.07 times more likely; BF
01
= 6.07, P(H
0
jData) = .86. How-
ever, as in Data Set 1, the predictive paths did not reliably differ
and a model where both paths were constrained to equality was
preferred to the freely estimated model, BF
01
= 13.79, P(H
0
j
Data) = .93. Comparing the “null”and “equal”models, the latter
was slightly preferred, BF
10
= 2.26, P(H
1
jData) = .70. Figure 8
visualizes the relative contributions of working memory capacity
and attention control to the 34% of explained variance in VA-
orient-S.
Figure 4
Structural Equation Model From Data Set 1 With the Unique Relationships of
Visual Arrays and Working Memory Capacity to Attention Control
Note. Bold numbers indicate significant values based on p,.05. VA = visual arrays.
Figure 5
Structural Equation Model From Data Set 1 With the Unique Relationships of Visual Arrays and
Attention Control to Working Memory Capacity
Note. Bold numbers indicate significant values based on p,.05. VA = visual arrays.
10 MARTIN ET AL.
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Next, we tested whether visual arrays capacity can predict atten-
tion control uniquely from working memory capacity. If variance
in visual arrays reflects nothing more than the capacity of working
memory, then visual arrays should not predict unique variance in
attention control. However, the model (see Figure 9) does show
that VA-orient-S uniquely predicts attention control above and
beyond working memory capacity. Furthermore, the predictive
factors could not be combined without loss of fit, and the depicted
model was strongly preferred, BF
10
= 25.81, P(H
1
jData) = .96.
This is further evidence that individual differences in VA-oreint-S
performance represents more than just the number of items stored
in visual working memory.
We then conducted a model with visual arrays and attention con-
trol uniquely predicting working memory capacity. If storage
capacity, independent of attention control, is reflected in visual
arrays capacity score, then it would be expected to predict working
memory capacity uniquely from attention control. The model (see
Figure 10) suggests that this is not the case. The kcapacity score on
VA-orient-S did not predict working memory capacity above and
beyond attention control. Furthermore, a “null”model where the
predictive visual arrays path was set to zero was preferred to
the freely estimated model, BF
01
= 6.06, P(H
0
jData) = .86.
Additionally, and contrary to Data Set 1, the freely estimated model
was slightly preferred to a model with the predictive paths con-
strained to equality, BF
10
=2.09,P(H
1
jData) = .68. Thus, for Data
Set 2, estimating the predictive path from visual arrays to working
memory capacity was statistically superfluous. Put differently,
attention control accounted for the relationship between selective
visual arrays and working memory capacity in this model.
Finally, we conducted a structural equation model to rule out
processing speed as a potential confounding factor.
10
We tested
whether processing speed and working memory capacity can
mediate the attention control –VA-orient-S relationship (see
Figure 11). Working memory capacity only partially mediated the
path from attention control to VA-orient-S; processing speed did
not mediate the path from attention control to VA-orient-S.
Figure 6
Structural Equation Model With Processing Speed and Working Memory Capacity Mediating the
Attention Control –VA-Orient-S Relationship
Note. FL_Cong_RT = mean reaction time on congruent trials in the Flanker task; Str_Cong_RT = mean reaction
time on congruent trials in the Stroop task. We multiplied the FL_Cong_RT and Str_Cong_RT values by 1to
reflect shorter reaction times as higher processing speed. To make this evident in the figure, the loadings onto the
processing speed factor are shown to be negative. Dotted lines represent paths that were not statistically significant,
p..05. VA = visual arrays. Bold numbers indicate significant values based on p,.05. The indirect effect through
working memory capacity, but not processing speed, was statistically significant.
10
As in Data Set 1, we conducted a post hoc structural equation model
estimating the residual correlation between working memory capacity and
processing speed, accounting for attention control (see Figure S2). This
was done because the mediation model tacitly assumes no residual
correlation between working memory capacity and processing speed
independent of attention control, which could contribute to lack of model
fit (although model fit was excellent). The residual correlation was not
significant (r=.08, p= .70).
VISUAL ARRAYS AND ATTENTION CONTROL 11
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Therefore, the effect of attention control on individual differences
in kcapacity scores cannot be attributed to processing speed or
working memory capacity.
Overall, the results replicated what was found in Data Set 1.
However, the unique relationship of attention control was numeri-
cally weaker than in Data Set 1. Converging evidence from all
four models suggested that VA-orient-S reflects attention control
to a greater degree than storage capacity. The exploratory analysis
was not as clean as in Data Set 1, but it still suggested that VA-ori-
ent-S wanted to load with measures of attention control (no memory
storage demand) just as much with working memory capacity tasks
(high memory storage demand). The structural equation models
showed that attention control, but not working memory capacity,
uniquely predicted variance in kcapacity scores on the VA-orient-S
task. The total variance in VA-orient-S was less than in Data Set 1,
and more of the variance explained was contributed by common
variance between attention control and working memory capacity.
On the one hand, our theoretical position identifies much of the var-
iability in working memory capacity with individual differences in
attention control (Engle et al., 1999). On the other hand, we hesitate
to endorse this explanation for the pattern of results in Data Set 2
because the current data are not conducive to a stringent test and
disconfirmation of that hypothesis. Finally, processing speed was
not able to account for the attention control–visual arrays
relationship.
Data Set 3
The tasks in Data Set 3 are more diverse than in Data Sets 1 and
2. There were three different versions of the visual arrays task; VA-
color, VA-orient, VA-orient-S. There were also two additional
measures of working memory capacity, the Running Spatial and
Running Digit Spans. The attention control tasks were the same as
those used in Data Set 2. Because there were additional visual
arrays tasks, we were able to test additional models to better under-
stand what factors might affect the degree to which visual arrays
performance reflects visual working memory or attention control. In
Data Set 3, there were 568 subjects and no more than 2% missing
values on any task. These data were collected from 2011–2013 and
Figure 7
Structural Equation Model From Data Set 2 With the Unique Relationships of Working Memory
Capacity and Attention Control to VA-Orient-S
Note. VA = visual arrays. Bold numbers indicate significant values based on p,.05.
Figure 8
Pie Chart Representing the Contributions Uniquely From Working
Memory Capacity/Attention Control and Common Variance
Between the Two in the 34% of Explained Variance in VA-Orient-S
Note. VA = visual arrays.
Table 2
Data Set 2 –Exploratory Factor Analysis With Oblimin Rotation
Factor
Variable F1 F2
OSpan 0.71 0.03
SymSpan 0.84 0.03
RotSpan 0.80 0.06
VA-orient-S 0.31 0.33
Antisaccade 0.01 0.78
Flanker 0.04 0.37
Stroop 0.16 0.13
Note. VA = visual arrays.
12 MARTIN ET AL.
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are associated with the following publications: Draheim et al.
(2016,2018), Martin et al. (2019),andShipstead et al. (2016).
Exploratory Factor Analysis
We conducted an exploratory factor analysis using principal
axis factoring with two factors and an oblimin rotation (Table 3).
Only one factor had an eigenvalue greater than 1, scree plot sug-
gested two factors, and parallel analysis suggested three factors.
When a model with three factors was specified only the Stroop
task loaded onto the third factor, so we decided on a two-factor
model. The OSpan, SymSpan, RotSpan, RunSpatial, and RunDigit
loaded most strongly onto the first factor (a working memory
capacity factor). The visual arrays task all loaded strongly onto the
second factor. The antisaccade loaded about equally on both fac-
tors. The flanker and Stroop did not load well onto either factor,
each loading under .30. The two factors were highly correlated,
r= .8.
Structural Equation Models
We conducted a structural equation model with working mem-
ory capacity and attention control predicting kcapacity scores on
each visual arrays task (see Figure 12). The nonselective visual
arrays task, VA-color and VA-orient, were uniquely predicted by
only working memory capacity. The selective visual array task,
VA-orient-S, was uniquely predicted only by attention control. We
tested this model against a “null”model in which all the nonsigni-
ficant paths were set to zero. The “null”model was greater than
1,100 times more likely than the freely estimated model, BF
01
=
1115.78, P(H
0
jData) ..99. We also tested a model where each
predictive path from attention control and working memory
Figure 9
Structural Equation Model From Data Set 2 With the Unique Relationships of Visual Arrays and
Working Memory Capacity to Attention Control
Note. VA = visual arrays. Bold numbers indicate significant values based on p,.05.
Figure 10
Structural Equation Model From Data Set 2 With the Unique Relationships of Visual Arrays and
Attention Control to Working Memory Capacity
Note. VA = visual arrays. Bold numbers indicate significant values based on p,.05.
VISUAL ARRAYS AND ATTENTION CONTROL 13
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capacity were constrained to equality (within task) across the
three visual arrays task types. This model was also strongly
preferred to the freely estimated model, BF
01
= 3596.19, P(H
0
j
Data) ..99. Thus, the magnitude of prediction for working
memory capacity versus attention control cannot be said to vary
across task type.
Keeping the important caveat that the magnitude of the working
memory capacity and attention control predictive paths do not reli-
ably differ for selective versus nonselective visual arrays, the pat-
tern of added incremental validity favors the interpretation that
attention control adds prediction over and above working memory
capacity only for selective visual arrays, but not nonselective vis-
ual arrays. For nonselective visual arrays, the pattern is reversed.
This is not to say that attention control does not play any role in
nonselective visual arrays tasks, nor that individual differences in
working memory capacity are orthogonal to selective visual arrays
performance. There is, after all, a considerable amount of common
variance explaining performance in each task type. However, it is
consistent with the notion that having a selective component in the
visual arrays task increases attention control demands. The unique
and common contributions of working memory capacity and atten-
tion control relative to the amount of explained variance in each
visual array task is illustrated in Figure 13. In the model, working
memory capacity and attention control explained 45% of variance
Figure 11
Structural Equation Model With Processing Speed and Working Memory Capacity Mediating the
Attention Control –VA-Orient-S Relationship
Note. FL_Cong_RT = mean reaction time on congruent trials in the Flanker task; Str_Cong_RT = mean
reaction time on congruent trials in the Stroop task. We multiplied the FL_Cong_RT and Str_Cong_RT val-
ues by 1toreflect shorter reaction times as higher processing speed. To make this evident in the figure, the
loadings onto the processing speed factor are shown to be negative. Dotted lines represent paths that were
not statistically significant, p..05. VA = visual arrays. Bold numbers indicate significant values based on
p,.05. The indirect effect through working memory capacity, but not processing speed, was statistically
significant.
Table 3
Data Set 3 –Exploratory Factor Analysis With Oblimin Rotation
Factor
Variable F1 F2
OSpan 0.80 0.11
SymSpan 0.72 0.06
RotSpan 0.76 0.02
RunSpatial 0.49 0.37
RunDigit 0.57 0.11
VA-color 0.06 0.72
VA-orient 0.08 0.81
VA-orient-S 0.11 0.69
Antisaccade 0.33 0.31
Flanker 0.07 0.18
Stroop 0.28 0.04
Note. VA = visual arrays.
14 MARTIN ET AL.
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in the VA-color task, 37% of variance in the VA-orient task, and
52% of variance in the VA-orient-S task.
As discussed in the Introduction, there may be differences
between the different versions of visual arrays. The VA-color and
VA-orient do not require selecting/or filtering out any items in the
display, whereas the VA-color-S and VA-orient-S do. Vogel and
colleagues have shown that effectively filtering out distractor
items from target items in the visual arrays tasks differentiates
high capacity and low capacity individuals (Vogel & Machizawa,
2004;Vogel, McCollough, et al., 2005). To test for a differentia-
tion between the selective and nonselective visual arrays tasks we
conducted a structural equation model with VA-orient-S loading
onto its own VA Selective factor and VA-color and VA-orient
loading onto a VA nonselective factor. The results of the model
(see Figure 14) showed that working memory capacity and the VA
selective factor uniquely predicted attention control, but the VA
nonselective factor did not, although the path values do not reli-
ably differ, BF
01
= 22.43, P(H
0
jData) = .96. This suggests that
the selective filtering in the visual arrays task predicts attention
control over and above the nonselective versions.
Next, we conducted a model with visual arrays and attention
control uniquely predicting working memory capacity. If storage
capacity, independent of attention control, is reflected in visual
arrays capacity score then it would be expected to predict working
memory capacity uniquely from attention control. Again, we split
the visual arrays task into selective and nonselective factors. The
model showed that only attention control and nonselective visual
arrays were uniquely predictive of working memory capacity (see
Figure 15). Setting the nonsignificant path from selective visual
arrays to zero did not harm model fit, BF
01
= 22.83, P(H
0
jData) =
.96. We also tested a model where the predictive paths for the two
visual arrays factors were constrained to be equal. While this con-
strained factor was slightly preferred over the freely estimated
model, BF
01
= 2.66, P(H
0
jData) = .73, adding this constraint did
decrease model fit according to a chi-square test, Dv
2
(1) = 4.39,
p= .04.
11
Data Set 4
In Data Set 4 there were a total of 215 subjects, each with less
than 3% missing data for any task. These data were collected from
2009–2010 and are related to the following publications: Shipstead
et al. (2012,2014,2015).
The tasks in Data Set 4 are similar to those in Data Set 3. The
main difference is that there was an additional visual arrays task
for a total of four versions of the task; VA-color, VA-orient, VA-
color-S, and VA-orient-S. This is the only data set that has more
than one of each visual array version (selective and nonselective),
which allows us to more strongly test differentiation between these
versions. However, the sample size is not very large. Data Set 4
also does not contain the Rotation Span and Running Spatial Span,
but it does include the Running Letter span.
Exploratory Factor Analysis
In an exploratory factor analysis (Table 4), three factors had an
eigenvalue greater than 1, scree plot suggested two factors, and paral-
lel analysis suggested three factors. The visual arrays tasks and anti-
saccade preferred to load onto the first factor. The RunLetter and
RunDigit preferred to load onto their own factor (the second factor)
and the OSpan, SymSpan, and Stroop preferred to load together. The
flanker did not load well onto any factor, each loading under .30. The
factors correlated from .4–.5 with each other. Although the explora-
tory factor analysis suggests the running span and complex span tasks
can be treated as separate factors, for the sake of comparison with the
previous data sets we conducted further models combing the tasks
onto a single working memory capacity factor. Note that we did run
the analysis with them separated but the overall interpretation of the
models remained the same.
Figure 12
Structural Equation Model From Data Set 3 With the Unique Relationships of Working Memory
Capacity and Attention Control to Each Visual Arrays Task
Note. VA = visual arrays. Bold numbers indicate significant values based on p,.05.
11
We also conducted a model with working memory capacity and
processing speed mediating the attention control-visual arrays relationship;
the interpretation was the same as in Data Sets 1 and 2 (see Figure S3 and
Figure S4).
VISUAL ARRAYS AND ATTENTION CONTROL 15
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Structural Equation Models
We conducted a structural equation model with working mem-
ory capacity and attention control predicting kcapacity scores on
each visual array task (see Figure 16). Only attention control, not
working memory capacity, uniquely predicted individual differen-
ces in visual arrays kcapacity scores, regardless of the type of
visual arrays task. We compared this model against a “null”
model in which all the nonsignificant working memory capacity
paths were set to zero, the “null”model was strongly preferred,
BF
01
= 13,889.01, P(H
0
jData) ..99. However, as with Data
Set 3, constraining paths from working memory capacity and
attention control to equality for each visual array task did not
worsen model fit, BF
01
= 2098.20, P(H
0
jData) ..99. However,
of the constrained models, the “null”model was preferred,
BF
01
= 6.62, P(H
0
jData) = .87. The unique and common contri-
butions of working memory capacity and attention control
relative to the amount of explained variance in each visual array
task is illustrated in Figure 17. In the model, working memory
capacity and attention control explained 35% of variance in the
VA-color task, 34% of variance in the VA-orient task, 35% of
variance in the VA-color-S task, and 42% of variance in the VA-
orient-S task. The model (see Figure 16) is also explaining most
of the variance between the visual arrays tasks (this is indicated
by the residual correlations on the far right of the model).
The VA-color and VA-color-S both contained trials with set-
sizes four, six, and eight. This allowed us to compare the effects
of set-size and selective components of the task. We conducted a
structural equation model with the set-size and selective compo-
nents separated out as; VA-color-4, VA-color-6, VA-color-8,
VA-color-S-4, VA-color-S-6, and VA-color-S-8 (see Figure 18).
Overall, the model does not suggest much of an effect of set-
size; in fact, working memory capacity and attention control are
slightly more related to visual arrays performance at smaller
Figure 13
Pie Chart Representing the Contributions Uniquely From Working Memory Capacity/Attention
Control and Common Variance Between the Two
Note. The model explained 45% of variance in the VA-color task, 37% of variance in the VA-orient task, and
52% of variance in the VA-orient-S task. VA = visual arrays.
Figure 14
Structural Equation Model From Data Set 3 Testing the Unique Relationships of VA Selective,
VA Nonselective, and Working Memory Capacity to Attention Control
Note. VA = visual arrays. Bold numbers indicate significant values based on p,.05.
16 MARTIN ET AL.
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set-sizes—contrary to a purely storage account of visual arrays.
The largest path numerically, from attention control to visual
arrays occurred at set-size 4 with a selective component. Admit-
tedly post hoc, this does make sense given an attention control
view of visual arrays. Successful filtering of nonrelevant items
on a set-size of four (eight total items in the display) can maxi-
mally reduce the load from eight items to four items. Given that
performance tends to peak at around four items, successful filter-
ing of nonrelevant items can lead to optimal performance. Com-
pare this to successful filtering of nonrelevant items on a set-size
of eight (16 total items in the display). Successful filtering, at
most, would lead to reducing the load from 16 to 8. While this
would likely improve performance, one would still be under non-
optimal load regardless of whether there is a selective component
to the task. Therefore, although attention control would be
involved in performance at lower and higher set-sizes, the impact
on performance would be greatest at lower set-sizes. However,
this would have to be studied more systematically in future studies
to draw any strong conclusions from this pattern of findings.
Next, we tested the same structural equation models as in Data
Set 3 in which we separated out selective and nonselective fac-
tors. In this Data Set, however, we had two task indicators on the
selective factor instead of just one. The model (see Figure 19)
showed that only the selective visual arrays latent factor had
unique variance predictive of attention control. Meanwhile, the
nonselective visual arrays and working memory capacity factors
were not uniquely related to attention control. setting all non-
significant paths to zero did not decrease model fit, and this
model was preferred to the freely estimated one, BF
01
= 40.61
P(H
0
jData) = .98. Further, while constraining the paths from
the visual arrays factors to equality also did not harm model fit,
BF
01
= 8.67, P(H
0
jData) = .90, the “null”model was the pre-
ferred model, BF
01
= 4.66, P(H
0
jData) = .82.
In a model in which selective and nonselective visual arrays are
predicting working memory capacity, neither set of tasks uniquely
predicted working memory capacity (see Figure 20). But note the
path values for attention control and VA nonselective (.46 and .27,
respectively). The nonsignificance of these path values could have
had to do with power issues as this study only had 215 subjects.
This is supported by the fact that the path values in Data Set 4 are
similar to that in Data Set 3 (in which they were significant). This
would support the conclusion that the nonselective visual arrays
tasks do include storage capacity related variance that is independ-
ent of attention control. However, the selective visual arrays tasks
may not.
12
Figure 15
Structural Equation Model From Data Set 3 Testing the Unique Relationships of VA Selective, VA
Nonselective, and Attention Control to Working Memory Capacity
Note. VA = visual arrays. Bold numbers indicate significant values based on p,.05.
Table 4
Data Set 4 –Exploratory Factor Analysis With Oblimin Rotation
Factor
Variable F1 F2 F3
OSpan 0.08 0.31 0.52
SymSpan 0.20 0.04 0.64
RunLetter 0.05 0.69 0.23
RunDigit 0.13 0.82 0.08
VA-color 0.64 0.04 0.06
VA-orient 0.72 0.05 0.02
VA-color-S 0.67 0.02 0.01
VA-orient-S 0.74 0.04 0.01
Antisaccade 0.54 0.01 0.13
Flanker 0.29 0.10 0.21
Stroop 0.16 0.22 0.38
Note. VA = visual arrays.
12
We also conducted a model with working memory capacity and
processing speed mediating the attention control-visual arrays relationship;
the interpretation was the same as in Data Sets 1 and 2 (see Figure S5 and
Figure S6).
VISUAL ARRAYS AND ATTENTION CONTROL 17
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Summary
We began this project as an empirical test of the theoretical na-
ture of visual arrays tasks. Specifically, we tested whether:
1. visual arrays tasks are more closely related to storage-
based measures of working memory capacity or to resist-
ance-to-interference aspects of attention control, and
2. the nature of the visual arrays task (i.e., non-selective or
selective) influences which constructs that type of visual
arrays task primarily reflects.
To address these questions, we conducted a series of statistical
tests across four independently collected data sets. The conserva-
tive interpretation of the overall pattern which emerged across all
four data sets is that visual arrays tasks (as a collective) are at the
very least not a pure measure of working memory capacity but are
multiply determined in terms of attention control and working
memory capacity. The more liberal interpretation is that visual
arrays tasks will reflect attention control more so than working
memory capacity when a selection component is included in the
task. Our pattern of results suggests that whereas nonselective
Figure 16
Structural Equation Model From Data Set 4 With the Unique Relationships of Working Memory
Capacity and Attention Control to Each Visual Array Task
Note. VA = visual arrays. Bold numbers indicate significant values based on p,.05.
Figure 17
Pie Chart Representing the Unique Contributions From Working Memory
Capacity/Attention Control and Common Variance Between the Two
Note. The model explained 35% of variance in the VA-color task, 34% of variance in the
VA-orient task, 35% of variance in the VA-color-S task, and 42% of variance in the VA-ori-
ent-S task. VA = visual arrays.
18 MARTIN ET AL.
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measures of visual arrays reflect some attention control properties
in addition to storage properties of working memory capacity,
selective visual arrays tasks reflect the ability to control and
manipulate attention more so than nonselection versions. Although
the archival nature of these data limits the ability to make causal
interpretations, the body of results as a whole, and their consistent
replication call into question the traditional interpretation of visual
arrays tasks as measures of visual storage capacity. Results and
implications are outlined below.
In all four data sets, the exploratory factor analyses showed that
both nonselective and selective visual arrays tasks loaded onto a
separate factor from accepted working memory capacity tasks,
preferring to load with other attention control tasks, or at least
with the antisaccade task (our most reliable measure of attention
control). Model fit and parsimony were generally optimized when
the selective visual arrays task was predicted by an attention
control factor only (i.e., when the path from working memory
capacity to visual arrays was set to zero), rather than by both
Figure 18
Structural Equation Model From Data Set 4 With the Unique Relationships of Working Memory
Capacity and Attention Control to Visual Arrays Broken Down Into Set-Sizes and Selective
Components
Note. VA = visual arrays. Bold numbers indicate significant values based on p,.05.
Figure 19
Structural Equation Model From Data Set 4 Testing the Unique Relationships of VA Selective, VA
Nonselective, and Working Memory Capacity to Attention Control
Note. VA = visual arrays. Bold numbers indicate significant values based on p,.05.
VISUAL ARRAYS AND ATTENTION CONTROL 19
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attention control and working memory capacity, although these
simultaneously estimated paths were not statistically different
from one another. Furthermore, selective visual arrays tasks
uniquely predicted attention control over and above working mem-
ory capacity and nonselective visual arrays. In contrast, nonselective
visual arrays tasks uniquely predicted working memory capacity
over and above attention control and selective visual arrays. These
results suggest that attention control related variance is at least as
predictive of selective visual arrays than is working memory
capacity related variance, if not more so. This is not necessarily the
case for nonselective visual arrays tasks.
Discussion
We have already outlined areas of support for the role of atten-
tion control in selective and nonselective visual arrays, including
domain generality, set-size and timing manipulations, and neuro-
physiological data. We will not readdress that evidence here, but
we would like to highlight a few additional interpretations that are
particularly relevant to the overlap in storage and attention control
processes in nonselective and selective visual arrays.
Generally speaking, we believe these results call into question
the idea that visual arrays measures are strictly visuospatial storage
tasks (Luck & Vogel, 1997). Our results echo other findings which
initially broadened the interpretation of the nature of nonselective
visual arrays tasks. Morey and Cowan (2004; see also Saults &
Cowan, 2007), for example, found that when a high verbal load
was added, nonselective visual arrays performance decreased. As
they argued, maintaining the higher verbal load required central
resources (see Baddeley & Hitch, 1974) and when these resources
were occupied, less attention was available for visual arrays per-
formance. This effect was apparent in the performance decre-
ments. In other words, visual arrays performance seemed to be
drawing on central resources rather than visual-specific working
memory resources.
Because this research is archival in nature, we did not propose a
specific mechanistic account of how attention control contributes
causally to performance on selective visual arrays tasks, we find
explanations offered by other researchers appealing. Fukuda et al.
(2015) proposed that attention must be reoriented to only a subset
of manageable items after an initial global capture to the over-
whelming number of items in the display. Work by Emrich and
Busseri (2015) suggests that the return from attention capture
or reorientation toward the array is not the defining feature of
performance on visual arrays tasks. Rather, contralateral delay
activity preceding the array presentation and the subsequent
engagement of the intention to filter was the primary indicator of
performance. This preparatory interpretation also fits with work by
Adams et al. (2015), which suggests that performance on the vis-
ual arrays can be considered in terms of a density function of
attention deployed not only within trial but over the course of the
session. These studies suggest that controlled processes for goal-
maintenance and preventing lapses of attention also play an impor-
tant role in visual arrays performance.
Limitations and Alternative Explanations
Although we have discussed many studies providing evidence for
mechanisms of attention control in visual arrays performance, it is
difficult to determine the extent to which individual variability is due
to one process over another, because causal closure is nearly impossi-
ble to achieve (or to know whether it has been achieved). If we have
failed to adequately measure one or more of our constructs of inter-
est, this could potentially undermine the presented analyses. This
was especially true of Data Sets 1 and 2 in which working memory
capacity was defined solely by complex span measures. Although
Figure 20
Structural Equation Model From Data Set 4 Testing the Unique Relationships of VA Selective, VA
Nonselective, and Attention Control to Working Memory Capacity
Note. VA = visual arrays. Bold numbers indicate significant values based on p,.05.
20 MARTIN ET AL.
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this is less of a concern for the other data sets, the possibility exists,
nonetheless. Furthermore, although we would argue that selective
visual arrays have strong face validity as indicators of attention
control, face validity can also mislead us about what underlying proc-
esses are at play. This is perhaps especially true given that these
results are explicitly interpreted within the context of the executive
attention framework of working memory capacity. As such, it is im-
portant to consider possible explanatory alternatives.
A potential challenge to these results comes from models of
working memory that do not require any kind of supervisory atten-
tion processes (and thus attention control) to account for differen-
ces in interference. One apparently competing framework to the
one offered here proposes that the ability to flexibly make, break,
and update arbitrary bindings between items in working memory
accounts for many interference effects (Oberauer, 2002;Oberauer
et al., 2007;Schubert & Rey-Mermet, 2019;Wilhelm et al., 2013).
This perspective posits no explicit role for supervisory or con-
trolled attention to form or remove bindings. One way this inter-
pretation might account for performance on a trial of a selective
visual arrays task resembles that of Fukuda et al. (2015) and pro-
ceeds thus: Upon the first presentation of a target array, all items
within the array are bound together into a single memory representa-
tion. Individual differences in unbinding will determine the degree to
which a person successfully removes nontarget items from the mem-
ory representation. Successfully (and rapidly) removing nontargets
may improve change-detection accuracy by reducing memory stor-
age demands and increasing the likelihood that memory targets will
be successfully retrieved in time to respond to the test array.
We do not regard this binding account as problematic. In fact,
we regard it as being potentially compatible with our own, pro-
vided that binding and unbinding are construed as capacity-limited
control processes (Allen et al., 2014;Fukuda & Vogel, 2009,
2011;Fukuda et al., 2015;Martin et al., 2019;Rizio & Dennis,
2013;Shipstead et al., 2016;Wang et al., 2019; but see Allen et
al., 2006). According to the executive attention account of work-
ing memory capacity, whereas individual differences in working
memory represent the ability to form and maintain bindings, the
role of executive attention is twofold in nature, both allowing for
the creation of bindings as well as unbinding or disengaging from
no longer relevant information. This unbinding aspect, which is
present in the selection but absent in the nonselection visual
arrays, would explain this difference between variance shared with
and independent of working memory capacity (for a more thorough
discussion on the functions of maintenance and disengagement as
they relate to binding and unbinding of memory representations, see
also Martin et al., 2019;Shipstead et al., 2016). The main difference
between the executive attention and binding accounts seems to be a
disagreement on whether this process of binding and unbinding is
related to the control of attention (Shipstead et al., 2016).
Additionally, we have received a significant amount of feedback
regarding the nature of other processes that might underlie perform-
ance on the visual arrays task including, but not limited to, speed of
processing and capacity. One possibility, for example, is that individ-
uals who are able to process data more rapidly are better able to
encode the arrays, resulting in higher performance (Vogel et al.,
2006). Alternatively, those with faster speed of processing may be
able to perform all the necessary information processing steps (what-
ever they may be) more quickly and completely than those with
slower speed of processing. This is especially concerning given the
time pressures typically imposed by the visual arrays paradigm (as
well as the antisaccade task) and is compounded by concerns that
our attention control tasks are contaminated by construct-irrelevant
sources of variation (e.g., speed and capacity demands). To address
this concern, we conducted post hoc mediation models where we
attempted to eliminate the effect of attention control on visual
arrays performance by way of speed of processing and working
memory capacity. For selective visual arrays, we were consistently
unable to do so. This indicates that the observed relationships
between attention control and selective visual arrays are not a mere
measurement artifact due to speed of processing. One important ca-
veat, however, is that speed of processing in these models is indi-
cated by RT on congruent Stroop and flanker trials, to which we
were limited by the archival nature of these data. Future studies
should include additional processing speed measures, such as one
or more inspection time tasks (Kranzler & Jensen, 1989), to further
explore this possibility.
A second alternative explanation of our results is that the com-
plex-span measures, running span measures, and visual arrays meas-
ures are reflecting distinct aspects of working memory capacity. In
fact, our results do suggest that the nonselection visual arrays tasks
are, in some instances, better explained by the more traditional span
measures of working memory capacity. However, the selective visual
arrays tasks were always closely related to nonstorage measures.
Even entertaining the possibility that measures such as the antisac-
cade do impose some burden on memory storage (which seems inev-
itable), such burden is likely minimal compared with the measures of
working memory capacity included here (see Roberts et al., 1994).
Regardless of the specific mechanisms one might propose between
the attention control tasks and visual arrays tasks, these data provide
evidence that the selective visual arrays tasks are primarily associated
with tasks that have little burden on storage capacity than with tasks
thatplaceaheavyburdenonmemorystorage.
One final possibility related to the previous one is that both the visual
arrays task and the antisaccade task might measure some facet of rapid
visual encoding related to working memory and/or attention rather than
something akin to domain-general attention control. The present analy-
ses do not rule out this interpretation, but a recent study by Tsukahara
et al. (in press) gives reason to doubt it. They found that an attention
control factor, defined by the antisaccade, Stroop, and flanker (all visual
tasks), fully mediated the relationships between working memory
capacity, fluid intelligence, and auditory discrimination ability. They
were similarly able to account for the relationship between working
memory capacity and fluid intelligence using a factor definedbythe
antisaccade, a selective visual arrays task (VA-orient-S), and another
visual task argued to reflect attention control. It is arguable why the
above mediations obtained, but what seems clear is that the antisaccade
and selective visual arrays are not reducible merely to indices of rapid
visual attention/memory encoding, since they account for the predic-
tive relationship between domain-general working memory capacity
and fluid intelligence
13
and a domain-specificauditory ability (see
also Shipstead & Yonehiro, 2016).
13
Working memory capacity was defined by two spatial complex spans
(the symmetry and rotation spans) and one verbal task (the operation span).
Fluid intelligence was defined by one spatial reasoning tests (Raven’s
Advanced Progressive Matrices) and two verbal reasoning tests (Letter sets
[Ekstrom et al., 1976] and Number Series [Thurstone, 1938]).
VISUAL ARRAYS AND ATTENTION CONTROL 21
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Conclusion
We hope that these results highlight the need for detailed and
repeated testing of changes in task design to improve our under-
standing of the constructs reflected by our tasks. Even small
changes in a task may change the cognitive components reflected
by the scores on that task. Although we believe these results to be
convincing in terms of identifying the constructs underlying visual
arrays performance, further inquiry is needed with regard to differ-
ences in the nature of nonselective and selective visual arrays
tasks.
Moreover, these results pose a more general demand to the field:
we cannot assume that tasks reflect the same construct based on
their name, superficial characteristics, or scoring procedure alone.
Determining construct validity requires relying on many different
aspects, psychometric properties, and even sample demographics
(for an integrative framework on construct validity see; Embret-
son, 1983;Embretson, 2017). Experimental studies provide a nec-
essary source of construct validity by clarifying the mechanisms
underlying the response processes in a given task (Cronbach,
1957). But we also have to consider correlational studies as a
source of external validity showing convergent and divergent rela-
tionships with other tasks and latent factors (Engle & Martin,
2018). We believe these results are theoretically important not
only to individuals who study differences in working memory
capacity and attention control, but also to the experimental com-
munity who may be using a single type of visual arrays task and
assuming the results generalize to all other visual arrays tasks.
Context of Research
This project was inspired by feedback related to our broader
program of research defining and measuring attention control (see
Draheim et al., 2018,2021). Specifically, in this line of research
we have been testing the degree to which theoretical versus mea-
surement concerns contribute to poor convergence among tasks
used to measure controlled attention. We have received significant,
warranted pushback regarding this line of research. We have con-
sistently found that versions of the visual arrays (change detection)
task are reliable indicators of controlled attention, particularly
when an attentional filtering/selection component is incorporated
the task (see also Tsukahara et al., in press). However, given the
history of the visual arrays as a measure of visual storage capacity,
we have had several reviewers disagree with this position. To
address these concerns, we reexamined more than a decade of
research to provide an empirical test of our position. We believe
these data support the position that the visual arrays task (with a
selection component) reflects individual differences in attention
control. We believe that by testing an experimental manipulation
at the latent level, we can better understand the extent to which
task manipulations can impact theoretical relationships.
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(Appendices follow)
24 MARTIN ET AL.
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Appendix A
Task Reliability
Table A1
Task Reliability Task Reliability
Data Set 1 Data Set 2
SymSpan .80 SymSpan .80
OSpan .63 OSpan .73
RotSpan .80 RotSpan .83
VA-orient-S .75 VA-orient-S .74
Antisaccade .92 Antisaccade .91
Flanker .69 Flanker .83
Stroop .72 Stroop .75
Data Set 3 Data Set 4
SymSpan .84 SymSpan .84
OSpan .86 OSpan .85
RotSpan .87 RunLetter .81
RunSpatial .84 RunDigit .88
RunDigit .90 VA-color .78
VA-color .84 VA-orient .74
VA-orient .73 VA-color-S .54
VA-orient-S .79 VA-orient-S .70
Antisaccade .81 Antisaccade .85
Flanker .66 Flanker .81
Stroop .60 Stroop .92
Note. VA = visual arrays. Reliabilities for Data Sets 3 and 4 are based on values reported in (Shipstead et al.,
2014,2015). The following methods were used to calculate reliabilities for Data Sets 1 and 2. For SymSpan,
OSpan, and RotSpan, the total number of items recalled in the correct serial position on each trial was used to
calculate cronbach’saas an estimate of reliability. For the VA-orient-S task, within each set size (five and
seven), half of the trials (even/odd split) were used to calculate kscores resulting in a total of four kscore; even
and odd kscores for each set size. The kscores from each set size were averaged to obtain two split-half k
scores for the task to calculate a split-half reliability with a spearman-brown correction as an estimate of reli-
ability. For the antisaccade task, accuracy on each trial was used to calculate a Cronbach’saas an estimate of
reliability. For the flanker and Stroop tasks, within each condition (congruent and incongruent), half of the trials
(even/odd split) were used to calculate mean reaction time per condition. A difference score (incongruent –con-
gruent) was calculated for even and odd trials resulting in two interference effects that were used to calculate a
split-half reliability with a spearman-brown correction as an estimate of reliability.
(Appendices continue)
VISUAL ARRAYS AND ATTENTION CONTROL 25
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Appendix B
Correlation Tables
Table B2
Data Set 2
Variable 1 2 3 4 5 6 7 8 9
1. OSpan
2. SymSpan .57
3. RotSpan .57 .69
4. Antisaccade .31 .38 .45
5. Flanker 2.21 2.25 2.18 2.30
6. Stroop 2.16 2.18 2.24 2.16 .16
7. VAorient_S_k .35 .41 .46 .41 2.20 2.14
8. FL_Cong_RT 2.25 2.28 2.33 2.41 .22 .16 2.29
9. Str_Cong_RT 2.25 2.25 2.31 2.33 .11 .26 2.30 .48
Note. FL_Cong_RT = mean reaction time on congruent trials in the Flanker task; Str_Cong_RT = mean reaction time on congruent trials in the Stroop
task; VA = visual arrays. Computed correlation used Pearson-method with pairwise-deletion. Correlations in bold are statistically significant, p,.05.
Table B1
Data Set 1
Variable 1 2 3 4 5 6 7 8 9
1. OSpan
2. SymSpan .53
3. RotSpan .46 .63
4. Antisaccade .27 .32 .43
5. Flanker .09 2.15 2.17 2.16
6. Stroop .02 2.11 .09 2.17 .17
7. VAorient_S_k .24 .39 .44 .46 2.14 2.16
8. FL_Cong_RT 2.12 2.21 2.21 2.37 .15 .25 2.15
9. Str_Cong_RT 2.12 2.23 2.26 2.34 .12 .32 2.28 .49
Note. FL_Cong_RT = mean reaction time on congruent trials in the Flanker task; Str_Cong_RT = mean reaction time on congruent trials in the Stroop
task; VA = visual arrays. Computed correlation used Pearson-method with pairwise-deletion. Correlations in bold are statistically significant, p,.05.
(Appendices continue)
26 MARTIN ET AL.
This document is copyrighted by the American Psychological Association or one of its allied publishers.
This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.
Received February 6, 2020
Revision received December 15, 2020
Accepted January 7, 2021 n
Table B4
Data Set 4
Variable 12345678910111213141516171819
1. OSpan
2. SymSpan .50
3. RunLetter .48 .45
4. RunDigit .40 .36 .65
5. Antisaccade .20 .40 .33 .34
6.. Flanker 2.16 2.23 2.15 2.18 2.28
7. Stroop 2.16 2.25 .12 .03 .13 .20
8. VAcolor_k .29 .40 .29 .40 .41 2.24 .12
9. VAorient_k .26 .39 .29 .39 .42 2.20 .09 .59
10. VAcolor_S_k .19 .31 .25 .33 .42 2.23 2.15 .47 .40
11. VAorient_S_k .21 .36 .36 .42 .45 2.22 2.23 .44 .59 .54
12. VAcolor_k.4 .23 .36 .26 .34 .42 2.20 .07 .83 .50 .38 .35
13. VAcolor_k.6 .28 .35 .31 .38 .35 2.18 .11 .85 .51 .40 .41 .68
14. VAcolor_k.8 .22 .32 .20 .31 .31 2.22 .12 .88 .50 .41 .38 .60 .54
15. VAcolor_S_k.4 .19 .30 .24 .30 .46 2.23 .10 .54 .51 .64 .48 .45 .46 .48
16. VAcolor_S_k.6 .16 .20 .24 .22 .36 2.18 .09 .35 .33 .72 .46 .33 .34 .27 .46
17. VAcolor_S_k.8 .11 .23 .15 .26 .24 2.15 2.14 .29 .22 .85 .36 .21 .23 .28 .31 .33
18. FL_Cong_RT .20 .38 .20 .24 .45 2.83 2.27 .36 .27 .36 .32 .33 .30 .30 .39 .23 .26
19. Str_Cong_RT .15 .42 .26 .30 .36 2.16 2.24 .44 .38 .39 .37 .41 .39 .36 .37 .21 .33 .43
Note. FL_Cong_RT = mean reaction time on congruent trials in the Flanker task; Str_Cong_RT = mean reaction time on congruent trials in the Stroop
task; VA = visual arrays. Computed correlation used the Pearson method with pairwise-deletion. Correlations in bold are statistically significant, p,.05.
Table B3
Data Set 3
Variable 12345678910111213
1. OSpan
2. SymSpan .54
3. RotSpan .53 .68
4. RunSpatial .53 .61 .60
5. RunDigit .52 .44 .49 .56
6. Antisaccade .38 .45 .44 .48 .40
7. Flanker 2.11 2.15 2.17 2.22 2.14 2.19
8. Stroop 2.30 2.19 2.18 2.24 2.23 2.22 .09
9. VAcolor_k .43 .47 .48 .59 .47 .42 2.15 2.23
10. VAorient_k .36 .46 .43 .55 .35 .38 2.18 2.17 .59
11. VAorient_S_k .43 .51 .50 .58 .47 .50 2.16 2.21 .60 .58
12. FL_Congruent_RT .25 .28 .27 .42 .35 .39 2.37 2.22 .30 .28 .35
13. Str_Congruent_RT .27 .31 .40 .40 .30 .31 2.15 2.24 .37 .30 .42 .50
Note. FL_Congruent_RT = mean reaction time on congruent trials in the Flanker task; Str_Congruent_RT = mean reaction time on congruent trials in
the Stroop task; VA = visual arrays. Computed correlation used Pearson-method with pairwise-deletion. Correlations in bold are statistically significant,
p,.05.
VISUAL ARRAYS AND ATTENTION CONTROL 27
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