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Quantity not quality: The relationship between fluid intelligence
and working memory capacity
Keisuke Fukuda, Edward Vogel, Ulrich Mayr, and Edward Awh
Abstract
A key motivation for understanding capacity in working memory (WM) is its relationship with
fluid intelligence. Recent evidence has suggested a 2-factor model that distinguishes between the
number of representations that can be maintained in WM and the resolution of those
representations. To determine how these factors relate to fluid intelligence, we conducted an
exploratory factor analysis on multiple number-limited and resolution-limited measures of WM
ability. The results strongly supported the 2-factor model, with fully orthogonal factors accounting
for performance in the number-limited and resolution-limited conditions. Furthermore, the reliable
relationship between WM capacity and fluid intelligence was exclusively supported by the number
factor (r = .66), while the resolution factor made no reliable contribution (r = −.05). Thus, the
relationship between WM capacity and standard measures of fluid intelligence is mediated by the
number of representations that can be simultaneously maintained in WM rather than by the
precision of those representations.
Working memory (WM) enables the active maintenance of information in a readily
accessible state. In addition to its core role in most large-scale models of cognition (e.g.,
ACT-R, Anderson, 1993; EPIC, Kieras & Meyer, 1997), a central motivation for research on
working memory is that it exhibits robust correlations with broader measures of intellectual
ability such as scholastic aptitude and fluid intelligence (Cowan et al., 2005; Cowan et al,
2006; Engle, 2002; Engle et al., 1999). The link between WM capacity and fluid intelligence
has been observed across a broad range of experimental paradigms. One prominent approach
has demonstrated correlations between fluid intelligence and WM capacity estimated using
“complex span measures” (e.g., Daneman & Carpenter, 1980; Turner & Engle, 1989) that
were designed to tap into both storage capacity and processing aspects of WM ability (e.g.,
Daneman & Carpenter, 1980; Engle et al, 1999; Kyllonen & Christal, 1990; Turner & Engle,
1989). Moreover, although several studies have emphasized the importance of the
processing component in complex span tasks for the link with fluid intelligence, subsequent
research has shown that even tasks that measure pure storage -- in the absence of secondary
processing loads -- exhibit clear correlations with fluid intelligence (Colom et al, 2005;
Cowan et al. 2005). Specifically, such correlations are revealed when the task design
prevents rehearsal and grouping processes that may skew a “pure” measure of storage
capacity (e.g., Cowan, 2001; Cowan, Chen, & Rouder, 2004; Unsworth & Engle, 2007a) 1.
For example, Cowan et al. (2005) examined the relationship between fluid intelligence and
WM capacity measured in a simple change detection task introduced by Luck and Vogel
(1997). Here, observers saw an array of multiple colored squares and then after a brief delay
Correspondence: Edward Awh, 1227 University, Eugene, Oregon 97405, awh@uoregon.edu, 541 346 4983.
Production Number:R631B
1The core argument is that some types of grouping or rehearsal strategies (e.g., subvocal rehearsal; or the elaboration of memoranda
into meaningful “chunks”) may artificially inflate capacity estimates. Because these strategies are more effective for some subjects
than others, allowing such strategies to determine variance in the capacity measure may obscure real relationships between storage
capacity and other measures.
NIH Public Access
Author Manuscript
Psychon Bull Rev. Author manuscript; available in PMC 2011 March 8.
Published in final edited form as:
Psychon Bull Rev
. 2010 October ; 17(5): 673–679. doi:10.3758/17.5.673.
NIH-PA Author Manuscript NIH-PA Author Manuscript NIH-PA Author Manuscript
indicated whether or not any of the items in a subsequent test array had changed or not.
Although this task did not impose any other attention-demanding tasks or interfering stimuli,
the resulting estimates of WM capacity were reliably correlated with fluid intelligence.
Thus, pure storage capacity alone is linked with the broader construct of fluid intelligence.
Evidence for a link between storage capacity in WM and fluid intelligence is an important
step in our understanding of the basic determinants of intelligence. In particular, such simple
tasks allow for relatively straightforward conclusions regarding the core cognitive
operations that play a role in fluid intelligence, thereby complementing the data from
complex span procedures that tap into a broader range of cognitive abilities, including dual
task coordination, resistance to interference, access to secondary memory, etc. (e.g., Mogle
et al., 2008; Unsworth & Engle, 2007b). Nevertheless, recent research has suggested that
storage capacity in WM may not be a unitary construct. We refer here to a distinction
between the number of items that can be held in working memory and the resolution or
precision of those representations. Xu and Chun (2006) provided neural evidence for such a
dissociation with an imaging study that revealed distinct neural regions whose activity
tracked the number of items that could be stored in working memory on the one hand, and
the complexity of the stored items on the other hand. Given that more precise
representations are required to support performance in memory tasks with complex stimuli,
the results of Xu and Chun (2006) suggest that dissociable neural processes mediate number
and resolution in visual working memory. In line with this hypothesis, Awh, Barton and
Vogel (2007) examined individual differences in the number and resolution of
representations in WM, and found no correlation between these measures (despite having
established the internal reliability of each measure). That is, subjects who could maintain the
largest number of items in working memory were not necessarily the subjects who had the
clearest memories. These data suggest a two-factor model in which number and resolution
represent distinct facets of WM ability.
The two-factor hypothesis raises a fundamental question about the relationship between
working memory storage capacity and fluid intelligence. If number and resolution are
distinct aspect of memory ability, which of these factors mediates the link with fluid
intelligence? At first glance, it is reasonable to expect both factors to predict performance in
standard measures of fluid intelligence. Consider two nonverbal measures of fluid
intelligence that are prevalent in the literature, Raven’s Progressive Matrices and Culture
Fair. In each case, subjects are required to identify a missing item that completes a larger
pattern defined across multiple complex objects.
To illustrate, Figure 1 depicts a problem styled in this fashion. The goal of the task is to
identify the patterns presented across the 8 figures and to indicate which item below (“A”,
“B”, or “C”) completes the pattern. In this example, the correct answer is “C”, consistent
with a pattern in which one additional vertical line appears for each rightward shift in the
matrix. Here, a compelling intuition is that patterns of this kind will be more efficiently
apprehended when more items can be simultaneously kept active in WM. At the same time,
determining the nature of the pattern also requires a sufficiently detailed representation of
these complex objects to capture variations in the critical feature.
The central goal of the present work, therefore, was to provide a rigorous test of which
components of storage capacity in WM mediate the relationship with fluid intelligence. The
procedures we used to measure number and resolution in WM were motivated by recent
evidence that the primary limiting factors in change detection depend critically on the
similarity between the sample items that are encoded into memory, and the test items that
are used to assess those memories (Awh, Barton & Vogel, 2007; Barton, Ester & Awh,
2009; Jiang, Shim & Makovski, 2008; Scolari, Vogel & Awh, 2008). When sample-test
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similarity is low – such that changes are relatively large – then accurate change detection
depends primarily on whether or not the critical item was represented in WM. This is a core
assumption of the analytic procedure for estimating capacity developed by Pashler (1988)
and refined by Cowan (2001). Thus, the probability of detecting such large changes provides
an estimate of how many items were encoded from the sample array. Importantly, this
interpretation of change detection performance has received strong converging support from
studies of neural activity during the delay period of this task. Both electrophysiological
(McCollough, Machizawa, & Vogel, 2007; Vogel & Machizawa, 2004; Vogel McCollough,
& Machizawa, 2005) and functional magnetic resonance imaging studies (Todd & Marois,
2004, 2005; Xu & Chun, 2006) have demonstrated that activity in the parietal cortex rises in
a monotonic fashion as the number of items stored in WM increases. Critically, individual
differences in neural responses during this task show that parietal activity reaches a plateau
at the same set size in which the observer’s capacity has been exhausted (McCollough,
Machizawa, & Vogel, 2007; Vogel & Machizawa, 2004; Todd & Marois, 2005). This strong
link between behavioral measures of (large) change detection and delay-specific neural
activity bolsters the face validity of each method for estimating the number of items stored
in WM. At the same time, both behavioral performance (Awh, Barton & Vogel, 2007) and
neural activity (Xu & Chun, 2006) are qualitatively different when observers are asked to
detect small changes between sample and test stimuli. Given that the same number of items
are stored in these small change tasks (Awh, Barton & Vogel, 2007; Xu & Chun, 2006), we
have argued that errors in detecting these small changes may depend on whether the
representations in WM have sufficient resolution for discriminating between psychologically
similar sample and test items. Thus, the present work employs a small-change detection task
to operationalize resolution in visual WM.
We collected multiple measures of number and resolution in visual WM, enabling a latent
variable analysis that attempted to identify the underlying “pure constructs” that determined
memory performance. This allowed a rigorous evaluation of whether these two aspects of
performance do indeed reflect distinct aspects of memory ability, as proposed by the two-
factor model. In addition, this approach provided a clear test of how these two aspects of
WM capacity relate to fluid intelligence.
Methods
Subjects
79 undergraduate students from University of Oregon participated in for monetary
compensation ($8/hour). Each subject performed the two intelligence tests (Culture Fair test
and RAPM) first and then performed the working memory task.
Fluid intelligence Measures
The Raven’s Advanced Progressive Matrices Test (RAPM) and the Cattell Culture Fair Test
(CFT) were used to estimate individuals’ fluid intelligence. The CFT consists of four subsets
of tasks each of which takes about 2.5 to 4 minutes. The score on each subtest was summed
to create a single metric for the CFT score. We also administered the Raven’s Advanced
Progressive Matrices (RAPM), using Set I as practice and Set 2 for measurement. First,
participants completed four questions on Set I for instruction, and were asked to complete as
many questions in Set II correctly possible in 30 mins. The Raven’s score was calculated as
the sum of correct answers in Set II.
Obtaining Separate Measures of Number and Resolution in Visual WM
To assess number and resolution in visual working memory, we adapted a change detection
procedure employed by Awh, Barton and Vogel (2007). The possible stimuli consisted of
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four geometric shapes that were modeled after the line drawings used in the two non-verbal
measures we used to assess fluid intelligence, Raven’s Progressive Matrices and Culture
Fair. The four shapes included two ovals and two rectangles. Thus, as Figure 2 illustrates,
changes between the possible shapes varied systematically between large changes (e.g.,
when an oval shape changed to a rectangular shape, or vice versa) and small changes (e.g.,
changes from one oval to another, or from one rectangle to the other). As the data will show,
our assumptions regarding which types of changes were “large” and “small” were confirmed
by large and reliable differences in change detection performance; accuracy in the big
change condition was more than twice as high as in the small change condition. Next, we
outline why performance in the large and small change conditions may be determined,
respectively, by the number and the resolution of the representations stored in working
memory.
The rationale was that the detection of large changes would be limited primarily by whether
or not the critical item was stored in working memory, because the changes were large
enough to minimize errors in the process of comparing an item in memory and the
corresponding test item. By contrast, during small change trials we reasoned that even when
the critical item was stored, the subjects’ ability to detect the changes would be primarily
determined by whether the critical item was stored with sufficient resolution to discriminate
the difference between the sample and test items (see Awh, Barton & Vogel, 2007 for
further discussion)2. Finally, we also included change detection trials with highly
discriminable colored squares so that performance in this well-characterized variant of the
change detection procedure could be compared with performance with the geometric shapes.
Stimuli
The stimuli in the change detection procedure were displayed on a centrally positioned light
grey region (19.5 × 19.5 degrees) that appeared over a dark grey background. Sample arrays
contained either 4 or 8 items, evenly divided between the four quadrants of the screen, with
a minimum center-to-center distance of 4 degrees between items. Colored squares (1.5
degrees on each side) were used to generate sample displays during color trials. The possible
colors were red, blue, green, yellow, black and white; these colors were randomly selected
with the constraint that no color appeared more than twice in a single sample array. During
shape trials, sample arrays were created by randomly selecting from the four possible shapes
(1.3 degrees on the short side and 2.5 degrees on the long side) with the constraint that at
least one rectangle and one oval were included in each array.
Procedure
1092 ms after the onset of a central fixation point, a sample array of either four or eight
objects was presented for 500 ms. A 1s retention interval started upon the offset of the
sample array, followed by the presentation of a single test item that remained visible until a
response key was pressed. Subjects reported whether the object was the same object as the
one presented at the same location in the memory array. The change detection procedure
included 9 blocks of 48 trials each. Within each block, 16 trials employed color stimuli (8
“same” and 8 “change” trials, divided equally over set sizes 4 and 8). Set size 4 trials were
included for two reasons. First, there has been some indication in the literature that
performance with smaller set sizes may have a weaker link with fluid intelligence, perhaps
because subjects differ in their ability to handle supra-span displays (Cusack et al, 2009);
2Of course, even in small change trials, the number of items stored determines the upper bound for performance. The experimental
rationale, therefore, rests on the assumption that when the changes are small, the primary source of behavioral variance shifts from
how many items are stored in memory, to whether the stored representations are clear enough to enable the detection of a relatively
subtle change.
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thus including both set sizes allowed us to replicate previous findings that set size may
mediate the strength of the relationship with fluid intelligence. Second, the set size 8 trials
are very difficult (given that they contain approximately twice the number of items that an
average subject can store), and the set size 4 trials may help to keep subjects from deciding
the task is intractable. The remaining 32 trials employed the geometric shapes (16 “same”
and 16 “change” trials, divided equally over set sizes 4 and 8). Shape memory arrays were
created by randomly selecting from the four possible shapes. When one of the shapes
changed (with probability .5), it was replaced by a shape randomly selected from the
remaining three shapes, such that approximately two thirds of change trials involved big
changes (i.e., from oval to rectangle or rectangle to oval) and the remaining one third of
change trials were small changes (i.e., from oval to oval or rectangle to rectangle). To derive
capacity estimates (k), we used the formula first invented by Pashler (1988) and refined by
Cowan (2001) ): (k) = set size * (hit rate − false alarm rate), where k represents the number
of objects stored, set size is the number of items in the sample array, hit rate is the
proportion of “change” trials correctly detected, and false alarm rate is the proportion of
“same” trials that elicited a “change” response. The k formula is a standard metric in the
visual working memory literature, because it corrects for response bias and enables a
common metric of performance across different set sizes3. In the primary SEM analysis, we
used the average k from set size 4 and 8 trials. When the raw correlations between WM
capacity and intelligence were examined separately for each set size, a qualitatively similar
pattern of correlations was observed (see Footnote 5)
Results
First, we employed an exploratory factor analysis to test the hypothesis that two separate
factors account for the number and the resolution of the representations that could be
maintained in visual working memory (see Tables 1. a and b for descriptive statistics and
full correlation matrix).
This analysis included five separate measures of change detection performance defined by
the type of item probed and the size of the change between the sample and test stimulus: (1)
color k (color changes were always big); (2) big oval k (changes from ovals to rectangles);
(3) small oval k (changes from one oval to the other); (4) big rect k (changes from rectangles
to ovals); and (5) small rect k (changes from one rectangle to the other). The two-factor
hypothesis predicted that capacity estimates from the three big change conditions (i.e., color
k, big oval k and big rect k) should load on a single factor related to the number of items that
could be held in working memory, while the two small change conditions (small oval k and
small rect k) should load on a distinct factor related to the resolution or precision of the
representations stored in working memory. The exploratory factor analysis confirmed that
performance in the big and small change trials was best accounted for by a two-factor
model. The three “big change” conditions (color k (.84), big oval k (.88), and big rect k (.
90)) all loaded strongly on a single factor, hereafter referred to as the “number” factor. By
contrast, the “small change” conditions (small oval k (.87), small rect k (.88)) loaded on an
orthogonal factor, hereafter referred to as the “resolution” factor (see Table 2).
There were no significant cross loadings (p= .15). These data therefore conform precisely to
the predictions of the two-factor model, suggesting that number and resolution are distinct
aspects of working memory ability.
3Also, note that a shared pool of “same” trials contributed to “k” estimates in the big and small change conditions. Here again, the
motivation was to provide a common metric for these two types of trials while correcting for the influence of response bias.
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Having found strong support for a two-factor model of storage capacity, we examined which
of these two aspects of storage capacity mediated the relationship with fluid intelligence. We
carried out a confirmatory factor analysis of a model that included two independent factors
for number and resolution and a third factor for fluid intelligence. The two measures of fluid
intelligence loaded strongly on a common factor for fluid intelligence, or “g” (RAPM (.83)
and CFT (.70)). The fit between the overall model and the observed data was excellent (χ2
(13,n = 79) = 10.845, p = .6238, RMSEA = .00, CFI = 1.0, see Figure 3).
Moreover, the analysis demonstrated that the number and resolution factors had very
different relationships with fluid intelligence. The number factor showed a strong positive
correlation with fluid intelligence (r = .66, S.E. = 0.1), but the resolution factor showed no
evidence of a reliable link with fluid intelligence (r = −.05, S.E. = 0.13). Moreover,
constraining the path from mnemonic resolution to fluid intelligence to be 0 did not change
the fit of the model ((χ2Difference (1,n = 79) = .286, p = .59) (Table 3), strengthening the
conclusion that mnemonic resolution was unrelated to fluid intelligence.
These results suggest that the relationship between WM capacity and fluid intelligence is
driven solely by the ability to hold multiple discrete representations in WM, and not by the
clarity of those representations4. Finally, although 79 participants is lower than the number
employed in many analyses of this kind, we note that the standard errors around the
correlations between fluid intelligence and slots (0.1) and resolution (0.13) are small. Thus,
given the very strong contrast between the links observed between fluid intelligence and the
two aspects of capacity (i.e., number and resolution), even a relatively large increase in the
number of observations would be unlikely to change the core conclusions of this study.
Conclusions
The present work provides a new insight into the relationship between WM capacity and
fluid intelligence. Using a simple change detection procedure, we obtained strong support
for a two-factor model of WM capacity, in which the number and resolution of the
representations in WM are determined by distinct aspects of memory ability. This two-factor
model enabled a straightforward test of which aspects of WM capacity mediate its link with
fluid intelligence. The data were very clear. The number of representations that could be
held in WM showed a robust correlation with fluid intelligence (r = .66), while mnemonic
resolution showed no trace of a reliable link with fluid intelligence (r = −.05). Thus, the
relationship between storage capacity in WM and fluid intelligence appears to be mediated
solely by the maximum number of items that can be simultaneously stored in WM, rather
than by the resolution or precision of those representations.
One important consequence of these results is that in designing and selecting working
memory tasks researchers need to be mindful of the aspects they want to have reflected in
the performance scores. Only tasks that assess sensitivity to large visual changes seem to
relate to complex reasoning abilities as assessed in fluid intelligence tasks. Although the
resolution aspect can be assessed reliably, future research is required to assess its external
validity and its generality. One interesting possibility goes back to Spearman’s distinction
4One alternative explanation of the correlation between big change performance and fluid intelligence deserves comment. Given that
big change trials were twice as frequent as small change trials, it is possible that the correlation between big change performance and
intelligence resulted intelligent subject being more likely to detect this contingency. Note, however, that the strength of the
correlations between fluid intelligence and number was very similar across the color and shape change detection trials, even though all
changes in the color condition were big (thereby obviating the need to “notice” this contingency). Moreover, even if big change
performance was affected by whether subjects noticed the greater frequency of those trials, this would not explain why there was no
apparent link between mnemonic resolution and fluid intelligence (despite high internal loadings that demonstrate the reliability of the
resolution measure). Thus, the core conclusion that number and resolution in working memory have different relationships with fluid
intelligence may hold even if sensitivity to trial proportions had an influence on big change performance.
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between general ability (g) and specific abilities (s): Possibly g is reflected in the number of
slots, whereas the resolution aspect reflects domain-specific, and possibly experience-
dependent characteristics of mnemonic processing.
Our findings fall in line with a recent observation that similar “chunk limits” have been
observed in studies of capacity limits during abstract reasoning tasks and storage in WM
(Halford, Cowan, & Andrews, 2007). Halford and colleagues (2007) suggested that a
common attentional resource might be recruited to maintain individuated items in WM on
the one hand, and to apprehend the interrelationships between relevant elements during
reasoning on the other hand. In each case, average capacity estimates hover in the range of
3–4 items or interrelationships. The present data corroborate this finding by demonstrating
that the abilities tracked by these memory and intelligence tasks strongly covary across
individuals. Thus, the number of items that can be held in this online memory system may
be a key limiting factor in our ability to apprehend abstract relationships between novel
items.
Number of Slots or Control over Slots?
The present data reveal a sharp contrast in how fluid intelligence relates to number and
resolution in visual working memory; while a robust correlation was found between the
number and g constructs, no similar link was observed between resolution and g.
Nevertheless, important questions remain regarding the core sources of variability in the
number construct. One intuitive account of this measure is that it reflects variability across
individuals in “how many” slots are available; from this perspective, low capacity
individuals are those that have less space in working memory. An alternative view, however,
is that apparent variations in the number of items stored may instead reflect individual
differences in “filtering efficiency” such that individuals with low capacity have difficulty
excluding irrelevant information from reaching WM (McNab & Klingberg, 2007; Vogel,
McCollough, & Machizawa 2005). In this case, even if the number of slots available was
relatively constant across observers, large variations in WM performance could emerge
based on individual differences in filtering efficiency. Both the “space” and “filtering”
accounts can account for individual differences in the number of relevant items represented
in WM, but they posit distinct reasons for these differences.
In favor of the “filtering” account, a broad range of work has revealed tight correlations
between WM capacity and filtering efficiency (Engle, 2002; Fukuda & Vogel, 2009; McNab
& Klingberg, 2007; Vogel, McCollough, & Machizawa, 2005). Indeed, a recent study
(Cusack et al, 2009) suggested that the link between visual WM and intelligence may be
best explained by selection efficacy during these memory tasks, rather than by the total
amount of “space” in WM5. At the same time, other studies have highlighted cases in which
group differences in memory performance seem better accounted for by variations in
“space” rather than “filtering” (e.g., Cowan et al, 2010; Gold et al., 2006); these results
suggest that it may be useful to maintain a distinction between “space” and “filtering”
effects on WM capacity. So far, it is not clear whether only one of these accounts can
explain all the variation across individuals in the storage of relevant items, or if these
abilities are separate but strongly covarying aspects of memory function. Thus, an important
goal for future work will be to determine whether “space” and “filtering” abilities account
for unique variance in broad measures of intellectual function.
5This argument was based on the observation that correlations between WM capacity and IQ were observed only for arrays larger than
four items. This motivated the hypothesis that those correlations are driven more by the nature of the response to supra-span arrays
rather than capacity per se. In the current data set, the raw correlations with fluid intelligence were similar (and statistically reliable)
between set size 4 (mean r-value = .34) and set size 8 (mean r-value = .38).
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Acknowledgments
Portions of this work were supported by NIH-R01MH087214-01 to E.A. and E.K.V. We thank Nash Unsworth for
valuable discussion of these findings.
References
Anderson, JR. Rules of the Mind. Hillsdale, NJ: Erlbaum; 1993.
Awh E, Barton B, Vogel EK. Visual working memory represents a fixed number of items, regardless
of complexity. Psychological Science 2007;18(7):622–628. [PubMed: 17614871]
Barton B, Ester EF, Awh E. Discrete resource allocation in visual working memory. J Exp Psychol
Hum Percept Perform 2009;35(5):1359–1367. [PubMed: 19803642]
Colom R, Flores-Mendoza C, Quiroga MaA, Privado J. Working Memory and General Intelligence:
The Role of Short-Term Storage. Personality and Individual Differences 2005;39:1005–1014.
Cowan N. The magical number 4 in short-term memory: A reconsideration of mental storage capacity.
Behavioral and Brain Sciences 2001;24:87–185. [PubMed: 11515286]
Cowan N, Chen Z, Rouder JN. Constant capacity in an immediate serial-recall task: A logical sequel to
Miller (1956). Psychological Science 2004;15:634–640. [PubMed: 15327636]
Cowan N, Elliott EM, Saults JS, Morey CC, Mattox SM, Hismjatullina A, Conway ARA. On the
Capacity of Attention: Its Estimation and Its Role in Working Memory and Cognitive Aptitudes.
Cognitive Psychology. 2005
Cowan N, Fristoe NM, Elliott EM, Brunner RP, Saults JS. Scope of attention, control of attention, and
intelligence in children and adults. Memory & Cognition 2006;34(8):1754–1768.
Cowan N, Morey CC, AuBuchon AM, Zwilling CE, Gilchrist AL. Seven-year-olds allocate attention
like adults unless working memory is overloaded. Developmental Science 2010;13:120–133.
[PubMed: 20121868]
Cusack R, Lehmann M, Veldsman M, Mitchell DJ. Encoding strategy and not visual working memory
capacity correlates with intelligence. Psychonomic Bulletin and Review 2009;16(4):641–647.
[PubMed: 19648446]
Daneman M, Carpenter PA. Individual differences in working memory and reading. Journal of Verbal
Learning & Verbal Behavior 1980;19:450–466.
Engle RW. Working memory capacity as executive attention. Current Directions in Psychological
Science 2002;11:19–23.
Engle RW, Tuholski SW, Laughlin J, Conway ARA. Working memory, short-term memory and
general fluid intelligence: A latent variable model approach. Journal of Experimental Psychology:
General 1999;128:309–331. [PubMed: 10513398]
Fukuda K, Vogel EK. Human variation in overriding attentional capture. Journal of Neuroscience
2009;29(27):8726–8733. [PubMed: 19587279]
Gold JM, Fuller RL, Robinson BM, McMahon RP, Braun EL, Luck SJ. Intact attentional control of
working memory encoding in schizophrenia. Journal of Abnormal Psychology 2006;115:658–673.
[PubMed: 17100524]
Halford GS, Cowan N, Andrews G. Separating cognitive capacity from knowledge: a new hypothesis.
Trends in Cognitive Sciences 2007;11:237–242.
Jiang YV, Shim WM, Makovski T. Visual working memory for line orientations and face identities.
Percept Psychophys 2008;70(8):1581–1591. [PubMed: 19064500]
Kieras D, Meyer DE. An overview of the EPIC architecture for cognition and performance with
application to human-computer interaction. Human-Computer Interaction 1997;12:391–438.
Kyllonen PC, Christal RE. Reasoning ability is (little more than) working-memory capacity?!
Intelligence 1990;14:389–433.
Luck SJ, Vogel EK. The capacity of visual working memory for features and conjunctions. Nature
1997 November 20;390:279–281. [PubMed: 9384378]
McCollough AW, Machizawa MG, Vogel EK. Electrophysiological measures of maintaining
representations in visual working memory. Cortex 2007;43(1):77–94. [PubMed: 17334209]
Fukuda et al. Page 8
Psychon Bull Rev. Author manuscript; available in PMC 2011 March 8.
NIH-PA Author Manuscript NIH-PA Author Manuscript NIH-PA Author Manuscript
McNab F, Klingberg T. Prefrontal cortex and basal ganglia control access to working memory. Nature
Neuroscience 2007;11:103–107.
Mogle JA, Lovett BJ, Stawski Rs, Sliwinski MJ. What’s so special about working memory? An
Examination of the relationships among working memory, secondary memory, and fluid
intelligence. Psychological Science 2008;19(11):1071–77. [PubMed: 19076475]
Pashler H. Familiarity and visual change detection. Percept Psychophys 1988;44(4):369–378.
[PubMed: 3226885]
Scolari M, Vogel EK, Awh E. Perceptual expertise enhances the resolution but not the number of
representations in working memory. Psychon Bull Rev 2008;15(1):215–222. [PubMed: 18605506]
Todd JJ, Marois R. Capacity limit of visual short-term memory in human posterior parietal cortex.
Nature 2004;428(6984):751–754. [PubMed: 15085133]
Todd JJ, Marois R. Posterior parietal cortex activity predicts individual differences in visual short-term
memory capacity. Cogn Affect Behav Neurosci 2005;5(2):144–155. [PubMed: 16180621]
Turner ML, Engle RW. Is working memory capacity task dependent? Journal of Memory & Language
1989;28:127–154.
Unsworth N, Engle RW. On the division of short-term and working memory: An examination of
simple and complex spans and their relation to higher order abilities. Psychological Bulletin
2007a;133:1038–1066. [PubMed: 17967093]
Unsworth N, Engle RW. The nature of individual differences in working memory capacity: Active
maintenance in primary memory and controlled search from secondary memory. Psychological
Review 2007b;114:104–132. [PubMed: 17227183]
Vogel EK, Machizawa MG. Neural activity predicts individual differences in visual working memory
capacity. Nature 2004;428(6984):748–751. [PubMed: 15085132]
Vogel EK, McCollough AW, Machizawa MG. Neural measures reveal individual differences in
controlling access to working memory. Nature 2005;438(7067):500–503. [PubMed: 16306992]
Xu Y, Chun MM. Dissociable neural mechanisms supporting visual short-term memory for objects.
Nature 2006;440:91–95. [PubMed: 16382240]
Fukuda et al. Page 9
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Figure 1.
A typical example of a fluid intelligence task
Note: The correct answer is C.
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Figure 2.
Illustration of a sample display (set size varied between 4 and 8), and the single-item probe
display that appeared after a 1 s retention period.
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Figure 3.
Results of the factor analysis. Based on the initial exploratory factor analysis, we generated
three latent factors for g, working memory slots, and working memory resolution. The g
factor was estimated from RAPM and CFT measures. The slots factor was generated from
Color k, Big Oval k, and Big Rect k. Lastly, the resolution factor was generated from Small
Oval k and Small Rect k. The resulting model above was simultaneously tested.
Note: RAPM = Raven’s Advanced Progressive Matrices, CFT = Cattel Culture Fair, Color k
= K estimate from color Conditions, Small Oval k = K estimate from within-categorical oval
conditions, Small Rect k = K estimate from within-categorical rectangle conditions, Big
Oval k = K estimate from big-change oval conditions, Big Rect k = K estimate from big-
change rectangle conditions.
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Table 1.a
Descriptive statistics for WM tasks and intelligence tasks
RAPM CFT Color Small oval k Small rect k Big oval k Big rect k
Mean 22.00 26.19 3.36 1.40 1.16 3.36 3.52
SD 4.61 4.53 0.92 1.13 1.05 1.17 1.13
Range 11.00, 32.00 37.00, 14.00 5.38, 1.06 5.50, −0.49 4.66, −1.17 5.85, 1.11 5.77, 0.81
Skewness −0.27 −0.52 −0.06 0.83 0.57 −0.03 0.00
Kurtosis −0.20 0.46 0.18 1.13 0.80 −0.72 −0.42
Note: RAPM = Raven’s Advanced Progressive Matrices, CFT = Cattel Culture Fair, Color k = K estimate from color Conditions, Small oval k = K estimate from within-categorical oval conditions, Small
rect k = K estimate from within-categorical rectangle conditions, Big oval k = K estimate from cross-categorical oval conditions, Big rect k = K estimate from cross-categorical rectangle conditions.
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Table 1.b
A correlation table for intelligence and WM capacity measures
RAPM CFT Color Small oval k Small rect k Big oval k Big rect k
RAPM 1
CFT .58*** 1
Color .46*** .41*** 1
Small Oval k .06 .00 .22 1
Small Rect k .04 .00 .13 .55*** 1
Big Oval k .44*** .34** .63*** .22 .13 1
Big Rect k .42*** .36** .62*** .06 −.01 .70*** 1
Note: RAPM = Raven’s Advanced Progressive Matrices, CFT = Cattel Culture Fair, Color k = K estimate from color Conditions, Small oval k = K estimate from within-categorical oval conditions, Small
rect k = K estimate from within-categorical rectangle conditions, Big oval k = K estimate from cross-categorical oval conditions, Big rect k = K estimate from cross-categorical rectangle conditions.
**= p < .01,
***= p < .001
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Table 2
Factor loadings of 5 WM capacity measures
Number Resolution
Color k .841
Big oval k .877
Big rect k .897
Small oval k .869
Small rect k .883
Note: Color k = K estimate from color Conditions, Small oval k = K estimate from within-categorical oval conditions, Small rect k = K estimate
from within-categorical rectangle conditions, Big oval k = K estimate from cross-categorical oval conditions, Big rect k = K estimate from cross-
categorical rectangle conditions. Loadings for missing cells were all less than .15.
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Table 3
Statistics for CFA analysis
Model dfMχ2(p-value) χ2Differencewith Model 1 (p-value) RMSEA (90 % CI) CFI
Model 1 (Figure 2) 13 10.845 (.6238) - .00 (.00, .09) 1.0
Model 2 14 11.131 (.6757) .286 (.5928) .00 (.00, .09) 1.0
Note: Chi-squares not significant at the .05 level indicate good fits to the data. Non-significant Chi-square difference with Model 1 indicates the model has equivalent fit with the data. Lower values of root
mean square error of approximation (RMSEA) indicate better fit. A RMSEA value lower than .1 indicates a good fit to the data. Values above .95 for Bentler’s comparative fit index (CFI) indicate excellent
fit.
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