INTELL-00602; No of Pages 11
Intelligence xxx (2010) xxx–xxx

Contents lists available at ScienceDirect

Intelligence

The relationship between n-back performance and matrix
reasoning — implications for training and transfer☆
Susanne M. Jaeggi a,⁎, Barbara Studer-Luethi b,c, Martin Buschkuehl a, Yi-Fen Su c,
John Jonides a, Walter J. Perrig b
a

Department of Psychology, University of Michigan, 530 Church Street, Ann Arbor, MI, 48109-1043, USA
Department of Psychology, University of Bern, Switzerland
c
Department of Educational Psychology and Counseling, National Taiwan Normal University, Taipei, Taiwan
b

a r t i c l e

i n f o

Article history:
Received 20 March 2010
Received in revised form 8 August 2010
Accepted 6 September 2010
Available online xxxx
Keywords:
Cognitive training
Fluid intelligence
Working memory

a b s t r a c t
We have previously demonstrated that training on a dual n-back task results in improvements in
fluid intelligence (Gf) as measured by matrix reasoning tasks. Here, we explored the underlying
mechanisms of this transfer effect in two studies, and we evaluated the transfer potential of a
single n-back task. In the first study, we demonstrated that dual and single n-back task
performances are approximately equally correlated with performance on two different tasks
measuring Gf, whereas the correlation with a task assessing working memory capacity was
smaller. Based on these results, the second study was aimed on testing the hypothesis that training
on a single n-back task yields the same improvement in Gf as training on a dual n-back task, but
that there should be less transfer to working memory capacity. We trained two groups of students
for four weeks with either a single or a dual n-back intervention. We investigated transfer effects
on working memory capacity and Gf comparing the two training groups' performance to controls
who received no training of any kind. Our results showed that both training groups improved
more on Gf than controls, thereby replicating and extending our prior results.
© 2010 Elsevier Inc. All rights reserved.

1. Introduction
Fluid intelligence (Gf) is defined as a complex human ability
that allows us to adapt our thinking to new cognitive problems

☆ This work was supported by a grant of The Michigan Center for
Advancing Safe Transportation throughout the Lifespan (MCASTL #DTRT07G-0058) to MB, a fellowship from the Swiss National Science Foundation
(PA001-117473) to SMJ, and a grant from the Office of Naval Research to JJ
(N00014-09-0213). Study 2 was conducted as a part of BSL's master thesis
with the guidance of the other co-authors and with the support of the
University of Bern and the National Taiwan Normal University. The authors
wish to thank Chao-Yi Ho and Philip Cheng for their help with the
construction of the Mandarin stimuli and the help translating the instructions, as well as Courtney Behnke, Kirti Thummala, and Patrick Bissett, Wu
Shan-Yun, Yi Han Chiu, and David Studer for their help with data collection,
and finally, Randall Engle's group for providing us with the automated
version of their automated operation span task.
⁎ Corresponding author.
E-mail address: sjaeggi@umich.edu (S.M. Jaeggi).

or situations for which we cannot rely on previously acquired
knowledge (e.g. Carpenter, Just, & Shell, 1990). Gf is considered
critical for a wide variety of cognitive tasks (Engle, Tuholski,
Laughlin, & Conway, 1999; Gray & Thompson, 2004), and it
seems to be one of the most important factors in learning
(Deary, Strand, Smith, & Fernandes, 2007; Neisser et al., 1996;
Rohde & Thompson, 2007; te Nijenhuis, van Vianen, & van der
Flier, 2007). There is considerable agreement that a substantial
proportion of the variance in Gf is hereditary (Baltes, Staudinger, & Lindenberger, 1999; Cattell, 1963; Gray & Thompson,
2004), but it has also been shown that social class and age
moderate the heritability of Gf (Haworth et al., 2009;
Turkheimer, Haley, Waldron, D'Onofrio, & Gottesman, 2003).
Although high heritability in principle does not preclude
alteration of Gf through environmental factors or interventions
(Jensen, 1981), evidence of such alteration has been sparse.
However, there is now accumulating evidence showing that
certain interventions seem to increase performance in Gf tasks

0160-2896/$ – see front matter © 2010 Elsevier Inc. All rights reserved.
doi:10.1016/j.intell.2010.09.001

Please cite this article as: Jaeggi, S.M., et al., The relationship between n-back performance and matrix reasoning — implications
for training and transfer, Intelligence (2010), doi:10.1016/j.intell.2010.09.001

2

S.M. Jaeggi et al. / Intelligence xxx (2010) xxx–xxx

(Buschkuehl & Jaeggi, 2010), although the mechanisms that
underlie such change are not well understood (Basak, Boot,
Voss, & Kramer, 2008; Jaeggi, Buschkuehl, Jonides, & Perrig,
2008; Klingberg et al., 2005; Klingberg, Forssberg, & Westerberg, 2002; Rueda, Rothbart, McCandliss, Saccomanno, &
Posner, 2005; Tranter & Koutstaal, 2007). For example, we
have shown that the n-back task can be used as a training
vehicle to improve performance on matrix reasoning tasks
which are commonly used as a typical measure of Gf (e.g. Gray &
Thompson, 2004; Kane & Engle, 2002; Snow, Kyllonen, &
Marshalek, 1984). In our study, subjects were pretested on
measures of Gf, after which they were given up to four weeks of
daily training on a dual n-back task (Jaeggi, Buschkuehl, Jonides,
& Perrig, 2008). The dual n-back task consisted of a position that
was pseudo-randomly marked on a computer screen in each
stimulus frame which subjects had to match for spatial position
to the stimulus presented n frames back in the sequence.
Simultaneously with the spatial task, subjects had to process an
auditory stream of stimuli in which a single letter was
presented in each auditory frame that had to be matched to
the letter that appeared n items ago. The value of n was
matched for the spatial and verbal tasks, both of which required
responses. The level of n changed during the experiment
according to the participants' performance to keep overall task
difficulty approximately constant. Following training, subjects
were given non-overlapping items from an instrument measuring Gf. The results showed that training on a dual n-back task
yielded improvements in Gf relative to a control group that did
not train.
Why was this training regimen successful? That is, what
mechanisms drive such transfer effects? We believe it is critical
that the training and the transfer tasks share overlapping
cognitive processes for transfer to succeed. Thus, we think that
the gain in Gf emerges because the processes that are engaged by
the training task also mediate performance in Gf tasks. We
proposed that the framework by Halford, Cowan, and Andrews
(2007) might serve as a useful model to understand why Gf can
be improved by means of a working memory task. Their claim is
that working memory and intelligence share a common capacity
constraint, which is driven by attentional control processes.
Other authors have come to a related conclusion (Gray, Chabris,
& Braver, 2003; Kane et al., 2004), and in particular, Carpenter,
Just, and Shell (1990) have proposed that the ability to derive
abstract relations and to maintain a large set of possible goals in
working memory accounts for individual differences in typical
tasks that measure Gf. The underlying neural circuitries provide
additional evidence for the shared variance between working
memory and Gf in that both seem to rely on similar neural
networks, most consistently located in lateral prefrontal and
parietal cortices (Gray, Chabris, & Braver, 2003; Kane & Engle,
2002). Thus, it seems plausible that the training of a certain
neural circuit might lead to transfer to other tasks that engage
similar or at least overlapping neural circuits. Indeed, recent
evidence shows that transfer occurs if the training and the
transfer task engage overlapping brain regions, but not if they
engage different regions (Dahlin, Neely, Larsson, Backman, &
Nyberg, 2008; see also Persson & Reuter-Lorenz, 2008).
But overlapping processes and neural circuits might not be
the only prerequisites for transfer. We believe that the training
task has to be very carefully designed in a certain way to
promote transfer. First, a successful training task must minimize

the development of strategies that are specific to the task in
question because the object of training must be changes in the
information processing system, not changes in the way one
particular task is performed (cf. Ericsson & Delaney, 1998).
Second, we think that it is very important to keep a persistently
high level of training demand while also considering interindividual performance differences. This can be achieved by
using an adaptive training method that continuously adjusts the
current training difficulty to the actual performance of each
subject. Third, we argue that it is necessary to stress the
information processing system during training, for example by
taxing more than one input modality at a time or by having the
subject engage in two tasks simultaneously (Oberauer, Lange, &
Engle, 2004). As we have shown in our work, the dual n-back
training paradigm is a task that fulfills these requirements and
subsequently leads to the predicted transfer effects (Jaeggi et al.,
2007; Jaeggi, Buschkuehl, Jonides, & Perrig, 2008). Nevertheless,
although various versions of the n-back task are widely used in
research, only few studies have examined the processes
involved in n-back performance (e.g. Hockey & Geffen, 2004;
Jaeggi, Buschkuehl, Perrig, & Meier, 2010; Kane, Conway, Miura,
& Colflesh, 2007). Therefore, little knowledge is available about
the cognitive processes that mediate performance in this task
and consequentially, about the processes underlying n-back
training that eventually promote transfer to Gf. In addition,
although the n-back task is commonly regarded as a measure of
working memory, its concurrent validity is still open to question
(Jaeggi, Buschkuehl, Perrig, & Meier, 2010; Jarrold & Towse,
2006; Kane, Conway, Miura, & Colflesh, 2007; Oberauer, 2005).
For example, research from Kane's lab as well as our own work
suggests that the n-back task and more traditional measures of
working memory capacity (e.g. reading span or operation span
tasks) do not share a great deal of common variance, although
they independently predict performance in Gf tasks (Jaeggi,
Buschkuehl, Perrig, & Meier, 2010; Kane, Conway, Miura, &
Colflesh, 2007). This is in line with findings from training on the
n-back task which leads to improvements in Gf (Jaeggi,
Buschkuehl, Jonides, & Perrig, 2008), but not in measures of
working memory capacity (Jaeggi, Buschkuehl, Jonides, &
Perrig, 2008; Li et al., 2008). Therefore, we do not know
whether training on an n-back task results in transfer to Gf due
to an improvement in basic working memory processes, or
whether there are other processes that are better predictive of
such transfer.
Study 1. The main goal of Study 1 was to document the results
of a correlational study investigating the relationship between
the n-back task and selected cognitive tasks chosen so that they
might reveal factors that underlie the transfer effect that we have
observed by training on the dual n-back task. Based on our own
work and Kane's work, we included measures of matrix
reasoning and a measure of working memory capacity (Jaeggi,
Buschkuehl, Perrig, & Meier, 2010; Kane, Conway, Miura, &
Colflesh, 2007). Further, as we were interested in investigating
the transfer potential of a simpler n-back task version as well as
the dual n-back task, we included both single and dual n-back
task versions. There are four reasons to investigate the transfer
potential of a single n-back task: First, the dual n-back task is
relatively new and not much is known about its constituent
processes (Jaeggi et al., 2007; Jaeggi, Buschkuehl, Jonides, &
Perrig, 2008; Jaeggi, Schmid, Buschkuehl, & Perrig, 2009; Jaeggi

Please cite this article as: Jaeggi, S.M., et al., The relationship between n-back performance and matrix reasoning — implications
for training and transfer, Intelligence (2010), doi:10.1016/j.intell.2010.09.001

S.M. Jaeggi et al. / Intelligence xxx (2010) xxx–xxx

et al., 2003). Second, the dual n-back task is inherently complex,
and so it is not easy to disentangle the underlying processes.
Third, the dual n-back task includes an obvious task-switching
component (i.e., going back and forth between the two stimulus
streams that must be tracked). This task-switching component
might contribute to increased reasoning performance because in
many matrix reasoning problems, it seems important to be able
to switch back and forth between different representations.
However, it is not at all clear that task-switching processes are an
essential component of Gf; thus, if task-switching processes are
not critical to matrix reasoning, then a single n-back task should
correlate just as well with Gf as a dual n-back task. Finally, the
dual n-back task is very challenging for participants, thereby
restricting its range of application mainly to healthy young
adults. We know from our previous research that a frequently
used and well-established single n-back task recruits similar
neural networks to a dual n-back task (Jaeggi et al., 2003), and
also, that single n-back tasks share common variance with Gf
tasks (e.g. Gray, Chabris, & Braver, 2003; Hockey & Geffen, 2004;
Jaeggi, Buschkuehl, Perrig, & Meier, 2010; Kane, Conway, Miura,
& Colflesh, 2007). Thus, we investigated the relationship
between single n-back performance and measures of Gf, and
whether and how this relationship is different from that of the
dual n-back task and Gf. We also investigated the role of working
memory capacity, hypothesizing that working memory capacity
predicts performance in n-back tasks, however, to a lesser extent
than Gf.
2. Method
2.1. Subjects
A total of 104 participants (65 women) with a mean age of
21.3 years (SD = 2.2) were tested. Subjects were recruited
from the student population of the University of Michigan
and were paid $14 per hour for participation.
2.2. Tasks and procedure
2.2.1. n-back tasks
2.2.1.1. Single n-back task. Participants were shown a sequence
of visual stimuli and they had to respond each time the current
stimulus was identical to the one presented n positions back in
the sequence. The stimulus material consisted of 8 random
shapes (Vanderplas & Garvin, 1959) which we have used
previously (Jaeggi et al., 2003). The shapes were all shown in
yellow and presented centrally on a black background for 500 ms
each, followed by a 2500 ms interstimulus interval. Participants
were required to press a pre-defined key for targets, and their
response window lasted from the onset of the stimulus until the
presentation of the next stimulus (3000 ms); no response was
required for non-targets. Participants were tested on 2-, 3-, and
4-back levels in that order, with each level presented for 3
consecutive blocks, resulting in a total of 9 blocks. A block
consisted of 20+n stimuli and contained 6 targets and 14+ n
non-targets each. The dependent measure was the proportion of
hits minus false alarms averaged over all n-back levels.
2.2.1.2. Dual n-back task. In contrast to the single n-back task,
participants were required to respond to two independent

3

streams of stimuli, a visual one and an auditory one. We used
8 spatial positions for the visual modality, and 8 letters for the
auditory modality (cf. Jaeggi et al., 2007; Jaeggi, Buschkuehl,
Jonides, & Perrig, 2008; Jaeggi, Schmid, Buschkuehl, & Perrig,
2009). Participants were required to press a key whenever
the currently presented square was at the same position as
the one n stimuli back in the series, and another key
whenever the presented letters matched the one that was
presented n stimuli back in the sequence. No responses were
required for non-targets. The value of n was always the same
for visual and auditory stimuli. There were 6 auditory and 6
visual targets per block of trials (4 appearing in only one
modality at a time, and 2 appearing in both modalities at the
same time; i.e. targets could occur in either one modality
stream only, or in both modality streams simultaneously),
and their positions were determined randomly. Otherwise,
the procedure, timing, number of blocks, and levels were
similar to the single n-back task. The dependent measure was
the proportion of hits minus false alarms averaged over both
modalities and all n-back levels.
2.2.2. Working memory task
We used the automated version of the operation span task
(OSPAN) as a complex measure of WMC (Kane et al., 2004;
Unsworth, Heitz, Schrock, & Engle, 2005). The task requires
participants to recall a sequence of stimuli in the correct order
in addition to completing a distracting processing task (cf.
Conway et al., 2005). We presented three sets of stimuli per
set size (i.e., the number of stimuli to be recalled), and the set
sizes ranged from 3 to 7. The score, i.e. the sum of all perfectly
recalled sets, served as a dependent measure representing
complex working memory span (Unsworth, Heitz, Schrock, &
Engle, 2005).
2.2.3. Fluid intelligence tasks
We assessed Gf by using two different matrix reasoning
tasks, either the A or B version of the Bochumer Matrices Test
(BOMAT; 29 items; Hossiep, Turck, & Hasella, 1999), and the
even or the odd items of Raven's Advanced Progressive
Matrices (APM; 18 items; Raven, 1990), both counterbalanced.
Both tests were given with a time restriction, a procedure
adopted by many researchers (e.g. Jaeggi, Buschkuehl, Jonides,
& Perrig, 2008; Kane, Conway, Miura, & Colflesh, 2007; Kane
et al., 2004; Salthouse, 1993; Salthouse, Atkinson, & Berish,
2003; Unsworth & Engle, 2005; Unsworth, Heitz, Schrock, &
Engle, 2005). The reasons for choosing time-restricted versions
were two: First, administering the APM with the standard time
restriction or untimed usually results in ceiling performance for
a considerable number of participants in our labs. With the
BOMAT, ceiling performance is less of an issue, but especially for
the BOMAT, the standard testing time is rather long; thus, our
second reason for short time limits was to keep total testing
time as short as possible. It should be noted though that scores
in timed versions of the APM are nicely predictive of scores in
untimed versions (Frearson & Eysenck, 1986; Hamel &
Schmittmann, 2006; Heron & Chown, 1967; Salthouse, 1993;
Unsworth & Engle, 2005).
After several practice trials (10 items for the BOMAT, 2
items from Set I for the APM), participants were allowed to
work for 10 min on the BOMAT, and 10 min on the APM

Please cite this article as: Jaeggi, S.M., et al., The relationship between n-back performance and matrix reasoning — implications
for training and transfer, Intelligence (2010), doi:10.1016/j.intell.2010.09.001

4

S.M. Jaeggi et al. / Intelligence xxx (2010) xxx–xxx

Table 1
Mean, standard deviation (SD), range, and reliability estimates (Cronbach's α)
for each of the used tasks.
Mean
n-back
Single n-back
(mean 2–4back)
Dual n-back
(mean 2–4back)
Working memory
OSPAN
Fluid intelligence
Raven's APM
BOMAT

SD

Range

Table 3
Direct multiple regression model for the single n-back task as outcome
variable.

Reliability

0.45

0.19

−0.01–0.89

0.79

0.45

0.16

0.07–0.82

0.91

55.58

13.92

20–75

0.73

10.88
7.44

2.87
2.42

4–18
2–12

0.74
0.58

Model 1 (R2 = .35)
Constant
OSPAN
Raven's APM
BOMAT
Model 2 (R2 = .33)
Constant
Raven's APM
BOMAT

B

SE B

β

−0.05
0.00
0.01
0.03

0.08
0.00
0.01
0.01

0.14
0.23*
0.42**

0.03
0.02
0.03

0.06
0.01
0.01

0.26*
0.41**

Note: **p b .01; *p b .05.

Note: N = 104.

(Set II). The number of correct solutions provided in this time
limit was used as the dependent variable.
2.2.4. Analyses
We used SPSS (Release 15) for all our data analyses. The
data were examined to determine whether they fulfilled the
assumptions necessary for multiple linear regression: We
checked for univariate and multivariate normality, multicollinearity, heteroscedasticity, independent errors, and
normally distributed errors and we found all these to be in
appropriate ranges. We calculated several multiple linear
regression models in order to determine which variables
were best suited to predict n-back performance, and also,
which variables were most predictive for performance in the
BOMAT and APM. We used a direct method by entering all
variables into the model and then removing the nonsignificant predictors one after another until only significant
predictors remained. With the significant predictors, we ran a
forward stepwise analysis in order to determine the individual contribution of each predictor.

for the single n-back task (Single n-back: BOMAT vs OSPAN:
Steiger's Z = 2.92, p b .01; APM vs OSPAN: Z = 2.04, p b .05;
Dual n-back: BOMAT vs OSPAN: Z = 1.20, p = ns.; APM vs
OSPAN: Z = 1.12, p = ns.).
In order to predict single n-back task performance, we first
entered all 3 predictors (OSPAN, APM, and BOMAT) into a
regression model. The model is reported in Table 3 showing
that single n-back performance was best predicted by the
BOMAT. The model resulting from the stepwise forward
analysis is reported in Table 4, showing that both the APM
and the BOMAT, but not the working memory measure
significantly predicted n-back performance.
As shown in Table 5, we entered the same predictors as
before, but with dual n-back performance as the outcome
measure. Similar to single n-back performance, dual n-back
performance was best predicted by the BOMAT. This time
however, all three predictors contributed significantly to the
variance in the model. The results of the stepwise forward
analysis are reported in Table 6.
In Tables 7 and 8, we show the results for the regression
analyses in which we predict performance in the two matrix

3. Results
Means, standard deviations, and reliability estimates for
all measures are reported in Table 1. The Pearson's correlations among the variables used for the regression analyses are
reported in Table 2.
Overall, our data revealed a strong relationship between
the single and dual n-back tasks with a correlation of r = .72,
indicating that the two versions share a considerable amount
of common variance (see Table 2). Further, the correlation of
both n-back tasks with the matrices tasks were stronger than
the correlations of the n-back and the working memory task,
although the difference only reached statistical significance
Table 2
Pearson correlation coefficients for the measures used in the regression
models.
Single n-back
Single n-back
Dual n-back
OSPAN
Raven's APM
BOMAT

0.72**
0.21*
0.44**
0.53**

Note: N = 104; **p b .01; *p b .05.

Dual n-back

0.26**
0.41**
0.40**

OSPAN

0.24*
0.05

APM

0.42**

Table 4
Stepwise forward analysis for the single n-back task as outcome variable.

Step 1
Constant
BOMAT
Step 2
Constant
BOMAT
Raven's APM

B

SE B

β

0.15
0.04

0.05
0.01

0.52***

0.03
0.03
0.02

0.06
0.01
0.01

0.41***
0.26**

Note: R2 = .28 for Step 1; ΔR2 = .05 for Step 2 (p's b .01); ***p b .001; **p b .01.

Table 5
Direct multiple regression model for the dual n-back task as outcome
variable.

BOMAT
(R2 = .26)
Constant
OSPAN
Raven's APM
BOMAT

B

SE B

β

0.03
0.00
0.01
0.02

0.08
0.00
0.01
0.01

0.19*
0.24*
0.29**

Note: **p b .01; *p b.05.

Please cite this article as: Jaeggi, S.M., et al., The relationship between n-back performance and matrix reasoning — implications
for training and transfer, Intelligence (2010), doi:10.1016/j.intell.2010.09.001

S.M. Jaeggi et al. / Intelligence xxx (2010) xxx–xxx
Table 6
Stepwise forward analysis for the dual n-back task as outcome variable.
B
Step 1
Constant
Raven's APM
Step 2
Constant
Raven's APM
BOMAT
Step 3
Constant
Raven's APM
BOMAT
OSPAN

SE B
0.06
0.01

0.41***

0.13
0.02
0.02

0.06
0.01
0.01

0.29**
0.28**

0.03
0.01
0.02
0.00

0.07
0.01
0.01
0.00

0.24*
0.29**
0.18*

Note: R2 = .16 for Step 1; ΔR2 = .06 for Step 2; ΔR2 = .03 for Step 3 (p 's b .01);
***p b .001; **p b .01; *p b .05.

reasoning measures. For both measures, it was the single n-back
task alone that accounted for the variance in the Gf tasks.
4. Discussion
The findings of Study 1 confirm other findings from the
literature (Jaeggi, Buschkuehl, Perrig, & Meier, 2010; Kane,
Conway, Miura, & Colflesh, 2007): Consistent with our
hypotheses, both n-back task variants were highly correlated,
and both were best predicted by Gf.
In general, matrix reasoning tasks seem to be better
predictors for both the single and the dual n-back tasks than a
measure of working memory capacity. As the reliability
estimates were appropriate for the n-back tasks, the lack of
correlation between the n-back tasks and the measure of
working memory capacity cannot be attributed to insufficient
reliability (Jaeggi, Buschkuehl, Perrig, & Meier, 2010). Rather, it
seems that performance for the two tasks relies on different
sources of variance, which might result from the different
memory processes that are involved in the two tasks: whereas
the n-back task relies on passive recognition processes,
performance in working memory capacity tasks requires active
and strategic recall processes (Kane, Conway, Miura, & Colflesh,
2007).
Despite the apparent process overlap in single and dual
n-back performance, we still observed differential cognitive
processes mediating performance in single or dual n-back tasks:
whereas single n-back performance was mostly predicted
Table 7
Direct multiple regression model for Raven's APM as outcome variable.

Model 1 (R2 = .23)
Constant
Single n-back
OSPAN
Dual n-back
Model 2 (R2 = .21)
Constant
Single n-back
OSPAN
Model 3 (R2 = .19)
Constant
Single n-back
Note: ***p b .001; *p b .05.

Table 8
Direct multiple regression model for the BOMAT as outcome variable.

β

0.20
0.02

B

SE B

β

6.05
4.56
0.03
2.79

1.14
1.96
0.02
2.24

0.29*
0.13
0.16

6.33
6.28
0.03

1.12
1.40
0.02

0.41*
0.15

7.83
6.78

0.67
1.38

0.44***

5

Model 1 (R2 = .28)
Constant
Single n-back
OSPAN
Dual n-back
Model 2 (R2 = .28)
Constant
Single n-back
OSPAN
Model 3 (R2 = .28)
Constant
Single n-back

B

SE B

β

4.82
6.50
−0.01
0.87

0.93
1.59
0.02
1.82

0.50***
−0.07
0.06

4.91
7.04
−0.01

0.90
1.13
0.02

0.54***
−0.07

4.35
6.86

0.54
1.10

0.52***

Note: ***p b .001.

by matrix reasoning, dual-task performance was mediated by
working memory capacity in addition to Gf. Further, the single
n-back task was the only predictor for both matrix reasoning
measures. Considering the rationale that transfer is more likely
to happen for tasks that share considerable variance, we can
conclude that training on both single and dual n-back tasks
should yield transfer to matrix reasoning, but that transfer to
working memory capacity should be less likely, especially in the
case of single n-back training. Considering the variance
explained in the matrix reasoning tasks, our data suggest that
the single n-back task might be an even better training vehicle
than the dual n-back task.
Study 2. In Study 2, we tested the implication of the findings
from Study 1 by investigating the transfer potential of a single
n-back task to measures of Gf as compared to training with a
dual n-back task, and also whether transfer occurs to a
measure of working memory capacity. Based on the rationale
and the results from Study 1, we hypothesized that both
training regimens should yield transfer to both matrices
tasks, but that the effect on working memory capacity should
be smaller than the effect on Gf due to the smaller intercorrelations evident in Study 1. We trained 46 undergraduate
students with either a single or a dual n-back task over the
course of one month, assessing their performance on trained
tasks, on variants of these tasks using different stimulus
material, on a measure of working memory, and on the two
matrices tasks that we used in Study 1. To control for re-test
effects, the performance of the trained groups was compared
to a control group (N = 43) that completed the same transfer
tasks in a pre- and post-test session, but that was not trained
between the two testing sessions.
5. Method
5.1. Participants
Ninety-nine undergraduates (mean age = 19.4 years; SD=
1.5; 76 women) from the National Taiwan Normal University
in Taipei volunteered to take part in the study. Fifty-two
(41 women) were assigned to the control group and 47
(35 women) were assigned to the experimental group. In
return for participation, participants earned course credit. In
addition, the training groups received NT$ 600 (about US$20)
as well as the training software after study completion. After

Please cite this article as: Jaeggi, S.M., et al., The relationship between n-back performance and matrix reasoning — implications
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S.M. Jaeggi et al. / Intelligence xxx (2010) xxx–xxx

the pretest, participants in the experimental group were
assigned to either the single or the dual n-back training
intervention. The two groups were matched by using the
software ‘Match’ (Van Casteren & Davis, 2007) based on
the following criteria: age, gender, pre-test performance in
the n-back baseline tasks (single and dual), as well as pre-test
performance in one of the matrices tasks (BOMAT). One
participant from the dual-task training regimen dropped out
after a few training sessions and these data were discarded
from further analyses. The final single n-back training group
consisted of 21 participants (mean age = 19.0 years, SD= 1.5;
17 women), and the dual n-back group consisted of 25
participants (mean age = 19.1 years, SD= 1.2; 18 women).
Since there were also drop-outs in the no-contact control
group, we had a final n of 43 participants (mean age = 19.4,
SD= 1.0; 34 women) in this group.
5.2. Training and transfer tasks
5.2.1. Training
We used two n-back interventions, an adaptive dual nback task that we used previously (Jaeggi, Buschkuehl,
Jonides, & Perrig, 2008), and an adaptive single n-back task
using only visospatial material (Jaeggi, Schmid, Buschkuehl, &
Perrig, 2009).
5.2.1.1. Dual n-back task. For the adaptive dual n-back task, we
used the same visual stimuli as used in Study 1. However, for
the auditory stimuli, we used 8 syllables of the Mandarin
phonetic system instead of letters from the Latin alphabet. In
order to match the task to each participant's ability, the level of
difficulty was varied by changing the level of n (Jonides et al.,
1997): After each block, each participant's individual performance was analyzed, and in the following block, the level of n
was adapted accordingly: If the participant made fewer than 3
mistakes per modality, the level of n increased by 1. It was
decreased by 1 if more than 5 mistakes were made, and in all
other cases, n remained unchanged. One training session
comprised 15 blocks consisting of 20 + n trials resulting in a
daily training time of approximately 17–20 min. Participants
were given feedback concerning their performance after each
block (percent correct for each modality). In addition, participants received feedback at the end of each training session
consisting of their performance score for each session that had
been completed, as well as a curve representing the scores of a
reference group consisting of all participants who completed
comparable training in our laboratory in other experiments
prior to this one.
5.2.1.2. Single n-back task. As a second intervention, we used
an adaptive single-task version of the n-back task requiring
the processing of the visuospatial modality only. Everything
else (i.e. training length, adaptivity of the level of the n-back
task based on subjects' performance, and feedback) was the
same as in the dual n-back intervention described above.
5.2.2. Transfer tasks
5.2.2.1. n-back. In order to assess baseline n-back performance, we used the same single n-back task with random
shapes that we used in Study 1 (n-back levels 2, 3, and 4). As

none of the training groups had trained with stimuli of this
type, we used this task to assess near transfer.

5.2.2.2. Working memory span. We used the automated
OSPAN as used in Study 1.

5.2.2.3. Matrix reasoning. As in Study 1, we administered two
standard matrix reasoning tests in order to measure Gf, the
short version of the Bochumer Matrizen-Test (BOMAT;
Hossiep, Turck, & Hasella, 1999), and the Raven's Advanced
Progressive Matrices (APM; Raven, 1990). Parallel versions (A
and B in the BOMAT consisting of 29 items each, as well as the
odd and even items in the APM consisting of 18 items each)
were used in order to prevent participants from getting the
same items in pre- and post-test (te Nijenhuis, van Vianen, &
van der Flier, 2007). The order of the versions was counterbalanced. We had slightly more testing time available than in
Study 1, thus, after some practice trials (10 items for the
BOMAT, 3 items for the APM, i.e. from set I), participants were
allowed to work for 16 min on the BOMAT, and for 11 min on
the APM. The dependent measure was the number of
correctly solved problems within this time limit.

5.2.3. Procedure
To assess the change in cognitive performance, all participants were pre- and post-tested at the same interval (3 days
before the start of training, and 3 days after training completion;
with a 5-week interval for the no-contact control group) with
the tests described above. Participants were tested in groups of
30–40 individuals, and they were divided into two groups of
15–20 students each. One group (consisting of participants from
all 3 intervention groups) first completed the n-back task and
the OSPAN followed by the matrix reasoning tasks (APM,
BOMAT), whereas the second group started with the matrices
tasks first and completed n-back and OSPAN afterwards.
After pre-testing, participants in the two training groups
trained on a daily basis, five times per week (not on weekends)
for a period of 4 weeks. Participants trained in small groups
of 10–15 students in a computer laboratory located at the
University.

6. Results
Descriptive data for each of the intervention groups and
test session are reported in Table 9. Note that there were no
significant group differences at pre-test in any of the criterion
measures.

6.1. Training data
First, we investigated specific training effects and tested
whether there are differential training effects as a function of
training group. As illustrated in Fig. 1, both training groups
improved their performance over the four weeks of training,
but the single-task group trained at a higher n-back level,
reflecting the lower complexity of the single task compared to
the dual task.

Please cite this article as: Jaeggi, S.M., et al., The relationship between n-back performance and matrix reasoning — implications
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S.M. Jaeggi et al. / Intelligence xxx (2010) xxx–xxx

7

Table 9
Descriptive data for the transfer measures as a function of group.
Pre-test

Single n-back training group
Single n-back
Operation span
Raven's APM
BOMAT
Dual n-back training group
Single n-back
Operation span
Raven's APM
BOMAT
No-contact control group
Single n-back
Operation span
Raven's APM
BOMAT

Post-test

Effect size
(Cohen's d)

N

Mean

SD

Min

Max

Mean

SD

Min

Max

20
21
21
21

.42
57.60
11.33
11.48

.15
12.83
2.28
3.11

.18
13
7
6

.68
75
14
16

.64
55.14
12.81
13.67

.18
13.91
2.27
3.17

.19
7
9
8

.91
75
18
20

1.33
−0.18
0.65
0.70

25
25
25
25

.37
57.79
11.32
10.88

.17
14.46
1.93
2.60

.00
14
8
5

.72
75
15
17

.64
56.92
13.36
12.28

.18
9.50
2.22
3.09

.30
37
9
8

1.00
71
18
19

1.54
−0.07
0.98
0.49

41
40
43
43

.33
52.73
11.58
10.79

.17
11.93
2.60
2.50

−.10
21
2
6

.63
75
17
16

.37
55.50
11.81
11.44

.22
12.36
2.27
2.58

−.12
29
6
8

.76
75
17
19

0.20
0.23
0.09
0.26

Fig. 1. Specific training effects. Performance increase in the trained task shown separately for each training group. For each session, the mean n-back level achieved
by the participants is presented. Error bars represent the standard error of the mean.

6.2. Near transfer effects
In order to assess near transfer effects, we calculated
repeated-measures ANOVAs with session (pre vs post) as a
within-subjects factor, and intervention (dual n-back, single
n-back, control) as a between-subject factor for the near
transfer measure, i.e. for the non-trained single n-back task.
For logistical reasons, not all participants were able to
complete this task, and the final sample size is indicated in
Table 9. Performance (Pr) was calculated as a composite score
consisting of the averaged 2-back, 3-back, and 4-back
accuracy. Our results showed a highly significant session ×
intervention interaction (F(2,82) = 15.74; p b .001, η2p = .28)1.
1

Although there were no significant group differences at pre-test, we ran
additional analyses of covariance controlling for pre-test performance for
each of the transfer measures which yielded similar results.

Pairwise comparisons showed that the performance gain was
largest in the dual n-back training group (t(24) = 8.42;
p b .001; d = 1.54), followed by the single n-back training
group (t(18) = 4.61; p b .001; d = 1.23), however there was
no difference in gain between the two training groups
(d = .34). The training groups improved more than the nocontact control group (d N 1) which showed no significant
performance increase in this task (t(40) = 1.72; p = .09;
d = .19).

6.3. Operation span task
There was no significant session × intervention interaction (F(2,82) = 2.11; p = ns., η2p = .05). Note that none of the
three groups showed significant performance differences
between pre- and post-test (all t b 2).

Please cite this article as: Jaeggi, S.M., et al., The relationship between n-back performance and matrix reasoning — implications
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8

S.M. Jaeggi et al. / Intelligence xxx (2010) xxx–xxx

Fig. 2. Transfer effects on matrix reasoning. Mean problems solved in each session illustrated for each group and Gf test. Note that there were no significant group
differences at pretest.

6.4. Matrix reasoning tasks
In order to assess transfer effects on matrix reasoning, we
calculated repeated-measures ANOVAs with session (pre vs
post) as a within-subject factor, and intervention (dual nback, single n-back, control) as a between-subject factor
separately for each matrix task (BOMAT and APM; see Fig. 2).
The results yielded significant intervention × session interactions for each task (BOMAT: F(2,85) = 3.45; p b .05,
η2p = .08; APM: F(2,85) = 5.03; p b .01, η2p = .11)2. Pairwise
comparisons showed that both training groups significantly
improved performance in both tasks (dual n-back training group:
BOMAT: t(24)= 2.38; p b .05; d = 0.49; APM: t(24) = 4.58;
pb .001; d=.98; single n-back training group: BOMAT: t(20)=
5.04; pb .001; d=0.70; APM: t(20)=3.13; pb .01; d =0.65), and
there was no difference in gain between the two groups in either
of the two tasks (d b .32). In contrast, the control group
only showed a marginally significant re-test effect on the
BOMAT, but not in the APM (BOMAT: t(42)=2.08; pb .05;
d=0.26; APM: t(42)=0.61; p=ns.; d=0.10).
7. Discussion
The goal of Study 2 was to investigate whether a single n-back
intervention is a useful alternative to the complex dual n-back
task that we used previously to demonstrate a transfer effect on
tests of Gf. We based our assumption regarding the effectiveness
of the single n-back task on our earlier findings showing that dual
and single n-back tasks recruit similar neural networks (Jaeggi
et al., 2003), and on the fact that single n-back performance
correlates with Gf as well as dual n-back performance (Experiment 1; Jaeggi, Buschkuehl, Perrig, & Meier, 2010).
Concerning the near transfer results, both intervention
groups improved their performance almost equally in the
2
The task order (A/odd in pre then B/even in post, or the other way
round) was entered as covariate in the ANOVAs.

random-shape variant of the baseline single n-back task in
spite of the fact that neither of the training groups had trained
with these stimuli. In contrast, there was only a negligible
performance increase for the control group. Thus, both
intervention groups were able to generalize their n-back
training performance to stimulus material and presentation
format which was unfamiliar to them, providing evidence
that the intervention had an effect on some general
underlying processes involved in n-back performance, rather
than just building up a very task- and material-specific skill.
As predicted, we found no transfer effects to a measure of
working memory capacity for the single n-back task group. We
also found no transfer for the dual n-back task group even
though Study 1 showed that dual n-back performance was
partially predicted by working memory capacity. We note,
however, that the correlation of OSPAN with dual-task
performance was considerably smaller than the correlation of
this task with both matrices tasks.
This finding might be surprising given that both the OSPAN
and the n-back tasks are considered WM tasks. However,
previous research has shown that these tasks do not share
considerable common variance, although they both seem to
predict variance in Gf tasks (e.g. Jaeggi, Buschkuehl, Perrig, &
Meier, 2010; Kane, Conway, Miura, & Colflesh, 2007). The lack of
correlation between the two WM tasks most likely results from
the fact that there are different processes involved in the two
tasks: whereas the main processes that drive performance in
the n-back tasks are familiarity- and recognition-based discrimination processes (Oberauer, 2005; Smith & Jonides, 1998),
complex WM span tasks, such as the OSPAN, require active
recall processes rather than recognition. This pattern is also
consistent with our prior findings of no effect on complex span
(Jaeggi et al., 2008). Indeed, Li et al. (2008) have even reported a
significant performance decrease after single n-back training in a
related complex span measure (rotation span). Thus, although
there was no significant performance difference between preand post-test in either of the groups in the present study, one

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S.M. Jaeggi et al. / Intelligence xxx (2010) xxx–xxx

could speculate that n-back training somehow interferes with
performance in complex span measures as participants might
rely more on recognition instead of recall processes at post-test
which might prevent any performance gain. Since both WM
tasks seem to be related via their relationship to Gf measures,
though, one might argue that one could also train on complex
span measures in order to get transfer to Gf. However, Chein and
Morrison (2010) trained their subjects on complex-span
measures, but they did not find any transfer to matrix reasoning.
But most interestingly, our results show transfer effects in
both matrix reasoning tasks after training. This replicates our
prior results (Jaeggi, Buschkuehl, Jonides, & Perrig, 2008), but
it also extends our findings by showing that a) the transfer
effect was present in more than just one Gf task, and b), that it
was also obtained by training on a single n-back task.
Although, matrices tasks like the APM and the BOMAT are
regarded as prototypical tasks to measure Gf, with the APM
representing the task with the highest Gf loading (e.g. Gray &
Thompson, 2004; Kane & Engle, 2002; Snow, Kyllonen, &
Marshalek, 1984), they are only an approximation of Gf. Thus,
we acknowledge that in order to capture the full range of Gf,
there should be testing with a more exhaustive battery of
tasks. That is, the current data do not allow us to firmly
determine whether the gains in matrix reasoning in our study
represent real gains in Gf, or whether they emerge because
some aspects of the training allowed participants to better
deal with the specific content of the matrices tasks themselves. A related issue is whether we captured Gf with the
timed versions of the matrices tasks we used, or whether we
“just” improved some task-specific abilities. In a time-limited
version of these tests, most subjects do not reach the end of
the test; this is especially true of the BOMAT. Moody (2009)
has argued that restricting the tests to just the early items
leaves out the items that have higher Gf loadings. This issue
has been addressed before by other researchers who
investigated whether there are differential age effects or
working memory involvement in the different parts of the
APM (Salthouse, 1993; Unsworth & Engle, 2005). These
studies found no evidence for differential processes in the
various items of the APM, at least for the first three quartiles
of the task; thus, it seems unlikely that a subset of items in the
APM measures something different than Gf. In our own data,
the transfer effects were actually more pronounced for the
second half of the test in the APM, which is reflected in a
significant 3-way interaction (session × APM-part × intervention; F(2,86) = 5.31; p b .01; η2p = .11). In the BOMAT, we
observed no differential transfer effects for the earlier vs later
items (F(2,86) = .64; p = ns.; η2p = .02). Thus, if there are any
differences in Gf loading in the various parts of the matrices
tasks, the present data suggest that the transfer effects are
roughly equivalent for the parts of the test that are claimed to
have higher vs lower Gf loadings.
Because we limited our intervention to versions of the n-back
task, one might wonder whether one could improve matrix
reasoning with any kind of cognitive training. That is, is there
something specific to components of the n-back task that
makes it unique or unusual? Of course, this remains an
empirical issue, but the sparse reports of transfer after cognitive
training in general suggest that the transfer effects obtained in
the present study do not represent a general effect of transfer
no matter the training task (e.g. Barnett & Ceci, 2002; Salomon

9

& Perkins, 1989; Verhaeghen, Marcoen, & Goossens, 1992;
Zelinski, 2009).
A limitation of Study 2 is that we used a no-contact control
group. One might argue that the training groups were simply
more motivated because they received more experimenter
attention and therefore showed more transfer (Hawthorne
effect). However, if the transfer was just due to motivational
factors, the training groups should have outperformed the
control group in all transfer measures. Thus, the lack of
improvement in WM capacity for the training groups might
be taken as a case against an unspecific effect of mere
motivation or arousal. Nevertheless, future studies should
replicate the present effects by carefully selecting an
appropriate active control group in order to rule out any
placebo or Hawthorne effects (Buschkuehl & Jaeggi, 2010;
Shipstead, Redick, & Engle, in press).
7.1. General discussion
In the two studies we aimed to explore the relationship
between n-back tasks and ability measures such as WMC and Gf,
and we also evaluated the transfer potential of a single n-back
task to these outcome measures. In the first study, we
demonstrated that dual and single n-back task performance is
equally well correlated with performance on two different tests
measuring Gf, whereas the correlation of these n-back tasks
with a task assessing working memory capacity was much
smaller. Based on these results, we were led to test the
hypotheses that training on a single n-back task might yield
the same improvement in Gf as training on a dual n-back task,
and that there should be less transfer to a measure of
working memory capacity. Thus, in Study 2, we investigated
transfer effects on working memory capacity and Gf by
training participants on either a single or on a dual n-back
task. Consistent with our hypotheses, our results showed
that although there was no transfer on a measure of working
memory capacity, both training groups improved more on Gf
than the no-contact control group. This pattern replicates
our prior results (Jaeggi, Buschkuehl, Jonides, & Perrig,
2008), but also goes beyond them by demonstrating that
there is transfer on two different matrix reasoning tasks, and
that single n-back training seems to be equally effective as
dual n-back training.
As there are still many unknown factors concerning training
and transfer (Willis & Schaie, 2009), one aim of the present
study was to shed light on the underlying mechanisms that
drive the transfer effects that we previously have found. We
outlined several features that we think are important for
training in order to get transfer. First of all, we proposed that the
training and transfer task should engage overlapping processes.
Our differential results showing transfer to matrix reasoning
but not OSPAN support this assumption, because the data from
Study 1 as well as earlier studies show that n-back and
measures of working memory capacity do not share much
common variance (Jaeggi, Buschkuehl, Perrig, & Meier, 2010;
Kane, Conway, Miura, & Colflesh, 2007). In contrast, n-back
performance and matrix reasoning share a great deal of
common variance; consequently, there was transfer as a result
of n-back training. We also proposed that it is important that
participants only minimally learn task-specific strategies in
order to prevent specific skill acquisition. We think that besides

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the transfer to matrix reasoning, the improvement in the near
transfer measure provides additional evidence that the participants trained on task-underlying processes rather than
relying on material-specific strategies. Further, we proposed
that it is important to maximally stress the information
processing system by using a very complex training paradigm,
in our case, a dual variant of the n-back task. However, the
results of both studies indicate that this is not necessary in order
to get transfer: Study 1 showed that the single n-back task is
equally related to matrix reasoning, and Study 2 showed that
single n-back training yields transfer to our Gf tasks as well.
Thus, using a dual task for training does not seem to be
necessary in order to obtain transfer to matrix reasoning.
Of course, there are many more research questions to be
addressed. For example, we still do not know whether it is
necessary to tailor the level of difficulty of the training task to
the changing performance level of the subjects as they
improve. We assume that adaptivity might be a crucial factor
for transfer because it ensures that the participants' executive
control system is sufficiently taxed to prevent automatic
processing. Further, we do not know how general the transfer
effects are, whether they extend to measures of daily living or
academic or professional success, how long-lasting the effects
are, what executive components are the critical ones to train,
and whether there are inter-individual differences that
moderate training and transfer. These and other questions
await further research. Nonetheless, our current work has
made progress in examining one of the critical issues raised
by our initial study: There is no need to rely on a dual task to
achieve improvement in matrix reasoning. Therefore, our
findings lead to an important message for training research:
In that the dual n-back task is quite complex in the processes
it engages, it is not an ideal task for many participant groups
other than young adults. The present results provide
empirical support that it is not necessary to train with this
complex task in order to improve Gf; thus, our results open a
wider range of application for our training approach in that
the single n-back task can be used for participants such as
children or older adults who would find the dual n-back task
too complex and too taxing. Furthermore, it makes the
investigation of the processes in training and transfer more
accessible because the processes engaged by the single nback task are better understood than the ones in dual n-back
tasks.
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