Complex span versus updating tasks of working memory: the gap is not that deep.
ABSTRACT How to best measure working memory capacity is an issue of ongoing debate. Besides established complex span tasks, which combine short-term memory demands with generally unrelated secondary tasks, there exists a set of paradigms characterized by continuous and simultaneous updating of several items in working memory, such as the n-back, memory updating, or alpha span tasks. With a latent variable analysis (N = 96) based on content-heterogeneous operationalizations of both task families, the authors found a latent correlation between a complex span factor and an updating factor that was not statistically different from unity (r = .96). Moreover, both factors predicted fluid intelligence (reasoning) equally well. The authors conclude that updating tasks measure working memory equally well as complex span tasks. Processes involved in building, maintaining, and updating arbitrary bindings may constitute the common working memory ability underlying performance on reasoning, complex span, and updating tasks.
- SourceAvailable from: Oliver Wilhelm[Show abstract] [Hide abstract]
ABSTRACT: In the present paper we investigate weekly fluctuations in the working memory capacity (WMC) assessed over a period of 2 years. We use dynamical system analysis, specifically a second order linear differential equation, to model weekly variability in WMC in a sample of 112 9th graders. In our longitudinal data we use a B-spline imputation method to deal with missing data. The results show a significant negative frequency parameter in the data, indicating a cyclical pattern in weekly memory updating performance across time. We use a multilevel modeling approach to capture individual differences in model parameters and find that a higher initial performance level and a slower improvement at the MU task is associated with a slower frequency of oscillation. Additionally, we conduct a simulation study examining the analysis procedure's performance using different numbers of B-spline knots and values of time delay embedding dimensions. Results show that the number of knots in the B-spline imputation influence accuracy more than the number of embedding dimensions.Frontiers in Psychology 01/2014; 5:687. · 2.80 Impact Factor
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ABSTRACT: Findings on working memory (WM) and inhibition in children with autism spectrum disorders (ASD) are contradictory and earlier studies largely ignored individual differences. As WM and inhibition seem to be related, children who experience WM deficits might also experience inhibition deficits. Moreover, these children possibly form a distinct subgroup, differing on other variables, such as cognitive functioning, symptom severity, behavior, and attention deficit hyperactivity disorder (ADHD) characteristics. We studied a large sample of children with and without ASD (8-12 years, IQ > 80) with classic experimental tasks (n-back task, ASD n = 77, control n = 45; stop task, ASD n = 74, control n = 43), and explored individual differences. The ASD group made more errors on the n-back task with increasing WM load, and had longer stop signal reaction times on the stop task when compared with controls. However, only 6 % of the ASD group showed both WM and inhibition deficits, and 71 % showed no deficits. Parents of children with WM and/or inhibition deficits tended to report more conduct problems on the disruptive behavior disorder rating scale. ADHD characteristics did not influence performance. Some children used medication during testing, which seemingly influenced stop task performance, but excluding these data did not change the main findings. Large individual differences in cognitive functioning are present, even within children with ASD with average or above average intelligence. However, whether individual differences in specific cognitive domains, such as WM and inhibition are as informative as individual differences in diagnosis, comorbidity, and general cognitive functioning, calls for future research.Journal of Neural Transmission 05/2014; · 3.05 Impact Factor
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ABSTRACT: Background Recent studies have suggested substantial fluctuations of cognitive performance in adults both across and within days, but very little is known about such fluctuations in children. Children's sleep behavior might have an important influence on their daily cognitive resources, but so far this has not been investigated in terms of naturally occurring within-person variations in children's everyday lives. Methods In an ambulatory assessment study, 110 elementary school children (8–11 years old) completed sleep items and working memory tasks on smartphones several times per day in school and at home for 4 weeks. Parents provided general information about the children and their sleep habits. Results We identified substantial fluctuations in the children's daily cognitive performance, self-reported nightly sleep quality, time in bed, and daytime tiredness. All three facets were predictive of performance fluctuations in children's school and daily life. Sleep quality and time in bed were predictive of performance in the morning, and afternoon performance was related to current tiredness. The children with a lower average performance level showed a higher within-person coupling between morning performance and sleep quality. Conclusions Our findings contribute important insights regarding a potential source of performance fluctuations in children. The effect of varying cognitive resources should be investigated further because it might impact children's daily social, emotional, and learning-related functioning. Theories about children's cognitive and educational development should consider fluctuations on micro-longitudinal scales (e.g., day-to-day) to identify possible mechanisms behind long-term changes.Journal of Child Psychology and Psychiatry 07/2014; · 5.42 Impact Factor
Complex Span Versus Updating Tasks of Working Memory:
The Gap Is Not That Deep
Florian Schmiedek and Andrea Hildebrandt
Max Planck Institute for Human Development
and Humboldt-Universita ¨t Berlin
Martin Lo ¨vde ´n
Max Planck Institute for Human Development
and Lund University
Humboldt-Universita ¨t Berlin
Max Planck Institute for Human Development
How to best measure working memory capacity is an issue of ongoing debate. Besides established
complex span tasks, which combine short-term memory demands with generally unrelated secondary
tasks, there exists a set of paradigms characterized by continuous and simultaneous updating of several
items in working memory, such as the n-back, memory updating, or alpha span tasks. With a latent
variable analysis (N ? 96) based on content-heterogeneous operationalizations of both task families, the
authors found a latent correlation between a complex span factor and an updating factor that was not
statistically different from unity (r ? .96). Moreover, both factors predicted fluid intelligence (reasoning)
equally well. The authors conclude that updating tasks measure working memory equally well as
complex span tasks. Processes involved in building, maintaining, and updating arbitrary bindings may
constitute the common working memory ability underlying performance on reasoning, complex span, and
Keywords: working memory, complex span tasks, n-back, fluid intelligence, structural equation modeling
Working memory (WM) is a construct of great importance in
general as well as applied cognitive psychology, with theoretical
and empirical relevance for a wide range of behaviors such as
reading comprehension, skill learning, and complex problem solv-
ing (Feldman Barrett, Tugade, & Engle, 2004). In research dem-
onstrating a strong relation between WM capacity and fluid intel-
ligence/reasoning (Kane et al., 2004; Kyllonen & Christal, 1990;
Su ¨ß, Oberauer, Wittmann, Wilhelm, & Schulze, 2002), it has
proven fruitful to combine experimentally informed task design
with an individual differences perspective. Measures of individual
differences, however, presume reliable and valid indicators of a
construct, which leads to the question of what defines a good WM
task (Conway et al., 2005; Oberauer, 2005).
Complex span tasks (CSTs; Daneman & Carpenter, 1980) are
well-established measures of WM capacity. Compared to simple
span tasks, in which participants have to recall a list of stimuli after
a brief retention interval, CSTs require the additional accomplish-
ment of an (often unrelated) secondary task, such as evaluating
equations. This combination of short-term storage and processing
requirements implements the basic definition of WM as simulta-
neous storage and processing (Baddeley, 2007). Because of poten-
tial trade-offs between the two components, CSTs come with the
problem that performance on the secondary task cannot easily be
disregarded when determining WM span on the basis of number of
items recalled (Conway et al., 2005).
Another prominent paradigm to measure WM performance is
the n-back task (Cohen et al., 1997). In this paradigm, participants
have to evaluate each stimulus presented in a sequence as to
whether it matches another stimulus presented earlier in the se-
quence, with a certain lag. In a verbal 3-back task, for example,
participants see a series of letters and have to decide for each
whether it matches the one seen three time steps back. This task is
frequently used in the cognitive neurosciences (Owen, McMillan,
Laird, & Bullmore, 2005), schizophrenia research (Glahn et al.,
2005), and cognitive aging research (e.g., Dobbs & Rule, 1989;
Kirchner, 1958; Schmiedek, Li, & Lindenberger, 2009).
Recently, Kane, Conway, Miura, and Colflesh (2007) attempted
to elucidate the relation between CSTs and n-back. They correlated
performance on one CST, operation span (Turner & Engle, 1989),
with different measures of a letter n-back task and found only
Florian Schmiedek and Andrea Hildebrandt, Center for Lifespan
Psychology, Max Planck Institute for Human Development, Berlin,
Germany; and Institute of Psychology, Humboldt-Universita ¨t Berlin, Ger-
many. Martin Lo ¨vde ´n, Center for Lifespan Psychology, Max Planck Insti-
tute for Human Development; and Department of Psychology, Lund Uni-
versity, Lund, Sweden. Oliver Wilhelm, Institute of Psychology,
Humboldt-Universita ¨t Berlin; and Ulman Lindenberger, Center for Lifes-
pan Psychology, Max Planck Institute for Human Development.
The present study was supported by the Max Planck Society, includ-
ing a grant from the innovation fund of the Max Planck Society
(M.FE.A.BILD0005); the Sofja Kovalevskaja Award (to Martin
Lo ¨vde ´n) of the Alexander von Humboldt Foundation donated by the
German Federal Ministry for Education and Research (BMBF), the
German Research Foundation (DFG; KFG 163), and the German Fed-
eral Ministry for Education and Research (BMBF; CAI).
Correspondence concerning this article should be addressed to Florian
Schmiedek, Institute of Psychology, Humboldt-Universita ¨t Berlin, Unter
den Linden 6, 10099 Berlin, Germany. E-mail: florian.schmiedek@
Journal of Experimental Psychology:
Learning, Memory, and Cognition
2009, Vol. 35, No. 4, 1089–1096
© 2009 American Psychological Association
weak correlations in the range of .20. Furthermore, when using the
two tasks to simultaneously predict performance on a marker task
of reasoning ability (Raven matrices), both accounted for indepen-
dent portions of variance. These findings led Kane et al. to con-
clude that the two paradigms “do not appear to be measures of the
same construct” (p. 620). Clearly, further research needs to address
this surprisingly small overlap of individual differences between
the two kinds of tasks.
The results of the study by Kane et al. (2007) were based on
single tasks of complex span and n-back, which limits their con-
clusiveness in two ways. First, correlations may be reduced by
different content domains contributing nonshared variance to the
tasks. Specifically, their n-back was based on letters as stimuli,
operation span combined words and numerical equations, and the
Raven is a figural–spatial reasoning task. Not surprisingly then,
Shamosh et al. (2008) reported a much higher correlation (r ? .55)
than Kane et al. between composites of four CSTs and two n-back
tasks, in which task-specific variance was reduced by means of
aggregation. Second, when reliabilities are less than perfect, anal-
yses at the level of observed variables underestimate true correla-
tions because they confound construct variance with content-
specific variance, task-specific variance, and measurement error.
This is also the case for composites of several variables, as
aggregation can only reduce but not eliminate the influence of
these factors. Both kinds of problems can be alleviated, however,
by using a latent variable approach with multiple task operation-
alizations from different content domains. This approach greatly
reduces the influence of error and content-specific variance,
thereby presenting a more accurate (i.e., unbiased) picture of the
construct overlap between the two approaches to measuring WM.
This argument can be pushed even further. We argue for using
operationalizations that are more diverse with respect to construct-
irrelevant task attributes for both classes of paradigms (cf. Little,
Lindenberger, & Nesselroade, 1999). Just as for the complex span
paradigm tasks as different as operation span, reading span (Dane-
man & Carpenter, 1980), counting span (Case, Kurland, & Gold-
berg, 1982), or rotation span (Shah & Miyake, 1996) have been
employed, one can also put n-back on a more general theoretical
basis, allowing for a broader range of possible operationalizations.
Specifically, a defining characteristic of the n-back is that it
requires a continuous process of building, maintaining, updating,
and releasing arbitrary bindings between items and temporal order
positions (cf. Friedman et al., 2006). According to Oberauer, Su ¨ß,
Wilhelm, and Sander (2007), WM capacity, and its shared variance
with reasoning ability, reflects a limited capacity for binding
arbitrary component representations. In the case of n-back, this
would be a limited capacity to reliably bind items to order posi-
tions and to unbind and update those at each step in the sequence.
The same requirement of building, maintaining, updating, and
releasing arbitrary bindings between stimuli and certain represen-
tational structures can be found for several other updating WM
tasks. For example, in the memory updating (MU) paradigm (Salt-
house, Babcock, & Shaw, 1991), participants have to memorize
several numbers, associated with a set of frames, and update those
numbers independently according to a series of arithmetic opera-
tions appearing in the frames. Here, the updating requirement
applies to numbers and spatial positions. In the study to be pre-
sented, we use a spatial version of the n-back, a numerical MU
task, and an adapted version of the alpha span task (Craik, 1986)
as operationalizations of updating WM tasks.
To summarize, we propose that an evaluation of different ap-
proaches to measure WM should be conducted in a larger theo-
retical and methodological context, comparing a set of CSTs with
a set of updating tasks with content-heterogeneous selections of
tasks from verbal, numerical, and figural–spatial domains for both
paradigms. Similarly, constructs on the criterion side, as reasoning,
should also be based on a content-heterogeneous sampling of
tasks. In the present study, we achieved all this by comparing a set
of three CSTs with three updating WM tasks and relating both at
a latent construct level to a broad factor of reasoning tasks.
We addressed a further issue in this study, also related to the
validity of the updating tasks, by using varying presentation times
(PTs) for these tasks. PT obviously is a crucial determinant of task
difficulty in tasks with paced continuous presentation of a se-
quence of items or operations, like all updating tasks used in the
present study. Therefore the question arises as to how PT affects
the psychometric properties of these tasks. A speed manipulation
with one fast and one slow PT for each task allowed us to
investigate whether this central task parameter of all updating WM
paradigms had an effect not only on mean performance but also on
the relations to CSTs and reasoning. For the validity of updating
WM tasks, it would be desirable if manipulating PT had little
effect on these relations. If this was the case, one could use
varying PTs to adjust task difficulty for a given measurement
purpose and target population and the task would remain a valid
indicator of WM.
The study consisted of two sessions. The first session was
attended by 108 people. Eleven participants did not return to the
second session, and 1 person attended the second session only.
Thus, our analyses are based on data from 96 participants. The
mean age of the sample was 24.9 years (SD ? 2.7); the percentage
of women was 47.2% and of men, 52.8%. The sample was com-
posed of an academically diverse student population (77%), pupils
and young adults in professional formation (10%), employees (8%,
including 1.7% academics), and unemployed (5%, including 3%
academics). Each participant was paid €50 in compensation.
Each of the two sessions lasted 3 hr, and the participants
attended both sessions within the time span of 1 week. The tasks
were completed in small groups of 2 to 5 participants. The WM
tasks and Raven’s Progressive Matrices were administrated on
personal computers (17-in. color monitors, 85 Hz rate, 1280 ?
1024 pixels resolution). Additionally, participants completed the
paper-and-pencil Berlin Structure of Intelligence (BIS) Test (Ja ¨ger,
Su ¨ß, & Beauducel, 1997).
ipants had to assess whether the position of a black filled circle that
appeared in a 4 ? 4 grid was identical to the position of the circle
We administered a figural–spatial 3-back task. Partic-
presented three steps back in the sequence. Participants were asked
to press the green key of a button box if the positions were
identical or the red key if they were not. Thirty-nine stimuli
were presented in each block of trials. The first three stimuli were
preparatory, because they had no reference items to be compared
with. Each block of trials consisted of 12 targets, 12 nontargets,
and 12 lures. Lures are items that match a stimulus presented
earlier, but not at the correct temporal distance. In each block, four
2-, 4-, and 5-back, but no 1-back, lures were used. Other than the
constraints mentioned, the stimulus sequence was random but
fixed across participants. PT for each stimulus was 500 ms. Inter-
stimulus intervals (ISIs) were 2,000 ms for slow and 1,000 ms for
fast blocks of trials. Participants had to complete 16 (first eight
slow and then eight fast) blocks in total.
Memory updating (MU).
Two rows of frames were presented
to the participants. The number of frames varied between 2 and 5
per row, defining memory load levels of two to five. At the
beginning of each trial block, single-digit numbers were displayed
simultaneously for 2,000 ms in each frame of the upper row.
Participants were asked to memorize those numbers for each frame.
Then, addition and subtraction operations (e.g., “? 2,” “– 4”) ap-
peared in the lower row of frames. Numbers in the corresponding
frame above had to be updated according to the operations. A
sequence of 4 updating operations were included in the 2-frames
version, 6 in the 3-frames version, 8 in the 4-frames version, and
10 in the 5-frames version, so that 2 updating operations applied to
each frame. Succeeding operations always applied to different
frames, in random order. Intermediate and end results for each
frame were always in the range of 0 to 9. The final values for
each frame had to be entered with the keyboard. A total of 32
blocks of trials were conducted. Participants had to complete 16
blocks (four for each load level) with a PT of the operations of
2,000 ms (ISI was 500 ms), and another set of 16 blocks (four per
load level) with a PT of 1,000 ms. The ISI for the slow as well as
for the speeded tasks was 500 ms.
Our task differed in some respects from the fa-
miliar version by Craik (1986). In the familiar version, after a list
of words is presented, participants have to recall the first letters of
the listed words in correct alphabetical order. In our version, a
sequence of 10 single consonant letters appeared. Together with
the presentation of each letter, a number (from 1 to 10) was
displayed below the letter. The letters had to continuously be
brought into alphabetical order and participants were asked to
respond to each letter–number pair whether the number corre-
sponded to the current alphabetical position of the letter among the
set of letters that had appeared so far. For example, the items in the
sequence could be “B – 1” (order: 1 ? B; correct response: yes),
“M – 2” (order: 1 ? B, 2 ? M; correct response: yes), “C – 2”
(order: 1 ? B, 2 ? C, 3 ? M; correct response: yes), “K – 4”
(order: 1 ? B, 2 ? C, 3 ? K, 4 ? M; correct response: no), “Z –
5” (order: 1 ? B, 2 ? C, 3 ? M, 4 ? K, 5 ? Z; correct response:
yes), and so on. Correspondence was confirmed by hitting the
green key, and mismatches, the red key. Five out of the 10 stimuli
were matches. The participants completed 16 blocks of trials. In
the first half of those blocks, stimuli were presented with a PT of
2,000 ms, in the second half the PT was 1,000 ms. In both cases ISI
was 2,000 ms.
Complex Span Tasks
version in that participants did not have to memorize words (see
Engle, Tuholski, Laughlin, & Conway, 1999) but rather single letters
(see Kane et al., 2004). Several sentences were presented successively
on the screen. Below each sentence, a letter was displayed. Partici-
pants had to decide whether the sentences were semantically correct
(e.g., “The first thing I do in the morning is feed the dog”) or incorrect
(e.g., “Yesterday in church, the daughter of Till made a terrible
plum”). Additionally, they were asked to memorize the letter and,
after a sequence of sentence–letter combinations, recall the letters in
their order of presentation. We included 12 blocks of trials, three for
each load level (of two to five).
We implemented the counting span very sim-
ilarly to Kane et al. (2004). Several displays of blue circles (4–9),
green circles (1–5), and blue squares (1–9) were presented. Par-
ticipants were asked to count the blue circles and hit the green key
if their number was even or the red key if the number was odd. The
requirement to decide whether the number was even or odd was
not included by Kane et al. The number of blue circles had to be
memorized for later recall in the order of their presentation. The
number of displays ranged from two to six per block of trials. A
total of 15 blocks was completed, three per load level.
This task combines recall of a sequence of
short and long arrows, radiating from the center of the display,
with a letter-rotation task (Kane et al., 2004; Wilhelm & Oberauer,
2006). First, a regular or mirror-reversed letter was displayed on
the screen. The letter could be rotated by 0, 45, 90, 135, 180, 225,
270, or 315 degrees. In the processing part of the task, participants
were asked to hit the green key when letters were displayed
regularly and the red key when they were mirror-reversed. After
each processing step (ranging from 2–5 per block of trials), short
or long arrows were shown. The arrows pointed in one of the eight
directions. At the end of one sequence, participants had to recall
the direction and length of the arrows in the order of their presen-
tation and indicate this by clicking on a computer screen layout
with the 16 possible positions of the arrow head. There were 12
blocks of trials to complete, three per load level.
We used a version that differed from the original
Raven’s Advanced Progressive Matrices (RAPM).
items of the RAPM (Raven, Raven, & Court, 1998) were admin-
istrated on the computer. An aggregate of these items was used as
one indicator variable of the latent reasoning factor.
From the reasoning scale of the BIS test (Ja ¨ger et al.,
1997; for English descriptions see Carroll, 1993; Su ¨ß & Beaudu-
cel, 2005; Wilhelm & Schulze, 2002), nine reasoning tasks (three
for each content category: verbal, numerical, and figural) were
used. Internal consistency of these tasks was high (Cronbach’s ? ?
.80). The nine tasks were z-standardized and aggregated into three
parcels that served as indicator variables for the latent reasoning
factor. Each parcel consisted of one verbal, one numerical, and one
For the updating tasks, we defined mean accuracies as depen-
dent variables. For the CSTs, we used a partial-credit unit-scoring
procedure (Conway et al., 2005). The proportions of elements
correctly recalled within each block of trials were computed and
averaged over blocks, with equal weight given to all memory load
levels of each CST. Accuracy on the processing component did not
enter into the score. The correlation between the recall score and
the processing accuracy was .73 for counting span, .49 for reading
span, and .16 for rotation span.
The data were screened to identify outliers. No individual’s score
deviated by more than 3.5 SDs from the mean of the sample. All the
analyses were therefore based on all 96 cases. Descriptive statistics
are summarized in Table 1. Internal consistencies were satisfactory to
high, except for the RAPM, which might be due to the fact that only
15 of the more difficult items of this test were used in this study. For
evidence regarding the satisfactory reliability of the BIS parcels, we
refer the reader to the test manual (Ja ¨ger et al., 1997).
PT of the stimuli was manipulated in the updating tasks (i.e., the
n-back, alpha span, and MU tasks). As anticipated, PT had an
impact on the means. The fast versions of the n-back, alpha span,
and MU tasks were more difficult than the slow versions. Table 1
displays the differences of the means (?M) and corresponding
paired t tests, which were all significant and of medium effect size.
A correlation matrix of all tasks is displayed in Table 2. All values
were positive. Some of them were not significant. However, this
concerned not only several correlations between CSTs and arbitrary
updating tasks but also the relation between two different CSTs.
According to our line of argument, the relation between the two
sets of WM tasks needs to be examined at the level of latent
variables, using a heterogeneous set of tasks. This strategy pro-
vides an unbiased picture of construct overlap between the mea-
surement paradigms because influences of unreliability and con-
tent heterogeneity are attenuated. To this end, we used
confirmatory factor analysis.
To examine the construct equivalence of the two approaches of
measuring WM, we estimated a pair of nested models. In a first
model (Model 1A; see Figure 1) CSTs loaded on one latent factor
and the slow and fast versions of the updating tasks loaded on a
second factor. The errors of the corresponding slow and fast task
versions were allowed to correlate. The correlation between the fac-
tors was freely estimated. The fit of Model 1A was reasonable,
?2(23) ? 36.64, comparative fit index (CFI) ? .97, root-mean-square
error of approximation (RMSEA) ? .07 (90% confidence interval
[CI] ? .02, .12), standardized root-mean residual (SRMR) ? .05, and
the correlation between the latent factors was very high (r ? .96). In
a nested version of Model 1A, the correlation between the latent
factors was fixed to 1 (Model 1B; see Figure 1). The following fit
indices resulted for Model 1B: ?2(24) ? 36.76, CFI ? .97, RM-
SEA ? .07 (90% CI ? .01, .11), SRMR ? .05.
We evaluated whether the free estimation of the correlation signif-
icantly improved the model fit with a chi-square difference test. The
chi-square difference between Models 1B and 1A was not significant,
??2(1) ? 0.12, indicating that fit did not improve significantly when
the correlation was freely estimated. Therefore, regarding individual
differences at the latent level, CSTs and updating tasks were measur-
ing the same construct.
an impact on the means. If PT played a different role when processing
fast than when processing slow versions of the updating tasks, the
speed manipulation should also affect the covariances. If this was the
case, then separate factors for the more or less speeded versions of
the updating tasks would not correlate to 1. We tested this by com-
paring two models (not shown in figures) in which the slow versions
of the three updating tasks loaded on one factor and the fast versions
on another factor (task-specific residuals were allowed to correlate).
The two factors correlated very highly (r ? .97; not significantly
different from r ? 1.00), ??2(1) ? 0.59. As a model with two latent
factors correlating perfectly is equivalent to a one-factor model, we
can conclude that that the fast and slow versions of the updating tasks
were measuring the same construct.
In the next step, we tested a model for reasoning ability (Model
2; not shown in a figure). An aggregate of the 15 RAPM items and
the BIS parcels loaded on the latent factor. This model had
Descriptive Statistics and Cronbach’s Alphas for All Variables
VariableNo. of blocks
updating fast; RS ? reading span; CS ? counting span; RoS ? rotation span; RAPM ? Raven’s Advanced Progressive Matrices; ? ? internal consistencies
(Cronbach’s alphas); ?M ? difference of means between slow and fast trials; d ? effect size measure (Cohen’s d).
?p ? .05.
NB_s ? n-back slow; NB_f ? n-back fast; AS_s ? alpha span slow; AS_f ? alpha span fast; MU_s ? memory updating slow; MU_f ? memory
excellent fit, ?2(2) ? 0.81, CFI ? 1.00, RMSEA ? .00 (90% CI ?
.00, .15), SRMR ? .01, and factor loadings were satisfactory (.43)
to high (.74 to .84).
Our concern was not only to test the internal structure of the
WM tasks and show that they are all measuring the same construct.
We also compared the two classes of WM paradigms with respect
to their relation to reasoning. For this purpose, we computed
structural models with three correlated latent variables—one for
CSTs, updating, and reasoning tasks, respectively. The structural
Models 3A and 3B are shown in Figure 2.
The correlations between the three latent factors were all freely
estimated in Model 3A. Fit indices of this model were very good,
?2(59) ? 76.47, CFI ? .97, RMSEA ? .05 (90% CI ? .00, .08),
SRMR ? .05. The two WM factors correlated to r ? .97, the CST
factor and the reasoning factor to r ? .78, and the updating factor
and reasoning to r ? .84.
With Model 3B, we tested whether the correlation of the latent
updating factor with reasoning was significantly higher than the
one of the CST factor. The correlations between updating and
reasoning and between span and reasoning were fixed to be equal
in Model 3B. Fit indices of Model 3B were also very good,
?2(60) ? 76.75, CFI ? .97, RMSEA ? .05 (90% CI ? .00, .08),
SRMR ? .05. Both WM factors correlated to r ? .82 with
reasoning and to r ? .99 with each other. The difference between
Models 3A and 3B was not significant, ??2(1) ? 0.28. Free
estimation of the correlations did not lead to significant improve-
ment of the model fit. Thus, at the latent level, associations of the
two different WM paradigms to reasoning were high and did not
reliably differ from each other.
The goal of the study was to examine the relation between
updating tasks of WM, such as the n-back, and CSTs by means of
a latent variable analysis, thereby overcoming the problem that
correlations are attenuated by task-specific and content-specific
Updating factor. Rectangles represent manifest variables. RS ? reading span; CS ? counting span; RoS ? rotation
fast; NB_s ? n-back slow; NB_f ? n-back fast. The errors of the slow and fast task versions were allowed to
correlate. The values for Model 1B are displayed in parentheses.
Models 1A and 1B. Ovals represent latent factors. SPAN ? Complex Span factor; UPDATING ?
Correlations Among All Tasks (N ? 96)
NB_sNB_fAS_s AS_f MU_sMU_f RS CS RoSRAPM K_1K_2 K_3K
updating fast; RS ? reading span; CS ? counting span; RoS ? rotation span; RAPM ? Raven’s Advanced Progressive Matrices; K_1 ? reasoning, Parcel
1 (Berlin Structure of Intelligence [BIS] test); K_2 ? reasoning, Parcel 2 (BIS test); K_3 ? reasoning, Parcel 3 (BIS test); K ? general reasoning (BIS
?p ? .05.
NB_s ? n-back slow; NB_f ? n-back fast; AS_s ? alpha span slow; AS_f ? alpha span fast; MU_s ? memory updating slow; MU_f ? memory
??p ? .01.
sources of individual variation as well as measurement error.
Results showed that the three updating tasks used here were
reliable indicators of a latent factor that was statistically identical
to a CST latent factor. Therefore, interindividual differences in
WM capacity can be equally well described with both families of
tasks. Consequently, the relations of both WM factors with rea-
soning are of equal magnitude.
What are the common sources of variance that produce the
perfect relation of CSTs to updating tasks at the latent level, or in
other words, what is common to all CSTs that is also common to
all updating tasks investigated here? At least three theoretical
accounts come to mind. First, the controlled attention view by
Engle and colleagues (e.g., Engle, 2002) proposes that the ability
to resist interference from internal and external distraction is
central to WM performance. It seems difficult to rule out that
individual differences in controlled attention might contribute to
task performance in CSTs as well as in updating tasks, as both
require a continuous focus on complex processing requirements. It
is also difficult, however, to specify how much of the common
variance of WM tasks can be explained by individual differences
in controlled attention.
Second, Unsworth and Engle (2007a, 2007b; see also Mogle,
Lovett, Stawski, & Sliwinski, 2008) have proposed that individual
differences in CSTs are partially due to individual differences in
the ability to maintain information accessible in primary memory
and partially due to individual differences in the ability to retrieve
information from secondary memory, with the latter being more
strongly responsible for the relation to fluid abilities. To reconcile
this view with the present findings, it would be necessary to
assume that retrieval processes from secondary memory also play
a central role in the updating tasks. The fact that for two of the
updating tasks, n-back and MU, the total number of items to be
maintained in primary memory at any time was within short-term
memory limits makes such an assumption difficult to entertain.
Third, it is possible to interpret the commonalities among the
WM tasks and to reasoning within the framework of Oberauer et
al. (2007). These authors suggested that building, maintaining, and
updating arbitrary bindings are the cognitive mechanisms shared
between WM and reasoning performance (for similar views and
supporting evidence from cognitive neuroscience, see Miller &
Cohen, 2001; Smith & Jonides, 1999). These demands are appar-
ent for the updating tasks used in our study but are also plausible
determinants of CST performance. Because CSTs require the
recall of items in correct serial order, there are some crucial
ingredients to successful performance: the reliable establishment
of bindings of content (words, numbers, directions) to context
(serial positions), its maintenance in the presence of an interfering
secondary task, and the necessary release and updating of bindings
from one trial to the next. Releasing of bindings might hereby play
a similarly important role as the creation of bindings (e.g., Durst-
ewitz, Kelc, & Gu ¨ntu ¨rku ¨n, 1999).
An important finding from this study was that even though
manipulating PT had the expected effect on means, it did not affect
the reliability and validity of the tasks in any important way. This
is encouraging, given that practical considerations will often re-
quire adjusting PTs to reach a certain level of accuracy. Regarding
our theorizing about individual differences in WM capacity, this
finding demonstrates that no additional source of variation unre-
factor; UPDATING ? Updating factor. Rectangles represent manifest variables. RAPM ? Raven’s Advanced
Progressive Matrices; BIS_P1? Reasoning scale of the Berlin Structure of Intelligence Test (BIS), Parcel 1;
BIS_P2? BIS Parcel 2; BIS_P3? BIS Parcel 3; RS ? reading span; CS ? counting span; RoS ? rotation span;
AS_s ? alpha span slow; AS_f ? alpha span fast; MU_s ? memory updating slow; MU_f ? memory updating
fast; NB_s ? n-back slow; NB_f ? n-back fast. The errors of the slow and fast task versions were allowed to
correlate. The values for Model 3B are displayed in parentheses.
Models 3A and 3B. Ovals represent latent factors. REA ? Reasoning factor; SPAN ? Complex Span
lated to higher cognition is introduced by decreasing the PTs of
updating tasks within a reasonable range; the decrease lowers
mean performance while keeping the rank order of interindividual
Our results are of particular interest for the large number of
researchers using the n-back task. Although earlier studies have
shown that MU and alpha span are reliable indicators of WM (e.g.,
Oberauer, Su ¨ß, Schulze, Wilhelm, & Wittmann, 2000), studies of
the construct validity of the n-back have been few and results have
been mixed. Here, we have shown that a spatial 3-back task is a
comparably good indicator of the updating WM factor as the other
two tasks. Although single-task operationalizations always are
problematic on conceptual and psychometric grounds, n-back is as
good a marker of WM as any of the other more established tasks
used here. It should be underscored again, however, that for
drawing conclusions at the construct level, a broader operational-
ization with several tasks from different content domains is pref-
erable to research designs based on individual tasks.
To conclude, we found a high latent correlation (.96) between a
CST factor and an updating factor that is not statistically different
from unity. Accordingly, both factors predict reasoning equally
well. Updating tasks measure WM equally well as CSTs. These
results indicate that reasoning, CSTs, and updating tasks share
common processing mechanisms. Building, maintaining, and up-
dating arbitrary bindings may constitute these mechanisms, but
further research including additional tasks designed to directly
assess bindings are needed to elucidate this assumption.
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Received June 23, 2008
Revision received February 4, 2009
Accepted February 6, 2009 ?