MEMORY SPAN TASKS Measuring Working Memory Capacity with


Running head: MEMORY SPAN TASKS
Measuring Working Memory Capacity with a Simple Span Task:
The Chunking Span and its Relationship to Fluid Intelligence
Mustapha Chekaf a, Nicolas Gauvrit b, Alessandro Guida c & Fabien Mathy d
a
Département de Psychologie, Université de Franche-Comté
b
c
d
CHArt Lab (PARIS-reasoning)
Département de Psychologie, Université Rennes II
Département de Psychologie, Université Nice Sophia Antipolis
Author note: Corresponding Author: Fabien Mathy, Département de Psychologie, Université Nice Sophia
Antipolis, Laboratoire BCL: Bases, Corpus, langage - UMR 7320, Campus SJA3, 24 avenue
des diables bleus, 06357 Nice CEDEX 4. Email: [email protected]. This research was
supported in part by a grant from the Région de Franche-Comté AAP2013 awarded to Fabien
Mathy and Mustapha Chekaf. We are grateful to Caroline Jacquin for her assistance in data
collection in Exp. 2. We are also grateful to the Attention & Working Memory Lab at Georgia
Tech for helpful discussion, and particularly to Tyler Harrisson who suggested two of the
structural equation models. Authors’ contribution: FM initiated the study and formulated the
hypotheses; MC and FM conceived and designed the experiments; MC run the experiments;
MC, NG, and FM analyzed the data; NG computed the algorithmic complexity; MC, NG,
AG, and FM wrote the paper. Work submitted in part to the Proceedings of the Cognitive
Science Society, 2015.
Body text word count: 20500
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Abstract
It has been assumed that short-term memory and working memory refer to the storage and the
storage + processing of information respectively. The two separate concepts have been
measured in simple and complex span tasks respectively, but here, a new span task was
developed to study how storage and processing interact in working memory and how they
relate to intelligence. This objective was reached by introducing a chunking factor in the new
span task that allowed manipulating the quantity of processing that can be used for storage
while using a procedure similar to simple span tasks. The main hypothesis was that the
storage × processing interaction induced by the chunking factor is an excellent indicator to
study the relationship between working memory capacity and intelligence, because both
(working memory and intelligence) depend on optimizing storage capacity. Two experiments
used an adaptation of the SIMON® game in which chunking opportunities were estimated
using an algorithmic complexity metric. The results show that the metric can be used to
predict memory performance and that intelligence is well predicted by the chunking span task.
2
Measuring Working Memory Capacity with a Simple Span Task: The Chunking Span
and its Relationship to Intelligence
The present study explores the limits of the short-term memory (STM) span, measured
by the length of the longest sequence that can be recalled over brief periods of time. One
crucial issue when measuring individuals’ memory spans is that they are inevitably related to
other processes that might inflate their measures, such as information reorganization into
chunks (e.g., Cowan, 2001; Cowan, Rouder, Blume, & Saults, 2012; Mathy & Feldman,
2012; Miller, 1956) and/or even long-term memory storage (e.g., Ericsson & Kintsch, 1995;
Gobet & Simon, 1996; Guida, Gobet, Tardieu, & Nicolas, 2012). This study aims to
investigate how information reorganization through chunking can be used to optimize
immediate recall by introducing a new simple span measure: the chunking span. It is based on
a measure of complexity that, we argue, captures the sum of information that can be grouped
to form chunks. In the paper, we examine how this new span measure relates to intelligence
and other immediate memory measures (used as an umbrella term for short-term memory and
working memory [WM]).
The first section deals with what we think represents the mainstream consensus in the
literature regarding the conceptualization of span tasks, including a brief review of the
respective advantages and disadvantages of STM spans and WM spans. We then describes the
rather paradoxical relation between these two kinds of measures and their respective STM and
WM concept targets. Finally we introduce the chunking span task that allows varying the
degree of involvement of storage and processing using a simple span task, which we believe
helps better characterize STM/WM capacity and the nature of its relationship with general
fluid intelligence .
3
Span tasks taxonomy
It has been commonly accepted that STM and WM refer to the (temporary) storage
and (temporary) storage + manipulation of information respectively (e.g., Baddeley & Hitch,
1974; Colom, Rebollo, Abad, & Shih, 2006; A. R. Conway, Cowan, Bunting, Therriault, &
Minkoff, 2002; Kane et al., 2004; Engle, Tuholski, Laughlin, & Conway, 1999; for an indepth analysis, see Aben, Stapert, Blokland, 2012; see Davelaar, 2013, for a short
explanation), and one of the most popular ideas has been that STM and WM are best
represented by simple and complex span tasks respectively (see Shipstead, Redick, & Engle,
2012). Simple span tasks traditionally require retaining a series of items (e.g., digits, words,
pictures), whereas in complex span tasks, participants have to maintain the to-be-recalled
material while continuously performing concurrent tasks (such as the famous articulatory
suppression, e.g., Baddeley, 2000; Baddeley, Thomson, & Buchanan, 1974; Baddeley, Lewis,
& Vallar, 1984) or while executing discontinuously interspersed elementary concurrent tasks
(e.g., Barrouillet, Bernardin, & Camos, 2004; Barrouillet, Bernardin, Portrat, Vergauwe, &
Camos, 2007). The reading span (Daneman & Carpenter, 1980) and the operation span
(Turner & Engle, 1989) are two famous examples of this dual-task paradigm, while digit and
letter spans (Miller, 1956) traditionally refer to simple span tasks.
By comparison with simple span tasks, the complex ones have had an advantage
because of the role they have regularly played in theoretical advances, especially in the role of
attention in WM (A. R. Conway et al., 2005; Engle, 2002; Oberauer, 2002). For example,
they can be used to determine how processing and storage compete simultaneously for
attention (e.g., Barouillet & Camos, 2012; Oberauer, Lewandowsky, Farrell, Jarrold, &
Greaves, 2012). Although maybe less challenging for the community of researchers, simple
span tasks are, however, still used in several intelligence tests (such as the Weschler's) since
4
their use with patients in diverse medical contexts is easy and the instructions are simple.
However, one main disadvantage of simple span tasks is that the STM capacity estimated
from the tasks can be inflated by practiced skills and strategies such as rehearsal and chunking
(Cowan, 2001; Ericsson, Chase, & Faloon, 1980; Miller, 1956).
For the last forty years (more or less since Baddeley and Hitch’s seminal 1974 paper)
there has been a consensus that WM is more important for complex activities than STM (e.g.,
Ehrlich & Delafoy, 1990; Klapp, Marshburn, & Lester, 1983; Perfetti & Lesgold, 1977), and
indeed complex spans have been reported to be better predictors of complex activities and
fluid intelligence than simple spans (Cantor, Engle, & Hamilton, 1991; A. R. Conway,
Cowan, Bunting, Therriault, & Minkoff, 2002; Daneman & Carpenter, 1980; Daneman &
Merikle, 1996; Dixon, LeFevre, & Twilley, 1988; Unsworth & Engle, 2007a, 2007b; but see
Colom, Rebollo, Abad, & Shih, 2006), and particularly for Raven's Advanced Progressive
Matrices (A. R. Conway et al., 2005). However, Unsworth and Engle (2007a) recently
showed that the prediction of simple spans of fluid intelligence could be increased, increasing
list-length. They observed that when list-length reached five, simple spans became as good as
complex spans, in terms of predicting fluid intelligence2 (for a comparable result, see Bailey,
Dunlosky, & Kane, 2011). One possible explanation is that long-length-lists need to be
reorganized by individuals in order to be stored (Chase & Simon, 1973; de Groot & Gobet,
1996; Miller, 1956), because they exceed immediate memory capacity. As such, the 7+/-2
estimation first found by Miller (1956) can be thought to represent an overestimation due to
chunking of the true capacity of immediate memory, now most often estimated as being about
2
According to Unsworth and Engle (2006), when the elements to store or process are larger than 3 to
4 elements, primary memory (similar to the kind of immediate memory proposed by James, 1890) is
insufficient and elements are displaced in secondary memory (similar to episodic long-term memory),
and the process of searching and retrieving from secondary memory would explain the commonalties
among long-list-length simple spans, complex spans and fluid intelligence. Another possibility, which
is developed in this paper, is to stress the fact that these commonalties are due to information
reorganization through chunking.
5
3 or 4 (e.g., Cowan, 2001; Cowan, 2005). Effectively, Mathy and Feldman (2012) modeled
the connection between the 7 and 4 magical numbers through chunking. From this standpoint,
our hypothesis is that the capability of simple spans (when using long-length-lists) to predict
fluid intelligence could be due to information reorganization into chunks.
The idea that information reorganization into chunks is an important characteristic of simple
spans is completely in accordance with a line of research developed by Bor and colleagues
(Bor, Cumming, Scott, & Owen, 2004; Bor, Duncan, Wiseman, & Owen, 2003; Bor & Owen,
2007; Bor & Seth, 2012). Instead of increasing list-lengths to trigger information
reorganization, Bor and colleagues introduced systematic regularities into the memoranda in
an attempt to induce a chunking process. They showed than when individuals could chunk
information thanks to structured material, their simple span increased as did activation in
lateral prefrontal areas, which the authors took as the cerebral substratum of information
reorganization. These results show that simple spans considered to be only “storage tasks” can
be viewed as storage + manipulation tasks as well, when systematic regularities are provided.
Even if this method has been used several times by Bor and colleagues (Bor et al., 2003,
2004; Bor & Owen, 2007), it was applied only recently using a metric of compression that
allows precisely manipulating the probability of chunking via measures of complexity (Mathy
& Feldman, 2012). This will be presented below when we present our chunking span task,
which allows a simple span to be changed gradually from a storage task to a storage +
manipulation task. This possibility to vary along this dimension (all other things being equal)
is made crucial by what we call the STM/WM paradox.
The STM/WM paradox
The STM/WM paradox derives from the fact that even if there is a mainstream
consensus that simple spans can be equated with storage and complex spans with storage +
6
manipulation of information, the picture is much more complex and reveals intertwined
concepts. For example, this entanglement led Oberauer, Lange and Engle (2004, p. 94) to
conclude that “it might be more fruitful to turn things around: simple span = complex span +
specialized mechanisms or strategies”. In fact, notwithstanding the well-known advantages
and disadvantages of both types of tasks, the distinction between the STM and WM constructs
that these tasks putatively represent is conceptually vague (some attempts at clarification are
still being provided, see Aben et al., 2012; Davelaar, 2013). Therefore, we believe that there
is still room for developing a new approach that could help clarify STM and WM taxonomy.
A prevailing idea in many studies is that the greatest benefit of complex span tasks is
to provide a well-controlled refined measure of the span (in comparison to simple span tasks),
because processing is directed away from the storage task (concurrently in dual-task set-ups
or intermittently in classic complex span tasks), preventing or controlling rehearsal or
elaboration of the memoranda. However, coincidently, and contrary to the fundamental
analysis of the dual tasks by Baddeley & Hitch (1974), the focus is rarely on the processing
component that is supposed to represent half of the core idea of the WM concept (Aben et al.,
2012; A. R. Conway et al., 2005; Unsworth, Redick, Heitz, & Engle, 2009). For instance, in
the dual-task paradigm, one could also measure performance on the concurrent task (which
directs the processing component away from the maintained items) to provide an index of
WM capacity, but by design (the concurrent task is not difficult per se), performance on the
concurrent task is at the ceiling level and thus it is more rarely used as a predictor3 (but see
Unsworth et al., 2009).
3
Another way to study the processing component as a predictor is to measure processing efficiency separately
and to partial it out in correlational studies (Salthouse & Babcock, 1991), but in this case, where single-task
(processing only) is measured to study its mediation between WM capacity and higher-order cognition, the
storage × processing interaction that is targeted in the present study cannot be determined.
7
In contrast, processing the memoranda is permitted in simple span tasks (e.g.,
participants are free to group a few digits in a digit span task), but paradoxically the target
construct of this task is only the storage component that is supposed to best represent the older
and supposedly less elaborate STM concept. This is one of the most challenging theoretical
frameworks to describe to psychology students: STM is thought to be primarily concerned
with storage but the simple tasks involve processing dedicated to the maintained items while
WM is primarily concerned with a storage + processing combination that subsequent
analyses overlook to focus mainly on storage performance.
One interesting task would be of course one that allows methodically sliding across
the [(storage) ... (storage + processing)] dimension while maintaining all other things equal.
So far, some tasks more directly focus on the storage + processing combination, such as the
backward span, the n-back, the letter-number sequencing subtest of the WAIS-IV (Wechsler,
2008), or the running span. Even if in all these tasks, the processing component can be fully
dedicated to the stored items, a characteristic that is targeted in the present study, two other
characteristics appear more problematic and have led us to propose the chunking span. The
first one is that the participants usually find these tasks very difficult, and we believe that the
difficulty inherent in these tasks does not leave much room for manipulating the processing
demand. Secondly and more importantly, in these tasks, the processing component cannot be
studied independently from the storage component, because the number of items to be
processed is linearly related to the number of items to be stored. Therefore there is no clear
separation between processing and storage because storage and processing both depend on a
similar number of items (i.e., the memorandum). This is also the case when one increases the
list-length in a simple span (Unsworth and Engle, 2006). As we will see, the chunking span
task allows increasing or decreasing the processing demand independently of the number of
8
elements to be remembered by varying the complexity of the lists. To anticipate and to give
an example, although the sequence "1223334444" requires 10 items to be sequentially
processed, only one chunk can be stored once one successfully recognizes the regular pattern
that makes the sequence easy to retain. This is not the case for "8316495207" where several
chunks must come into play. Hence, our idea was to develop a memory span task in which
both storage and processing could be measured simultaneously and independently, and we
argue that this can be done by manipulating complexity and by inducing a chunking process.
Chunking span tasks
Our new task is based on the framework of SIMON®, a classic memory game from the
80s that can be played on a device that has four colored buttons (red, green, yellow, blue).
The game consists of reproducing a sequence of colors by pressing the corresponding buttons.
The device lights up the colored buttons at random and increases the number of colors by
adding a supplementary color at the end of the previous sequence whenever the reproduction
by the player is correct. The game progresses until the player makes a mistake. Gendle and
Ransom (2006) reported a procedure for measuring a WM span using SIMON® and they
showed that the procedure is resistant to practice effects. Other studies have shown that this
setting has many advantages for studying different populations with speech or hearing
pathologies (C. M. Conway, Karpicke, & Pisoni, 2007; Humes & Floyd, 2005; Karpicke &
Pisoni, 2000, 2004). There were two important differences between the original game and the
present adaptation. First, a given chosen sequence was not presented progressively but
entirely in a single presentation. For instance, instead of being presented with a “1) blue, 2)
blue-red, 3) blue-red-red, etc.”, that is, three series of the same increasing sequence until a
mistake was made, the participant in this case would be given a blue-red-red sequence from
the outset. If correct, a new sequence was given, possibly using a different complete length,
9
so there was no sequence of increasing length that could have favored a long-term memory
process. Second, no sounds were associated with any of the colors. The new task was developed on the bases of the rationale that sequences of colors
contain regularities that can be mathematized to estimate a chunking or compression process.
Individuals have a tendency to organize information into chunks in order to reduce the
quantity of information to retain (Anderson, Bothell, Lebiere, & Matessa, 1998; Cowan,
Chen, & Rouder, 2004; Ericsson et al., 1980; Logan, 2004; Miller, 1956, 1958; NavehBenjamin, Cowan, Kilb, & Chen, 2007; Perlman, Pothos, Edwards, & Tzelgov, 2010;
Perruchet & Pacteau, 1990; Tulving & Patkau, 1962). Chunking can be separated into two
very different processes, chunk creation and chunk retrieval (Guida, Gobet, & Nicolas, 2013;
Guida et al., 2012). The first occurs when individuals do not have strong knowledge of the
information they are processing. During chunk creation, individuals use the focus of attention
(Oakes, Ross-Sheehy, & Luck, 2006; Wheeler & Treisman, 2002) to bind separate elements,
and reorganize the information they are processing into groups of elements or chunks. This
has been integrated in various models: Cowan and Chen (2009), for example, suggested that
one crucial function of the focus of attention (e.g., Cowan, 2001, 2005) is effectively to allow
binding; Oberauer’s region of direct access has (among other functions) the same aim (e.g.,
Oberauer, 2002; Oberauer & Lange, 2009); and Baddeley’s episodic buffer (Baddeley, 2000;
Baddeley, 2001) was also put forward to allow an explanation of binding. But once
individuals have the knowledge to recognize groups of elements (e.g., “f,” “b,” “i”), they do
not need any more to create but only to retrieve chunks from LTM.
Chunking retrieval has had considerable impact on the study of immediate recall
(Boucher, 2006; Cowan et al., 2004; Gilbert, Boucher, & Jemel, 2014; Gilchrist, Cowan, &
Naveh-Benjamin, 2008; Guida et al., 2012; Maybery, Parmentier, & Jones, 2002; Ng &
10
Maybery, 2002), but less is known about the role of immediate memory in the creation of
chunks in novel situations (Feigenson & Halberda, 2008; Kibbe & Feigenson, 2014; Moher,
Tuerk, & Feigenson, 2012; Solway et al. 2014) and about the reciprocity of WM and
chunking (Rabinovich, Varona, Tristan, & Afraimovich, 2014). Because the presence of
regularity in the to-be-recalled material can account for greater capacities than expected (for
instance, this is the case in the visual WM domain, Brady, Konkle, & Alvarez, 2009, 2011;
Brady & Tenenbaum, 2013; temporal clustering, Farrell, 2008, 2012; but also when social
cues are used to expand memory, Stahl & Feigenson, 2014), many efforts have been made to
hinder grouping in WM span tasks to obtain a rigorous estimation of the span (Cowan, 2001).
Only a few studies have manipulated chunking, for instance, by using learned co-occurrences
of words, sequences structured by artificial grammar (e.g., Chen & Cowan, 2005; Cowan,
Chen, & Rouder, 2004; Gilchrist et al., 2008; Majerus, Perez, & Oberaurer, 2012; NavehBenjamin et al., 2007), or multi-word chunks (Cowan, Rouder, Blume, & Saults, 2012).
However, this method is based on having participants acquire long-term representations
(explicitly or implicitly) before studying their subsequent use in span tasks, and this method
involves a recognition process of previously encountered repetitions of sequences (e.g.,
Botvinick & Plaut, 2006; Burgess & Hitch, 1999; Cumming, Page, & Norris, 2003; French,
Addyman, & Mareschal, 2011; Robinet, Lemaire, & Gordon 2011; Szmalec, Page, & Duyck,
2012).
An alternative to this method is to prompt the formation of chunks in immediate
memory while avoiding long-term learning effects (Bor et al., 2003, 2004; Bor & Owen,
2007; Mathy & Feldman, 2012). Prompting the formation of chunks can be done by
introducing systematic regularities in order to measure whether they can be encoded at once
in a more compact way, without repeatedly testing the participants with the same sequences.
11
The present study continues this line of research by demonstrating that participants exposed to
simple sequences of colors show higher recall for more regular sequences without any
relation to particular prior knowledge in long-term memory (although this is true for the
sequences themselves, not for the colors which constitute the sequences). We show that the
compressibility of the sequences contributes to the grouping process of the sequences of
colors.
Complexity for short strings
The present study aims to provide a precise estimate of the compressibility of the tobe-remembered sequences of colors when prompting the formation of chunks in immediate
memory. Note that contrary to previous studies (e.g., Burgess and Hitch, 1999) that could
identify grouping effects by the presence of mini serial position curves during recall (another
possibility is to study transitional-error probabilities, Johnson, 1969), the present study only
seeks to estimate chunking opportunities more globally (i.e, for the entire to-be-remembered
sequence), and as such, it does not focus on how chunks can be built up sequentially.
Chunking opportunity can be defined as the probability of a sequence to be re-encoded so it
can be retained using a series of meaningful blocks of information instead of independent
items (for instance 0-11-11-0 instead of 011110 using a simple linear separation, 0-2*11-0 by
further grouping the two similar blocks, or 011-110 using symmetry). The compressibility
estimate that we develop here is adequate to capture any kind of regularity within sequences,
which can be used by participants to simplify the recall process.
To estimate the chunking opportunities that the participants could be offered within
thousands of different sequences, a compressibility metric was sought to provide an
12
estimation of any possible grouping process5. More complexity simply means less chunking
opportunities, which also indicates that memorization has to be mostly based on storage
capability. Less complexity means that a sequence can be re-encoded for optimizing storage
and in this case, processing takes precedence over storage. A major difficulty one encounters
in this type of study is due to the apparent lack of a normalized measure of compressibility—
or complexity. Some formal measures such as entropy are actually widely used as proxy for
complexity, but they have come under harsh criticism (Gauvrit, Zenil, Delahaye, & SolerToscano, 2014).
We believe that the notion of compression is potentially helpful to relate chunking and
intelligence (see Baum, 2004, or Hutter, 2005, who developed similar ideas in artificial
intelligence), because many human complex mental activities still fit our quite low storage
capabilities. The accepted notion of (algorithmic) complexity in computer science was
developed by Kolmogorov (1965) and later refined by Chaitin (1966). It bridges compression
and complexity in a single definition: The algorithmic complexity of a sequence is the length
of the shortest program (run on a Universal Turing Machine), that will build the sequence and
halts (Li & Vitányi, 2009). The algorithmic complexity of long strings can be estimated and
this estimation has already been applied to different domains (e.g., in genetics, Ryabko,
5
There is still a lack of consensus on whether chunking is perceptual or conceptual (Gilbert, Boucher,
& Jemel, 2014), and on wether is is different from grouping. Feigenson and Halberda (2008), for
instance, distinguished a form of chunking that requires conceptual recoding (e.g., parsing
PBSBBCCNN into PBS-BBC-CNN, based on existing concepts in long-term memory) from a second
form of chunking that only requires a recoding process. They developed the idea that ‘‘eggplant,
screwdriver, carrot, artichoke, hammer, pliers’’ is easier to remember than ‘‘eggplant, broccoli, carrot,
artichoke, cucumber, zucchini’’ because it can be parsed into three units of two conceptual types
without any need to refer to a pre-existing ‘‘eggplant–carrot–artichoke’’ concept. The recoding
process here is based on semantics, but the authors developed a third definition of chunking that bases
the parsing process on spatiotemporal information (a classic example is dividing phone numbers into
groups by proximity). This last idea is similar to Mathy and Feldman’s (2012), who attempted to
quantify an immediate chunking process by systematically introducing sequential patterns in the to-beremembered material that are unrelated to knowledge in long-term memory. In the present study as
well, although the colors are long-term memory concepts, the sequence yellow-red-yellow-red can
easily be encoded without relying on any specific conceptual knowledge to form a new more compact
representation such as “Twice yellow-red”.
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Reznikova, Druzyaka, & Panteleeva, 2013; Yagil, 2009; e.g., in neurology, Fernandez et al.,
2011, 2012; Machado, Miranda, Morya, Amaro Jr, & Sameshima, 2010), but contrary to long
strings, the algorithmic complexity of short strings (3-50 symbols or values) could not be
estimated before recent developments in computer science. However, thanks to recent
breakthroughs, it is now possible to obtain a reliable estimation of the algorithmic complexity
of short strings (Delahaye & Zenil, 2012; Soler-Toscano, Zenil, Delahaye, & Gauvrit, 2013,
2014). The method has already been used in psychology (e.g., Kempe, Gauvrit & Forsyth,
2015; Dieguez, Wagner-Egger & Gauvrit, in press) and it is now implemented as an Rpackage named ACSS (Algorithmic Complexity for Short Strings; Gauvrit, Singmann, SolerToscano, & Zenil, 2015). Algorithmic complexity is correlated to the human perception of
randomness (Gauvrit, Soler-Toscano, & Zenil, 2014), and in this paper we hypothesize that it
is a simple proxy for chunking opportunities.
The basic idea at the root of the algorithmic complexity for short strings (acss)
algorithm is to take advantage of the link between algorithmic complexity and algorithmic
probability. The algorithmic probability m(s) of a string s is defined as the probability that a
randomly chosen deterministic program, running on a Universal Turing Machine produces s
and halts. This probability is related to algorithmic complexity by way of the algorithmic
coding theorem which states that K(s) ~ –log2(m(s)), where K(s) is the algorithmic complexity
of s. Instead of choosing random programs on a fixed Turing machine, one can equivalently
choose random Turing machines and have it run on a blank tape. This has been done on huge
samples of Turing machines (more than 10 billion Turing Machines), and led to a distribution
d of strings, approximating m. The algorithmic complexity for short strings of a string s,
acss(s) is defined as –log2(d), an approximation of K(s) by use of the coding theorem (see
Gauvrit, Singmann, Soler-Toscano, & Zenil, 2015).
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Relationship between storage × processing and intelligence
One last (but certainly not least) prediction regarding the benefit of studying how
chunking processes affect capacity is related to the relationship between chunking and
intelligence. Many studies using latent variables have suggested that WM capacity accounts
for 30% to 50% of the variance in g (A. R. Conway, Kane, & Engle, 2003; A. R. Conway et
al., 2005). In comparison, simple span tasks account for less covariance (Shipstead et al.,
2012). Again, one interesting exception of crucial importance for the present study is that this
discrepancy in terms of variance is no longer true when the simple span tasks make use of
longer sequences, for instance above 5 items (Unsworth & Engle, 2006, 2007a; see also
Bailey et al., 2011; Unsworth & Engle, 2007b). Therefore simple spans can potentially
account for the same percentage of the variance in g as complex spans.
We pose that the saturation of the storage component occurs for the most complex
sequences, since they offer no possibility to process and reorganize information. However,
less complex sequences are assumed to favor the occurrence of chunking via reorganization
and should thus involve storage × processing7. The two respective kind of sequences mimic
in a way complex span tasks and simple span tasks respectively, and we naturally expect
smaller spans for the most complex sequences. This difference has already been put forward
7
In this context, the variation of complexity is important because it is assumed that the most
complex sequences cannot be easily reorganized and as such they reduce processing
opportunities and mainly involve storage. We say "mainly" instead of "totally", since
algorithmic complexity is not computable, which means that there can always be a way to
reduce the complexity of a sequence that is left unnoticed by a given metric. Consequently,
there might always be a residual portion of processing involved because the participants are
free to group some items using any kind of simplification method. One example would be that
a participant notices that the "red-blue-yellow-green" sequence resembles the Mauritian
national flag. Although there is a slight chance that non-compressible sequences can be
simplified, there is a greater chance that the memorization of most compressible sequences
can be optimized. The simpler sequences require memory optimization because of their
regularity, which should further solicit the processing demand.
15
by Bor and colleagues (Bor et al., 2003, 2004; Bor & Owen, 2007). When comparing cerebral
activity during a simple span with chunkable material (material with systematic regularities)
versus less chunkable material, they observed an increase of activation in lateral prefrontal
areas when some material could be chunked, which the authors interpreted as due to
information reorganization. Moreover this activation pattern has been linked to intelligence,
as a similar neural network has also been found activated in the n-back task, complex spans,
and fluid reasoning (Bor & Owen, 2007; Colom, Jung, & Haier, 2007; Duncan, 2006; Gray,
Chabris, & Braver, 2003). According to Duncan, Schramm, Thompson, and Dumontheil
(2012, p. 868), this shows that fluid intelligence could play a role in “the organizational
process of detecting and using novel chunks”.
Capitalizing on this idea, we predicted that the mnemonic span for the less complex
sequences should better correlate with intelligence because it is in this condition that
participants are able to create novel chunks, which can eventually optimize their storage
capacity. Another reason (however linked) for making the same prediction is that intelligence
tests generally require processing and storing information in conjunction, therefore less
complex sequences should better correlate with intelligence since it is in this condition that
they allow an estimate of the storage × processing construct. One may note that the targeted
interaction between storage and processing that results from the hypothesized optimization
process conflicts with preceding efforts in the literature to separate the storage and processing
mechanisms (Cowan, 2001), but we believe that in fine, higher-cognition depends on the
storage × processing capacity rather than each one separately. Experiment 1 aimed at
studying the storage × processing capacity and its relationships to other span tasks and IQ.
Experiment 2 used two conditions to separate storage and storage × processing capacities,
and investigate their relationships to other span tasks and IQ. Experiment 1 was very liberal in
terms of randomly choosing the sequences of colors, which lead us to develop a specific
16
estimation of memory capacity, whereas Experiment 2 used similar sequences across
participants that allowed us to use a more standard scoring method for computing a memory
span.
Although there are already reports studying the relationship between the components
of the WM system and intelligence at the latent variable level (see Chuderski et al., 2012;
Colom et al., 2004, 2008; Krumm et al., 2009; Martinez et al., 2011 for examples), the present
study combines experimental and correlational approaches because of the exploratory nature
of the new task.
Experiment 1
Experiment 1 develops a chunking memory span task based on an algorithmic
complexity metric for short strings and study how it related to intelligence. This metric
enabled us to estimate the storage × processing capacity in STM, by measuring the most
complex sequence that could be remembered by each participant. The sequences were drawn
at random in order to study complexity effects independently from participant’s individual
performance, but with the main goal of having a maximum number of different sequences to
fit a global performance function. We predicted that performance would decrease with
complexity because complexity hinders the capacity to compress information. It was also
predicted that performance on the chunking span task would better correlate with other span
tasks that solicit a combination of storage and processing, but particularly when processing is
dedicated to the stored items such as a memory updating task (i.e., this is not the case in
complex span tasks). Finally, it was predicted that the storage × processing component
estimated by the chunking span task would predict IQ better than any other types of span
tasks because this task involves a process of storage optimization that requires full function of
the processing component.
17
One interesting battery developed by Lewandowsky, Oberauer, Yang and Ecker
(2010), the Working Memory Capacity Battery (WMCB) allowed us to test which of the
storage-processing combinations best predicts IQ, and whether proximity with our task could
be predicted by the storage-processing combination specific to each task. For the two
complex span tasks of the WMCB, processing is directed away from the stored items. For the
spatial span task of the WMCB, the processing component is left uncontrolled and in this
case, the processing component is not fully involved but only moderately dedicated to the
stored items. The memory updating task of the WMCB can however be regarded as a difficult
task in which processing is fully dedicated to the manipulation of the stored items. Again, the
processing component is not fully involved in this task because the number of items updated
is linearly dependent on the number of stored items, meaning that if the participant's storage
capacity is low, processing of the items is also directly limited. Our hypothesis was that our
task draws on a clearer storage × processing combination in which the processing component
can be used to optimize storage capacity, and in this particular case, the number of items that
are processed sometimes exceeds the number of groups that are stored. In this latter case,
storage capability (in terms of the number of chunks that can be stored) can be limited, but the
number of items that can be packed into the chunks is less constrained. Accordingly, the
chunking span task is expected to better correlate with the simple span task and the memory
updating task than with the complex span tasks.
Method
Participants
One hundred and eighty-three students enrolled at the Université de Franche-Comté,
France (Mage = 21; SD = 2.8) volunteered to participate in this experiment and received course
credits in exchange for their participation.
18
Procedure
Depending on their availability and their need for course credits, the volunteers took
part in one, two or three tests of our computerized adaptation of the electronic game
SIMON®, the Working Memory Capacity Battery (WMCB) and the Raven’s Advanced
Progressive Matrices (APM) (Raven, 1962). All the volunteers were administered our Simon
task, some were also administered the WMCB (27), the Raven (26), or both (85). In all of the
cases, the administration respected a strict chronology: 1) Simon, 2) Raven, 3) WMCB.
Chunking span task. Each trial began with a fixation cross in the center of the screen
(1000ms). The to-be-memorized sequence, consisting of a series of colored squares appearing
one after the other, was then displayed (see Figure 1). Then in the recall phase, four colored
buttons were displayed and participants could click on them to recall the whole sequence they
had memorized and then validate their answer. After each recall phase, feedback (‘perfect’ or
‘not exactly’) was displayed according to the accuracy of the response.
We built two versions of the adapted Simon task, thus, participants were either
administered a spatial version or a nonspatial one. In the first version (N = 106), the colored
squares were spatially located on the screen and were briefly lit up to constitute the to-beremembered sequence, as in the original game. To discourage spatial encoding, the colors
were randomly assigned to the locations for each new trial. In the second version (N = 77),
the colors were displayed one after another in the center of the screen in order to avoid any
visuo-spatial strategy of encoding. To further discourage spatial strategies in the two versions,
the colors were randomly assigned to the buttons in the response screen for each trial, which
resulted in the colors never being in the same locations between trials. Our results showed no
significant difference between these two conditions, thus both data sets were compiled in the
following. 19
Each session consisted of a single block of 50 sequences varying in length (from one
to ten) and in the number of possible colors (from one to four). New sequences were
generated for each participant, with random colors and orders, with the aim of avoiding
ascending presentation of the length or the complexity of the items (two items, then three,
then four, etc.) and to hinder opportunities to develop strategies based on expectation of
complexity or the number of the to-be-remembered items, in order to avoid any learning or
prediction effect. The choice was made to generate random sequences and to measure their
complexity a posteriori (as described below). A total of 9150 sequences (183 subjects × 50
sequences) were presented (average length = 6.24), each session lasted 25 min on average.
Figure 1. Example of a sequence of three colors for the chunking memory span task adapted
from the SIMON® game.
20
Working Memory Capacity Battery (WMCB). Lewandowsky, Oberauer, Yang, &
Ecker (2010) developed this battery for assessing WM capacity through four tasks: an
updating task (memory updating, MU), two span tasks (operation and sentence span, OS and
SS), and a spatial span task (spatial short-term memory, SSTM). This battery was developed
using MATLAB (MathWorks Ltd.) and the Psychophysics Toolbox (Brainard, 1997; Pelli,
1997). On each trial of MU, the participants were required to store a series of numbers in
memory (from 3 to 5), which appeared in respective frames one after another for 1 second
each. Next, only the empty frames remained on the screen, and this was followed by a
sequence of several cues corresponding to arithmetic operations such as “+ 3” or “- 5” that
were displayed in the frames one at a time in a random frame. The participants had to apply
these operations to update the memorized sequence of digits. In both OS and SS, a complex
span task paradigm was used so that the participants saw an alternating sequence of to-beremembered consonants and to-be-judged propositions (the correctness of equations in the
'OS' task, or the meaningfulness of the sentences in the 'SS' task). The participants were
required to memorize the whole sequence of consonants for immediate serial recall. In SSTM,
the participants were required to remember the location of dots in a 10 × 10 grid. The dots
were presented one by one in random cells. After the sequence was terminated, the
participants were cued to reproduce the pattern of dots using a mouse. They were instructed
that the exact position of the dots or the order was irrelevant; they mostly had to remember
the pattern made by the spatial relations between the dots. Completing the four tasks required
45 minutes on average. Raven’s Advanced Progressive Matrices After a practice session using the 12
questions in set #1, the participants were asked to complete the matrices in set #2 which
contained 36 matrices, during a timed session averaging 40 minutes. The participants were
21
expected to select the correct missing cell of a matrix from a set of eight propositions. Correct
completion of a matrix was scored one point, so the range of possible raw scores was 0–36.
Results
Effects of the sequence lengths and the number of colors per sequence First, we conducted a repeated-measures ANOVA with the length of the sequence as a
repeated factor, and using the mean proportion of perfectly recalled sequences for each
participant as a dependent variable (i.e., proportion of trials in which all items in a sequence
were correctly recall8). Performance varied across lengths, F(9, 177) = 234.2, p < .001,
η2 = .9, with the proportion regularly decreasing as a function of length. Figure 2 shows the
performance curve based on the aggregated data by participant, by length and also as a
function of the number of different colors that appeared within the sequences. The three
performance curves resemble an S-shaped function as in previous studies (e.g., Crannell &
Parrish, 1957).
We then focused on a subset of the data in order to study the interaction between
Length and Number of colors. We selected trials for which Length exceeded three items and
we conducted a 7 (4, 5, 6, 7, 8, 9 or 10 items) × 3 (2, 3 or 4 different colors within sequences)
repeated-measures ANOVA. There was still a significant main effect of the Length factor
(respectively, Ms = .91, .82, .64, .49, .32, .2 and .13; SEs = .01, .01, .02, .02, .02, .01 and
0.01), F(6,1092) = 560.8, p < .01, ηp2 = .75, and a significant main effect of the number of
8
Because repetitions occur within sequences, the proportion of correctly recalled items was
not computed as it unfortunately involves more complex scoring methods based on alignment
algorithms (Mathy & Varré, 2013) which are not yet considered as standardized scoring
procedures. 22
colors per sequence, (Ms = .6, .47 and .42; SEs = .01, .01 and .01), F(2,364) = 132.4, p < .01,
ηp2= .42. Posthoc analysis (Bonferroni corrections were made for the pairwise comparisons)
showed a systematic significant decrease between each Length condition and between each
Number of colors condition. Finally, there was a significant interaction between Length and
Number of colors, F (12, 2184) = 5.8, p < .01, ηp2 = 0.03: the effect of Length increased with
the number of colors. Although this is a coarse estimation of chunking opportunities, the
results show that memorization was facilitated by using sequences made of a fewer number of
colors, and particularly when the sequences were longer.
23
Figure 2. Proportion of perfectly recalled sequences of colors as a function of sequence length
and as a function of the number of different colors within sequences. Note: Error bars are +/one standard error.
Effect of complexity
To confirm the reliability of our complexity measure, we split the data into two groups
of sequences of equivalent complexity for each participant. This split-half method enabled
simulating a situation in which the participants had taken two equivalent tests. We obtained
an adequate evidence of reliability between the two groups of sequences (r = .63, p < .001;
Spearman-Brown coefficient = .77).
A simple first analysis targeting both the effect of the number of colors and the effect of
complexity on accuracy (i.e., the sequence is perfectly recalled) showed that complexity
(β
= −.62) took precedence over the number of colors (β = −.04) in a multiple linear
regression analysis, when all of the 9150 trials were considered. To investigate more precisely
the combined effects of complexity and list-length on recall in more detail, we used a logistic
regression approach. A stepwise forward model selection based on BIC criterion suggested
dropping the interaction term (see Table 1). This model showed a significant negative effect
of complexity (z(9147) = -23.84, p < .001, standardized coefficient = -5.70 [non standardized:
-.69]) as shown in Figure 3, and a significant positive effect of length (z(9147) = 16.27, p <
.001, standardized coefficient = 3.74 [non standardized: 1.46]). Although length had a
detrimental effect on recall, this effect was more than compensated by the detrimental effect
of complexity, meaning that long simple strings were easier to recall than shorter but more
complex strings. In other words, the effect of complexity was stronger than the effect of
length (Table 1).
24
Table 1
Stepwise forward selection of several models based on BIC criterion. At each stage, for a
given model (model ~ v, meaning that the base model is computed as a function of x to predict
performance correct), the variables are listed in increasing BIC order after other variables
are introduced. The final model includes complexity and length, but no interaction term. For
instance, in the last model computed as a function of Complexity and Length, adding the
interaction term increases the BIC, so the simplest model is chosen.
Base model
Variable included
Deviance
BIC
Intercept only
Complexity
8093.7
8111.9
Length
8462.3
8480.5
None (intercept
only)
12477.5
12486.6
correct ~ Complexity
Length
7805.2
7832.6
None (Complexity
only)
8093.7
8111.9
correct ~
Complexity and
Length
None (Complexity
and Length only)
7805.2
7832.6
Interaction
7800.0
7836.5
Figure 4 showed how performance decreased as a function of complexity in each
length condition. The decreasing linear trend was significant for lengths 4, 6, 7, 8, 9 and 10 (r
= -.34, p < .001; r = -.39, p < .001; r = -.41, p < .001; r = -.35, p < .001; r = -.45, p < .001; r =
-.43, p < .001, respectively), which shows that the memory process could effectively be
optimized for the less complex sequences. 25
Figure 3. Proportion of perfectly recalled sequences of colors as a function of complexity.
Note: Error bars are +/- one standard error.
One interesting result of our complexity measure was based on the comparison
between the complexity of the stimulus sequence and the response sequence. When the
participants failed to recall the right sequence, they showed a tendency to produce a simpler
string in terms of algorithmic complexity. The mean complexity of the stimulus sequence was
25.3, but the mean complexity of the responses was only 23.3 across all trials (t(9149) =
26.24, p < .001, Cohen’s paired d = .27).
26
Figure 4. Proportion correct as a function of complexity, by sequence length. Error bars are
+/- one standard error.
To test whether participants with a greater score on the Raven better optimized their
encoding of the most simple sequences (when the length of the sequences remained constant),
we further separated the sample of participants into two groups (high IQ vs. low IQ) using the
median of the Raven's scores. We also separated all the sequences of length > 5 (keeping the
shorter sequences in the data set produced floor effects) into two complexity levels (low vs.
high complexity) by selecting the sequences below the tenth percentile and above the
ninetieth percentile of the complexity metric. The repeated-measures ANOVA, with
complexity level (high vs. low) as a within-subjects factor and IQ level (high vs. low) as a
between-subjects factor showed a significant interaction, F(1,109) = 15, p < .01, ηp2 = .12,
which was, however, mostly accounted for by the almost null performance in the high
complexity condition in both groups (Figure 5). 27
0.9
IQ < 50th %
IQ > 50th %
0.8
0.7
Prop. correct
0.6
0.5
0.4
0.3
0.2
0.1
0
< 10th %
> 90th %
Complexity
Figure 5. Proportion of correct recalled sequences of colors as a function of complexity
(below 10th percentile vs. above 90th percentile) and IQ (below 50th percentile vs. above
50th percentile). Error bars are +/- one standard error.
To ensure that this result was not obscured by a floor effect on the most complex sequences,
and to gain more power, a subsequent mixed-model analysis was done on accuracy per trial
with complexity as a within-subjects factor (the complexity variable was split into four
quartiles to obtain a smaller number of levels), IQ as a between-subject factor (22 levels,
since there were only 22 types of IQ scores), and subject as a random factor, which showed
significant effects of complexity (F(2,15183.4) = 2143, p < .001), IQ (F(5,20.9) = 31.6, p <
.001), and interaction, F(42,12.9) = 15.1, p < .001 (Figure 6 shows the interaction between
28
complexity and IQ, as performance slightly increased for lower complexity sequences in the
highest IQ group).
&',
9
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Figure 6. Proportion of correct recalled sequences of colors as a function of complexity and
IQ. Note: Both the complexity and IQ variables were split into quartiles before aggregating
the data by participant. Error bars are +/- one standard error.
Correlations and factor analyses
Table 2 shows the correlations between measures aggregated by participants,
including the different span measures of the WMCB (MU, OS, SS, and SSTM, and WM was
the global score for the entire battery), the Raven (M = 23.6, slightly above the 50th
percentile; SD = 4.1; which corresponds to an average IQ of 101.2, SD = 11.7; N = 113), and
the average capacity for the Simon span task. Because the participants were not administered
29
the same sequences, we computed a logistic regression for each subject to find the critical
decrease in performance that occurs half-way down the logistic curve (i.e., the inflection
point). This inflection point is therefore based on complexity and simply means that the
participants failed on sequences more than 50% of the time when complexity was above the
inflection point.
Table 2
Correlation matrix for Experiment 1. Note: Raven, Raven’s Advanced Progressive Matrices
raw scores; SIMON, individual inflection points of performance on the chunking span task
based on an adaptation of the SIMON game, using the individual logistic regression curve on
the complexity axis; MU, memory updating; OS, operation span; SS, sentence span; SSTM,
spatial short-term memory. MU, OS, SS, and SSTM are the four subtests of the Working
Memory Capacity Battery (WM is the composite score obtained using the battery); **
p < .001
SIMON
WM
MU
OS
SS
SSTM
Raven
.428**
.437**
.545**
.297**
.326**
.406**
SIMON
_
.531**
.572**
.457**
.376**
.515**
WM
_
.630**
.767**
.824**
.630**
MU
_
.499**
.466**
.506**
OS
_
.651**
.374**
SS
_
.345**
30
A first glance at the correlation matrix shows that in terms of prediction of the Raven, the
Simon is comparable to the composite WM score produced by the WMCB (respectively r =
.428 and r = .437, and this range of correlations corresponds to that found in the literature).
One important aspect to recall is that both MU and SSTM allow the stored items to be
processed while both OS and SS are standard complex span tasks that separate processing and
storage. Accordingly, performance on the Simon span task should better correlate with MU
and also with SSTM. A second prediction was based on the idea that the storage × processing
product (reflected by tasks in which the stored items are fully processed) would better predict
the average score of the Raven. The correlation between MU and the Raven was effectively
the highest (r = .572), and the Simon was the second task to better correlate with the Raven.
The Simon also best correlated with both MU and SSTM.
One difficulty is that the covariance between the tasks does not allow any task to correlate
significantly better than another with the Raven, and the difference between this particular
correlation and others was not found to be significant using Steiger's (1980) formula. We
addressed this concern by conducting a principal component analysis to extract two factors
(which were expected to separate a storage component from a processing component).
Specifically, the factor model was rotated using varimax, after a preliminary verification of
the Kaiser-Meyer-Olkin measure of sampling adequacy (.827 being a high value according to
Kaiser) and Bartlett’s test of sphericity (χ2(15) = 180, p < .001), providing evidence that the
patterns of correlations would yield reliable distinct factors. Factor loadings for Raven,
Simon, MU, OS, SS, and SSTM were respectively .79, .73, .74, .28, .20, and .75 on the first
component and .08, .35, .39, .85, .88, and .21 on the second component (see Figure 7A), and
the two components accounted for 40% and 30% of the variance respectively (the respective
sums of squared loadings being 2.4 and 1.8, instead of the 3.3 and .89 eigenvalues for the
31
unrotated initial solution). Oblique rotation of the factors (using the direct oblimin method),
produced a greater separation of the tasks on the two factors on the component plot, with
factor loadings for Raven, Simon, MU, OS, SS, and SSTM being respectively .86, .72, .72,
.08, -.02, and .77 on the first component and -.15, .16, .21, .86, .91, and .00 on the second
component (see Figure 7B). We interpreted the two factors as clearly separating the complex
span tasks (in which processing is estimated alone, while processing is saturated) and the
tasks in which processing was dedicated to storage, but it is still difficult to see how the
processing and storage components are separated in these analyses by the respective factors.
A
B
32
Figure 7. Resulting component plot in rotated space for Exp. 1 from the exploratory factor
analysis using PCA and varimax (subplot A) or Oblimin (subplot B). OS, operation span; SS,
sentence span; SIM, chunking span task based an adapted version of the SIMON game;
SSTM, spatial short-term memory; MU, memory updating; Raven, Raven’s APM.
To better estimate the relationship between storage, processing, IQ and span tasks, the data
were submitted to confirmatory factor analysis (CFA) using IBM SPSS AMOS 21. A latent
variable representing a construct in which storage and processing are separated during the
task and another latent variable representing a construct in which both processes interact (the
processing component) were sufficient to accommodate performance. The fit of the model
shown in Figure 8A was excellent (χ2(7) = 2.85, p = .90; CFI, comparative fit index = 1.0;
RMSEA, root mean squared of approximation = 0.0; RMR, root-mean square residual = .002;
AIC and BIC criterions were both the lowest in comparison to a saturated model with all the
variables correlated with one another and an independence model with all the variables
uncorrelated), with a caveat that the data fails to fit the recommended conditions for
33
computing a CFA (see Conway et al., 2002, Wang et al., 2015), particularly because one
factor is defined by only two indicators and because the correlation between the two factors
reveal collinearity issues. These results suggest that the Raven is better predicted by the
construct in which storage and processing are combined (r = .64, corresponding to 41% of
shared variance, instead of r = .36 when separated), a construct that can be reflected in the
present study by our chunking span task, a memory updating task, and a simple span task. To
make sure that the absence of SSTM would not weaken the predictions too much, we tested a
similar model that did not integrate the SSTM task (Figure 8B). In this case, we observed
increased regression weights towards the Raven (.85 instead of .80, and -.26 instead of -.22,
and a percentage of shared variance with the Raven of 43% instead of 41%; (χ2(3) = 1.22, p
= .75). Figure 8C shows that when a factor already reflects all of the span tasks, a second
factor reflecting only the tasks for which Storage and Processing are supposed to be
combined still account independently for the Raven. The substraction of the less restrictive
model (Figure 8A) from the more restrictive model (Figure 8D) showed that constraining the
two paths to the Raven to be equal significantly reduced the model's ability to fit the data (χ2
(9 - 7 = 2) = 54.95 - 2.85 = 52.1), meaning that the .80 loading in Model A can be considered
significantly greater than -.22.
34
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Figure 8. Path models from confirmatory factor analysis from Exp. 1 with (A) and without
(B) the SSTM task. For comparison, a third model (C) used a factor reflecting all of the span
tasks versus another factor reflecting only the three tasks in which storage and processing
were combined in the task. A fourth model (D) further constrained the parameters between
the Raven and the latent variables to 1 (dotted lines), and a table (E) recapitulates the fit of
each of the models. OS, operation span; SS, sentence span; SIM, chunking span task based
on an adaptation of the SIMON game; SSTM, spatial short-term memory; MU, memory
updating; S and P, storage and processing; Raven, Raven’s APM. The numbers above the
arrows from a latent variable (oval) to an observed variable (rectangle) represent the
standardized estimates of the loadings of each task onto each construct. The paths connecting
the latent variables (ovals) to each other represent their correlation. Error variances were not
correlated. The numbers above the observed variables are the R-squared values.
Discussion The objective of the first experiment was to investigate a span task integrating a
chunking factor in order to manipulate the storage × processing interaction process. Our
experimental setup was developed to allow the participants to chunk the to-be-remembered
material in order to optimize storage. The chunking factor was estimated using a
compressibility metric, to follow up on a previous conceptualization that a chunking process
can be viewed as producing a maximally compressed representation (Mathy & Feldman,
2012). Using an algorithmic complexity metric for short strings, we acknowledge the
difficulty in representing the chunking process precisely sequence by sequence and we
preferred to adopt a more general approach stipulating that any regularity should be found and
recoded by participants, particularly those with the greatest processing capacity. The
37
hypothetical storage × processing construct in which processing is fully dedicated to storage,
represents the largest difference with other constructs reflected by other span tasks since 1)
processing is separated from storage in complex span tasks, and 2) processing is moderately
involved in simple span tasks. One further hypothesis was that this compound variable should
help characterize the nature of the relationship between WM capacity and general
intelligence. Taken together, our results suggest that chunking opportunities (for instance, when
fewer colors are used to build a sequence, resulting in low complexity) favors the recall
process, and more interestingly the advantage of having more repetitions of colors interacting
with sequence length. This interaction shows that the chunking factor best applies to longer
sequences, a result that recalls the observation made in the Introduction section that longer
sequences in simple span tasks (i.e, > 5 or 6 items) are more likely to reveal a higher
processing demand. More precisely, our complexity metric plainly predicts a decline in
performance as sequences become more complex, and a systematic decreasing trend across
sequence lengths was observed. Although length had a detrimental effect on recall, the effect
of complexity was found stronger than the effect of length. Capacity (i.e., how the participants
could deal with complexity) was then estimated by an individual inflection point along the
complexity axis of accuracy performance. This variable was found to correlate with the
Raven, which tends to indicate that the participants who show higher storage × processing
capacity tend to obtain higher scores on the Raven. The correlation is comparable to the one
obtained from a composite measure of WM capacity (using the WMCB). However, an
exploratory analysis showed that the chunking span task saturated two principal factors in a
way very similar to the Raven and to other tasks in which processing is also dedicated to
storage (involving updating or short-term memory), contrary to complex span tasks which are
usually one of the most famous tasks to estimate fluid intelligence. A confirmatory factor
38
analysis confirmed the greater predictability of the Raven with a latent variable in which the
storage and processing components were combined, in opposition to a latent variable which
represented the complex span tasks (in which storage and processing were separated). The
correlation between the “Storage and Processing Combined” latent variable shares 41% of the
variance with the Raven, which seems quite satisfying compared to 50% obtained by Kane,
Hambrick, and Conway (2005) from more than 3000 participants and 14 different data sets to
estimate the shared variance between WM capacity and general intelligence constructs (see
also Ackerman, Beier, & Boyle, 2005, for a contrasting point of view). Our results also
confirm previous findings that memory updating can be a good predictor of Gf (e.g.,
Friedman, Miyake, Corley, Young, Defries, & Hewitt, 2006; Schmiedek, Hildebrandt,
Lövdén, Wilhelm, & Lindenberger, 2009; Salthouse, 2014), but here we considered that the
updating task could be associated with a chunking span task under the same construct.
Effectively, even though they seem to have nothing much in common, in both of these tasks
processing is dedicated to storage.
Another result showing a higher recall from high-IQ participants for the less complex
sequences further emphasizes the link between general intelligence and the optimization of
storage. Our results showed less variation of performance for the more complex sequences for
both IQ groups.
Although this first experiment was helpful to decipher the utility of a chunking span in
the prediction of general intelligence, there was, however, a practical difficulty to make
comparisons between low-complexity conditions and high-complexity conditions since the
participants were not administered the same sequences. We expected a clear demarcation of
IQ groups within the low-complexity condition, but low vs. high IQ groups were not clearly
distinguished enough on the basis of sequence complexity (although our results still indicate a
significant interaction between complexity and IQ when both variables were split in
39
quartiles). The second experiment attempts a more direct comparison of performance when
the sequences are simple vs. when the sequences are more complex. Another weakness of
Experiment 1 is that a specific scoring method was used to estimate the different spans. The
second experiment attempts a more direct comparison of the simple vs. complex sequences,
by use of a common scoring method. Experiment 2
Experiment 2 was set up to better separate the storage and the storage × processing
components by using complex versus simple sequences respectively. Two versions of the
chunking span task were created, one based on the most complex sequences of Experiment 1,
and the second based on the simplest sequences of Experiment 1. The complex sequences
targeted the storage-only demand because such sequences allow little or no compression. On
the contrary, the simplest sequences targeted the storage × processing demand since the
regularities could be used by participants to optimize storage. Also, Experiment 1 estimated capacity from an inflexion point obtained across
individuals who were not administered the same sequences of colors. Another goal of the
second experiment was to provide estimates of the span based on a similar set of sequences
given to the participants in progressive order (from sequences of minimal length to the longest
length achieved) to ensure a more proper evaluation of capacity. Performance on our
chunking span tasks was compared to other simple span tasks in a commercial test (WAISIV) and again to a measure of general intelligence (Raven’s Advanced Progressive Matrices).
Experiment 1 showed that complex span tasks were less correlated to a storage × processing
construct, so we chose to focus on simple span tasks for which processing is partly dedicated
to the storage process. It was hypothesized that the spans obtained from the Simon chunking
span tasks would better correlate with the Raven. Effectively, the spans of the WAIS either
40
moderately involve processing (forward condition) or simply require linearly processing the
stored items (backward or sequencing conditions). In the case of the backward and the
sequencing conditions, processing cannot be regarded as subserving storage, because
processing intervenes only after the items are stored (see Thomas, Milner, & Haberlandt,
2003, who showed that the sequences are initially stored before being processed). The span
estimated during a chunking process is the only one that truly involves an optimization
process based on the processing component being at the service of the storage component. If
the span results from the participant’s storage capacity which hierarchically depends on an
optimization process (storage capacity is supposed to be fixed for a given individual, but any
form of structuration of the stimulus sequence can contribute to extending the number of
stored items), we hypothesize that chunking span tasks will best correlate with intelligence.
The rationale is that during the Raven, participants also use storage and processing in
conjunction to solve the problems.
Method
Participants
A total of 107 undergraduate students volunteered to participate in this experiment and
received course credits in exchange for their participation (M = 22.9, SD = 5.9). All
participants were administered a chunking span task and three subtests measuring the span
from the WAIS-IV; 95 of the students agreed to be tested with the Raven’s APM (which was
optional for getting course credits). The average IQ for this sample was 100.2 (SD = 13.4).
Procedure
41
The tests were administered in the following order: the Simon chunking span task, the
WM subtests of the WAIS-IV and finally, and optionally, the Raven.
Simon chunking span task
The procedure was designed to better match a standard memory span task in which a
progression of difficulty is involved. Thus, the length of the presented sequences
progressively increased, starting with length two, then three, etc. Two different sequences
with a given length were presented (to match the number of repetitions per length in the WM
subtests of the WAIS), and the session automatically stopped after the participant failed to
correctly recall the two sequences of a given length. Scoring of the span followed that of the
WAIS, in which the longest span attained at least once was considered as the subject’s span.
Each participant was administered two complexity conditions (counterbalanced between
participants). The sequences in each condition were taken from the 9150 sequences that were
generated in Exp. 1. Based on the distribution of the sequences’ given complexity, all the
sequences were ranked according to their complexity (the 100th percentile corresponded to
the most complex sequences), and a series of sequences was chosen at the 50th or the 100th
percentile to constitute the two experimental conditions (the sequences below the 50th
percentile were judged too easy to constitute an interesting experimental condition). By
construction, the Simple condition was conducive to inducing a chunking process, while the
Complex condition allowed less chunking opportunities and as such was considered as mostly
soliciting the storage component. WAIS-IV working memory subtests. The participants were administered three WM
subtests from the WAIS-IV (Wechsler, 2008): the Digit Span Forward (DSF) which requires
recalling a series of digits in correct order, the Digit Span Backward (DSB) which requires
42
recalling a series of digits in reverse order, and the Digit Span Sequencing (DSS) which
requires recalling a series of digits in ascending order. The two last subtests clearly require
mental manipulation of the stored items, in comparison to the first subtest which is considered
the simpler short-term memory test. The scoring procedure followed the recommendation of
the WAIS, the longest span attained at least once was considered the subject’s span. Note that
although these tasks are supposed to index a WM construct in the WAIS, these subtests are
closer to simple span tasks and might better reflect a STM construct (See Unsworth & Engle,
2007).
Raven’s Advanced Progressive Matrices. As in Exp. 1, the participants were asked
to complete the matrices of set #2 which contained 36 matrices after doing set #1 which was
used as a warm-up. The range of possible raw scores was 0–36.
Results
To estimate the reliability of our task, we split the data into two groups (odd vs. even
trial numbers) within each sequence length. Participants showed equivalent performance at
the even and odd trials for each condition (Simple condition: r = .62, p < .001; SpearmanBrown coef. = .77; Complex condition: r = .59, p < .001; Spearman-Brown coef. = .74) and
adequate evidence of reliability was obtained given such a short procedure. For comparison,
we applied the same method to the digit span tasks, and we obtained estimates of reliability
within the same range (Forward condition: r = .45, p < .05; Spearman-Brown coef. = .63;
Backward condition: r = .66, p <.001; Spearman-Brown coef. = .78).
The mean complexity of the recalled sequences was again lower than that of the to-beremembered sequences (t(2653) = 13.20, p < .001, Cohen’s paired d = 0.26). Once again, we
43
investigated the effect of length and complexity on perfect recall by way of logistic
regression. A stepwise forward logistic model selection based on a BIC criterion suggested
dropping the interaction term, as shown in Table 3.
Table 3. Stepwise forward selection model based on BIC criterion. At each stage (model), the
variables are listed in increasing BIC order. The final model includes complexity and length,
but no interaction term.
Base model
Variable included
Deviance
BIC
Intercept only
Complexity
1672.9
1688.6
Length
1737.3
1753.0
None
2957.1
2965.0
Correct ~ complexity
Length
1632.0
1655.6
None
1672.9
1688.6
Correct ~
Complexity and
Length
None
1632
1655.6
Interaction
1632
1663.5
A logistic regression on the 2654 trials was done on the proportion correct of perfectly
recalled sequences as a function of complexity and length (see Figure 9). It confirmed the
detrimental effect of complexity on recall (z(2651) = 9.77, p < .001, standardized coefficient
= -6.41 [non standardized: -.95]) and also an effect of length (z = 6.273, p < .001,
standardized coefficient = 3.94 [non standardized: 2.01948]). Overall this first result indicates
44
that the memory process could effectively be optimized for less complex sequences. One
interesting point is that the inflection curve is close to the one obtained in Experiment 1 (20.2
in comparison to 21.7 for Experiment 1), which means that allowing a greater amount of time
to participants did not lead them to increase performance much. Still this difference was
found statistically reliable (t(270) = 4.5, p < .001; Cohen’s d = .50), although this difference
must be tempered by the fact that the sequences of Exp. 2 were in general shorter (4.7 colors
per sequence instead of 6.2 colors in Experiment 1, t(5497) = 33, p < .001; Cohen’s d = .63).
Also, the difference between the two inflection points only reflected a difference of .7 colors
recalled (7 in Experiment 1 and 6.3 in Experiment 2).
45
Figure 9. Proportion correct as a function of complexity of the Simon span tasks (with the
conditions Simple and Complex mixed) in Exp. 2. Error bars are +/- one standard error.
The decreasing mean spans reported in Figure 10 for DSB, Simon Complex, DSF,
DSS, and Simon Simple are respectively 5.1 (SD = 1.3), 5.6 (SD = 1.0), 6.5 (SD = 1.1), 6.7
(SD = 1.4) and 6.8 (SD = 1.0). A repeated-measures ANOVA on the mean span was
conducted with the type of span task as a within-subjects factor (Simon Simple, Simon
Complex, DSF, DSB, DSS) on the data collapsed by participants. The result of the ANOVA
was significant (F (4,424) = 68.7, p < .001, ŋp² = .39), indicating that almost 40% of the
variance was accounted for by the type of span task factor. 46
Figure 10. Mean span as a function of type of span task in Exp. 2. Note: Simple, Simon
chunking span task, simple version; DSS, Digit Span Sequencing; DSF, Digit Span Forward;
Complex, Simon chunking span task, complex version; DSB, Digit Span Backward.
Posthoc analysis (Bonferroni corrections were made for the pairwise comparisons)
showed significant systematic pairwise differences except between Simon Simple and DSS,
and between DSS and DSF. A noteworthy difference was found between the two respective
mean spans for the two conditions in the chunking span tasks (M = 1.25; SD = 1.1), but
surprisingly, the small difference of 1.25 on average means that between one and two
additional colors were grouped on average within the simpler sequences.
Table 4
Correlation matrix for Experiment 2. Note: Raven, Raven’s Advanced Progressive Matrices
raw scores; COMPL, mean span on the Simon chunking span task in the complex condition
(with chunking opportunities reduced); SIMPL, mean span on the Simon chunking span task
in the simple condition (with chunking opportunities induced); DSF, Digit Span Forward;
DSB, Digit Span Backward; DSS, Digit Span Sequencing; ** p < .001
COMPL
DSF
DSB
DSS
Raven
SIMPL
.422**
.294**
.337**
.157
.413**
COMPL
.229*
.353**
.310**
.385**
DSF
.473**
.273**
.290**
DSB
.476**
.446**
DSS
.297**
47
Despite the moderate difference between the two mean spans observed between the simple
and complex conditions, Table 4 shows that these two conditions highly correlated (r = .42),
in comparison with other variables. Similarly, DSF and DSB shared the greatest percentage of
variance (r = .47), as well as DSB and DSS (r = .48). Thus the digit spans showed high
mutual correlation, but none of the digit span tasks correlated more with either Simon simple
or Simon Complex than the two together. One possibility is that the participants could still
chunk many of the most complex sequences, making the two Simon conditions akin, and
accounting for the slight difference of 1.25 colors reported above. The possibility that
participants chunk the less compressible sequences does not contradict compressibility
theories because the estimate of the compressibility of a string is averaged across possible
Turing machines. For a given complex string, a particular machine can still be able to perform
compression. Another possibility is that participants verbalized the tasks in both conditions,
and pronunciation of the sequences of colors was limited by the duration of rehearsal. In that
case, chunking would not have been as beneficial as expected if only the number of colors to
be pronounced determined capacity. Regarding correlations with the Raven, the highest
correlation was found with DSB, but the multicollinearity of the data makes interpretation of
the pairwise correlations difficult. Principal component analysis was used to explore our data and to extract two factors (which
were expected to separate the chunking span tasks and the WM span task), and the factor
model was then rotated using varimax, after a preliminary verification of the Kaiser-MeyerOlkin measure of sampling adequacy (.796 being a high value according to Kaiser) and
Bartlett’s test of sphericity (χ2(15) = 123, p < .001) to indicate if the patterns of correlations
would yield reliable distinct factors. Factor loadings for COMPL, SIMPL, DSF, DSB, DSS,
and Raven were respectively .21, .09, .78, .77, .71, and .33 on the first component and .75,
48
.83, .10, .32, .20, and .66 for the second component (see Figure 11A), and the two
components accounted for 31% and 31% of the variance respectively (the respective sums of
squared loadings being 1.9 and 1.8, instead of the 2.8 and .93 eigenvalues for the unrotated
initial solution). Oblique rotation of the factors (using the direct oblimin method) produced a
greater separation of the tasks on the two factors on the component plot. Factor loadings for
COMPL, SIMPL, DSF, DSB, DSS, and Raven were respectively .04, -.11, .83, .75, -.72, and
.19 on the first component and .76, .88, -.10, .15, .04, and .63 for the second component (see
Figure 11B). The two factors clearly separated the digit span tasks and the chunking span
tasks. It is worth noting that the Raven loaded with the second set of tasks.
A
B
49
Figure 11. Resulting component plot in rotated space for Exp. 2 from the exploratory factor
analysis using PCA and Varimax (subplot A) or Oblimin (subplot B). Note: SIMPL, Simon
chunking span task, version Simple; COMPL, Simon chunking span task, version Complex;
DSF, DSB and DSS, Digit Span Forward, Backward and Sequencing (WAIS-IV); Raven,
Raven’s Advanced Progressive Matrices.
The data were submitted to a confirmatory factor analysis using IBM SPSS AMOS 21 in
order to test the prediction that tasks allowing the processing and storage components to fully
function together in association to optimize storage are better predictors of general
intelligence than the STM span tasks of the WAIS. A latent variable representing a chunking
construct (derived from the Simon span tasks) and another latent variable representing a
simpler STM construct (derived from the digit span tasks of the WAIS9) were sufficient to
9
Again, we chose to label the latent variable STM instead of WM because the digit span tasks can be seen as
simple span tasks (See Unsworth & Engle, 2007).
50
accommodate performance. The fit of the model shown in Figure 12 was excellent (χ2(7) =
3.2, p = .87; CFI, comparative fit index = 1.0; RMSEA, root mean squared of approximation
= 0.0; RMR, root-mean square residual = .049; AIC and BIC criterions were both the lowest
in comparison to a saturated model with all the variables correlated with one another and an
independence model with all the variables uncorrelated), but again, as for Figure 8, with a
caveat that the data fails to fit the recommended conditions for computing a CFA (because
one factor is defined by only two indicators and because the correlation between the two
factors reveal collinearity issues. These results suggests that the Raven is best predicted by the
Chunking latent variable, a construct that can be reflected in the present study by the two
chunking span tasks. Figure 12B shows that a factor reflecting only the tasks for which
Storage and Processing are supposed to be combined still account independently for the
Raven once a first factor reflects all of the span tasks. The substraction of the less restrictive
model (Figure 8C) from the more restrictive model (Figure 8A) showed that constraining the
two paths to the Raven to be equal significantly reduced the model's ability to fit the data (χ2
(9 - 7 = 2 ) = 16.65 – 3.24 = 13.41), meaning that the .42 loading in Model A can be
considered significantly greater than -.27.
A
51
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Figure 12. Path models for confirmatory factor analysis from Exp. 2. An initial model (A) is
compared with two other models: In (B), we used a factor reflecting all of the span tasks
versus another factor reflecting only the three tasks in which storage and processing were
combined in the task; In (C), we further constrained the parameters between the Raven and
the latent variables to 1 (dotted lines). The table (D) recapitulates the fit of each of the
models. All the correlations and loadings are standardized estimates. The numbers above the
observed variables are the R-squared values. Simple, Simon Simple; Complex, Simon
Complex; DSF, DSB and DSS, Digit Span Forward, Backward and Sequencing (WAIS-IV);
Raven, Raven’s Advanced Progressive Matrices; WM, traditional working memory construct;
Chunking, chunking construct
53
Discussion
The main goal of the second experiment was to provide several estimates of the STM span
using similar scoring method. Performance on our chunking span tasks was therefore
compared to three other simple span tasks (Forward, Backward and Sequencing digit span
tasks of the WAIS-IV) using the scoring method provided by the WAIS. The chunking span
task was hypothesized to best correlate with the Raven because both require to make sense of
complexity while storing information, a process that might require optimizing storage
capacity to free up memory and leave room for more complex reasoning. Experiment 2 was
also devised to better separate the storage and the storage × processing demands by allowing
two degrees of involvement of the processing component: low for the less compressible
sequences that constituted the first condition (Complex version of the SIMON chunking span
task) and high for the second condition that included more compressible sequences (Simple
version). The average span was found very close in the two conditions, with an average
difference of only 1.2 additional colors recalled in the Simple condition of the chunking span
task than in the Complex condition. Although this difference was low, the correlation of the
Simple version still slightly better correlated with the Raven than the Complex version. The
verbalization of the colors could account for the fact that the span revolved around 7 for both
the less compressible and the most compressible sequences, as if the participants were
rehearsing the sequences of colors verbally without taking profit of the mathematical
regularities (this is acknowledged as a limitation of our study in the General Discussion).
Nevertheless, when the two tasks were used to estimate a latent variable covering a chunking
process, the prediction of the Raven was found larger than for the three digit span tasks.
General Discussion
Chunking and intelligence
54
Our goal was to develop a chunking span task in which storage and processing can fully to
study its relation with intelligence. The quantity of chunking was estimated by computing the
algorithmic complexity of the to-be-remembered series of colors appearing one after the other
in a task inspired by the Simon game. The modification of this quantity allowed us to slide
across the [(storage) ... (storage + processing)] dimension as we posited that more chunking
opportunities should involve a greater amount of processing. The chunking process was also
thought to avoid separating the memory contents from the material to be processed. We then
addressed one primary question: Is chunking a reliable predictor of intelligence when
chunking is implemented in a simple span task? To answer this question, we used
confirmatory factor analysis and structural equation modeling with 290 young adults to test
hypotheses about the nature of the WM and STM constructs and their relations to general
intelligence. The nonconventional idea of the present study is that our chunking span tasks are
simple span tasks that can target a WM construct.
We hypothesized that chunking and intelligence both rely on individuals' storage
capacity, which hierarchically depends on an optimization process (see also Duncan et al.,
2012). Storage capacity is supposed to be fixed for a given individual, but any form of
structuration of the stimulus sequence can contribute to extending the number of stored items.
This optimization process could be helpful to make sense of the regularities that can be found
in the items of the Raven or in the to-be-recalled sequences of repeated colors. The rationale
was that participants use storage and processing in conjunction to solve the problems of the
Raven and to chunk the colors of the to-be-remembered sequences of repeated colors, or, as
put forward by Duncan et al. (2012, p. 868), fluid intelligence can be used in “the
organizational process of detecting and using novel chunks”.
55
In two experiments, we found that the chunking spans were structurally closer to the
performance on the Raven than any complex span task of the WMCB and any of the simple
span tasks of the WAIS. The memory updating tasks and the spatial STM task of the WMCB
had more shared variance with the chunking span tasks and the Raven, suggesting that the
Raven is best predicted when processing and storage function together in a span task. This
confirms a result by Mathy and Varré (2013) who showed that a span task using alphanumeric
lists that included a few repetitions of items (thus inducing a chunking process) better
correlated with the memory updating task of the WMCB than similar task that included no
repetition of items. One important result is that our chunking span tasks compete with the
well-known complex span tasks in which the to-be-recalled items are interspersed with other
activities unrelated to the retention of the items (e.g., Kane, Hambrick, & Conway, 2005).
This result was refined in Exp. 2 which showed that the simple span tasks better account for
the Raven when they involve a chunking factor than when the simple span tasks do not
integrate any possible chunking processes. The present study shows that simple span tasks
can effectively compete with complex span tasks, and this was achieved here by prompting
the creation of chunks in immediate memory while avoiding a long-term learning effect.
These findings are broadly consistent with previous studies (see Unsworth & Engle,
2007a) suggesting that prediction of fluid intelligence by simple spans reached that
of complex spans by increasing list-lengths. Another example where reorganization seems to
explain the high correlation between simple span and intelligence is the conceptual span task
(Haarmann, Davelaar, & Usher, 2003). In this task, words are presented successively as in a
classic word span, except that the words are drawn from three semantic categories that are
used to aid recall of the words. Haarmann et al. (2003) observed that the conceptual span
correlated better with reasoning than the reading span. According to the authors, this was due
56
to the fact that this simple span was supposed to tap the construct of semantic STM (e.g.,
Hanten & Martin, 2000; Martin & Romani, 1994). However, Kane and Miyake (2007) later
suggested that the capacity of the conceptual span (semantic or not) to correlate
with intelligence or high cognitive processes depends on a clustering ability. Effectively,
when the to-be-remembered words were presented in a clustered fashion, the conceptual span
task lost its ability to predict intelligence compared to an unclustered version. Therefore,
it seems likely that the span tasks better correlate with higher cognitive processes when they
prompt reorganization of information.
The present study concludes that processing and storage should be examined together
when processing is fully dedicated to the stored items, and we believe that the interaction
between storage and processing that best represents chunking provides a true index of
WM capacity. Thus, among the span task taxonomy that was discussed in the Introduction
section, the chunking span seems to be a good candidate for predicting intelligence and
measuring WM. This is in line with Unsworth et al. (2009) who argue that processing and
storage should be examined together because WM is capable of processing and storing
information simultaneously. Effectively, in complex spans, the interaction between storage
and processing has also been put forward, particularly by Towse, Cowan, Hitch and
Horton (2008) in the recall reconstruction hypothesis. This hypothesis was based on
observations made with the reading span task (e.g., Cowan et al., 2003; Hitch, Towse, &
Hutton, 2001) which showed that the sentences (the processing part of the task) can be used to
reconstruct the target words (the storage part of the task). This hypothesis supports the study
by Cowan et al. (2003) in which long pauses were often needed to recall the words. Towse et
al.’s (2008) hypothesis puts forward two important assertions: 1) processing and storage
need not always be thought of as completely separate events, and 2) processing and storage
57
are not necessarily competitive components of WM tasks that, for instance, compete for
cognitive resources (e.g., Barrouillet, Bernardin, & Camos, 2004; Barrouillet, Plancher,
Guida, & Camos, 2012; Case, 1985) or interfere with each other (Oberauer, Farrell, Jarrold,
Pasiecznik, & Greaves, 2012; Oberauer, Lewandowsky, Farrell, Jarrold, & Greaves, 2012;
Saito & Miyake, 2004). As highlighted and synthesized by the recall reconstruction
hypothesis (see also Towse, Hitch, Horton, & Harvey, 2010), processing and storage can also
interact synergistically (e.g., Cowan et al., 2003; Hitch et al., 2001; Guida, Tardieu, &
Nicolas, 2009; Osaka, Nishizaki, Komori, & Osaka, 2002; Schroeder, Copeland, & BiesHernandez, 2012). Interestingly, this has not been observed in all WM tasks. For instance,
Cowan et al. (2003) failed to observe this interaction in a digit WM task. Such an interaction
has only been observed so far in reading span tasks in which, as suggested by Cowan et al.
(2003), participants can retrieve the semantic or linguistic structure and use it as a cue to
recall the sentence-final words. Therefore, the linguistic domain seems more prone to induce
an interaction between storage and processing. Our chunking span shows that it is also
possible to induce this interaction outside of the linguistic realm even if it is done with a
simple span as in our case.
Uncontrolled chunking ?
One risk of devising a task in which processing is fully dedicated to storage is putting
aside uncontrolled specific strategies for simply remembering more information. One caveat
has been that the elaboration of memoranda into meaningful chunks inflates capacity, and
because this strategy can be more effective for some subjects, "allowing such strategies to
determine variance in the capacity measure may obscure real relationships between storage
capacity and other measures" (Fukuda, Vogel, Mayr, and Awh, 2010, p. 679). Effectively,
58
strategies might artificially improve a person’s measured span. However, the present study is
based on the assumption that one way to control specific individual strategies is to allow
people to develop the same strategies by introducing systematic regularities into the
memoranda (without asking them to do something in particular). In the present study, these
regularities were fit by an algorithmic complexity metric. Our results show that the average
complexity reached by the participants between Exp. 1 and Exp. 2 is quite close when
considering the two inflection points in performance as a function of complexity. This
difference was still statistically significant, but corresponded to only .7 additional colors
recalled in Experiment 1 (which lasted about 25 minutes) than in Experiment 2 (which lasted
about 5 minutes). This confirms the observation of Gendle and Ransom (2006) that the Simon
game is resistant to practice effects. This also means that the average spans between the two
experiments were not influenced much by elaborated strategies that could have been
developed better while allowing a greater amount of time to participants.
One remaining risk is that intelligence might be best measured by chunking span tasks
because these tasks require intelligence in the first place. We believe that the optimization
process that goes with associating the colors one another is an elementary process that can
only be a basis for developing higher order cognition, but intelligence cannot be reduced to
such an elementary process. Intelligence could therefore be predicted by such tasks without
totally underlying the perception of patterns and they reorganization in immediate memory.
Capacity limit
One last interesting result of the present study is that our chunking span tasks lead to greater
spans than the 4±1 capacity usually associated with the WM construct, and do not conclude
with a trade-off between processing and storage. One point of view is that any span task with
extra processes (chunking in the present study) would necessarily lead to lower spans in the
59
case of a trade-off between processing and storage (see Logan, 2004. p. 219). Another point
of view is that more processing is supposed to be associated with better compression and
should result in a greater number of items stored here. This is only true if the recoding process
does not take more space than necessary. Effectively, more encoding does not necessarily
involve shorter representations. For instance, and to simplify the idea, blue-red-blue-blueblue-red (or brbbbr) can be elegantly recoded as xbbx using x=br as a new chunk, simply
because br is redundant. However, this supposes that brbbbr is replaced with the longer
"x=br;xbbx" because the recoding of br into x needs to be remembered anyhow. The resulting
compressed representation xbbx cannot be dissociated from the compression process that
includes x=br. The new description x=br;xbbx is now 10-symbols long instead of the original
sequence brbbbr which is 7-symbols long. A compressed sequence should better optimize
storage, but the method is only useful when the recoding scheme helps gain space. This is not
the case for this example. The gain can be estimated using an information-theoretic criterion
such as the Minimum-Description-Length (MDL) principle (Robinet, Lemaire, & Gordon,
2011). For instance, the method would work for a longer original sequence such as
brbbbrbrbrbrbrbr (16 symbols) because x=br;xbbxxxxxx (14 symbols) is shorter. The new
code "x=br;xbbxxxxxx" could be further maximally compressed using x=br;xbb6x but again,
a new code needs to specify that a number symbol (e.g., 6) indicates a repetition. Therefore,
short strings can still be recoded while there is a risk of increasing the original length.
Whether it leads to a longer or a shorter description, the recoding process could have a direct
relationship with the level of processing principle (Craik and Lockhart, 1972), which states
that memory trace is a function of the depth to which processing is performed. In the present
case, recoding a sequence with a longer description but with a more structured representation
could still help the recall process.
60
Limitations
We present here, one limitation concerning our study. In Experiment 2, the results showed an
average difference of only 1.2 more colors recalled in the Simple condition of the chunking
span task than in the Complex condition. When the two spans were divided by one another to
estimate processing efficiency, we found a negative correlation between processing and
storage. This means that the greater the capacity for the most complex sequences (e.g., 7) the
less it is likely that the participants can increase their capacity for the simpler sequences (e.g.,
the span still revolves around 7). Notwithstanding the possibility that some participants have a
great storage capacity but a null processing efficiency because they do not obtain better
results in the Simple condition than in the Complex condition, a first more plausible
interpretation is that some participants make more effort to organize the less compressible
sequences, which does not leave much room for the most compressible sequences. Another
possible interpretation is that the limitation is due to the use of phonological representations
that limit the duration of rehearsal. No matter the compressibility of the sequences, the
number of colors to be pronounced covertly would, for instance, be limited by the two-second
limit on the phonological store, and indeed many participants declared that they
spontaneously verbalized the to-be-recalled sequences.
One last test was therefore conducted by dividing the two spans obtained for the simple and
complex versions of the chunking span task for each participant. This aimed at estimating the
number of items that could be packed by the participants, which reflected their processing
capability (this directly measures an average chunk-creation ability). In this case, the
61
correlation between this estimate of the processing component and Raven was not found
significant (r = -.04) while the correlation between processing was found negative with
storage (r = -.59, p < .001) and positive with storage × processing (r = .46, p < .001). This
means that the greater the capacity was for the most complex sequences (e.g., 7) the less
likely it was that the participants could increase their capacity for the most simple sequences
(e.g., the span still revolved around 7). Overall, our tasks do not seem to be able to express as
simply as we first expected three clearly separated estimates of storage, storage × processing,
and storage × processing/ storage = processing constructs.
Conclusion
The rationale of the present study was that sequences of colors of the Simon game contain
regularities that can be mathematized to estimate a chunking process, and that the quantity of
chunking induced in a to-be-recalled sequence can represent the processing demand. The
chunking span task allows the processing and storage components to fully interact to optimize
storage. Although it is not commonly accepted in the literature that span tasks can take benefit
from favoring the processing of the stored items (which explains the plethora of complex span
tasks in the literature), the chunking span task was found a reliable predictor of general
intelligence in comparison to other simple or complex span tasks. Our conclusion is that
chunking span tasks can predict IQ better than any other types of span tasks because this task
involves a process of storage optimization that requires full function of the processing
component.
62
63
References
Aben, B., Stapert, S., & Blokland, A. (2012). About the distinction between working memory
and short-term memory. Frontiers in Psychology, 3.
Ackerman, P. L., Beier, M. E., & Boyle, M. O. (2005). Working memory and intelligence:
The same or different constructs? Psychological Bulletin, 131(1), 30–60.
Alvarez, G. A., & Cavanagh, P. (2004). The capacity of visual short-term memory is set both
by visual information load and by number of objects. Psychological Science, 15(2),
106–111.
Anderson, J. R., Bothell, D., Lebiere, C., & Matessa, M. (1998). An integrated theory of list
memory. Journal of Memory and Language, 38(4), 341–380.
Baddeley, A. D. (2000). The episodic buffer: a new component of working memory? Trends
in Cognitive Sciences, 4(11), 417–423.
Baddeley, A. D. (2001). Is working memory still working? American Psychologist, 56(11),
851.
Baddeley, A. D., & Hitch, G. (1974). Working memory. Psychology of Learning and
Motivation, 8, 47–89.
Baddeley, A. D., Lewis, V., & Vallar, G. (1984). Exploring the articulatory loop. The
Quarterly Journal of Experimental Psychology Section A, 36(2), 233‑252.
Baddeley, A. D., Thomson, N., & Buchanan, M. (1975). Word length and the structure of
short-term memory. Journal of Verbal Learning and Verbal Behavior, 14(6), 575–
589.
Bailey, H., Dunlosky, J., & Kane, M. J. (2011). Contribution of strategy use to performance
on complex and simple span tasks. Memory & Cognition, 39(3), 447–461.
64
Barrouillet, P., Bernardin, S., & Camos, V. (2004). Time constraints and resource sharing in
adults’ working memory spans. Journal of Experimental Psychology: General, 133(1),
83.
Barrouillet, P., Bernardin, S., Portrat, S., Vergauwe, E., & Camos, V. (2007). Time and
cognitive load in working memory. Journal of Experimental Psychology: Learning,
Memory, and Cognition, 33(3), 570.
Barrouillet, P., & Camos, V. (2012). As time goes by temporal constraints in working
memory. Current Directions in Psychological Science, 21(6), 413–419.
Barrouillet, P., Plancher, G., Guida, A., & Camos, V. (2013). Forgetting at short term: When
do event-based interference and temporal factors have an effect? Acta Psychologica,
142(2), 155–167.
Baum, E. B. (2004). What is thought? Cambridge, MA: MIT press.
Bor, D., Cumming, N., Scott, C. E., & Owen, A. M. (2004). Prefrontal cortical involvement in
verbal encoding strategies. European Journal of Neuroscience, 19(12), 3365–3370.
Bor, D., Duncan, J., Wiseman, R. J., & Owen, A. M. (2003). Encoding strategies dissociate
prefrontal activity from working memory demand. Neuron, 37(2), 361–367.
Bor, D., & Owen, A. M. (2007). A common prefrontal–parietal network for mnemonic and
mathematical recoding strategies within working memory. Cerebral Cortex, 17(4),
778–786.
Bor, D., & Seth, A. K. (2012). Consciousness and the prefrontal parietal network: insights
from attention, working memory, and chunking. Frontiers in Psychology, 3, 63.
Botvinick, M. M., & Plaut, D. C. (2006). Short-term memory for serial order: a recurrent
neural network model. Psychological Review, 113(2), 201.
Boucher, V. J. (2006). On the function of stress rhythms in speech: Evidence of a link with
grouping effects on serial memory. Language and Speech, 49(4), 495–519.
65
Brady, T. F., Konkle, T., & Alvarez, G. A. (2009). Compression in visual working memory:
using statistical regularities to form more efficient memory representations. Journal of
Experimental Psychology: General, 138(4), 487.
Brady, T. F., Konkle, T., & Alvarez, G. A. (2011). A review of visual memory capacity:
Beyond individual items and toward structured representations. Journal of Vision,
11(5), 4.
Brady, T. F., & Tenenbaum, J. B. (2013). A probabilistic model of visual working memory:
Incorporating higher order regularities into working memory capacity estimates.
Psychological Review, 120(1), 85.
Brainard, D. H. (1997). The psychophysics toolbox. Spatial Vision, 10, 433–436.
Burgess, N., & Hitch, G. J. (1999). Memory for serial order: A network model of the
phonological loop and its timing. Psychological Review, 106(3), 551.
Cantor, J., Engle, R. W., & Hamilton, G. (1991). Short-term memory, working memory, and
verbal abilities: How do they relate? Intelligence, 15(2), 229–246.
Case, R. (1985). Intellectual development: Birth to adulthood. New York, NY: Academic
Press.
Chaitin, G. J. (1966). On the length of programs for computing finite binary sequences.
Journal of the ACM, 13(4), 547–569.
Chase, W. G., & Simon, H. A. (1973). Perception in chess. Cognitive Psychology, 4(1), 55–
81.
Chen, Z., & Cowan, N. (2005). Chunk limits and length limits in immediate recall: A
reconciliation. Journal of Experimental Psychology. Learning, Memory, and
Cognition, 31(6), 1235‑1249.
Chuderski, A., Taraday, M., Nęcka, E., & Smoleń, T. (2012). Storage capacity explains fluid
intelligence but executive control does not. Intelligence, 40(3), 278-295.
66
Colom, R., Abad, F. J., Quiroga, M. Á., Shih, P. C., & Flores-Mendoza, C. (2008). Working
memory and intelligence are highly related constructs, but why?. Intelligence, 36(6),
584-606.
Colom, R., Jung, R. E., & Haier, R. J. (2007). General intelligence and memory span:
evidence for a common neuroanatomic framework. Cognitive Neuropsychology,
24(8), 867–878.
Colom, R., Rebollo, I., Abad, F. J., & Shih, P. C. (2006). Complex span tasks, simple span
tasks, and cognitive abilities: A reanalysis of key studies. Memory & Cognition, 34(1),
158–171.
Colom, R., Rebollo, I., Palacios, A., Juan-Espinosa, M., & Kyllonen, P. C. (2004). Working
memory is (almost) perfectly predicted by g. Intelligence, 32(3), 277-296.
Conway, A. R., Cowan, N., Bunting, M. F., Therriault, D. J., & Minkoff, S. R. (2002). A
latent variable analysis of working memory capacity, short-term memory capacity,
processing speed, and general fluid intelligence. Intelligence, 30(2), 163–183.
Conway, A. R., Kane, M. J., Bunting, M. F., Hambrick, D. Z., Wilhelm, O., & Engle, R. W.
(2005). Working memory span tasks: A methodological review and user’s guide,
Psychonomic Bulletin & Review, 12(5), 769–786.
Conway, A. R., Kane, M. J., & Engle, R. W. (2003). Working memory capacity and its
relation to general intelligence. Trends in cognitive sciences, 7(12), 547-552.
Conway, C. M., Karpicke, J., & Pisoni, D. B. (2007). Contribution of implicit sequence
learning to spoken language processing: Some preliminary findings with hearing
adults. Journal of Deaf Studies and Deaf Education, 12(3), 317–334.
Cowan, N. (2001). The magical number 4 in short-term memory: a reconsideration of mental
storage capacity. The Behavioral and Brain Sciences, 24(1), 87‑114.
Cowan, N. (2005). Working memory capacity. Hove, East Sussex, UK: Psychology Press.
67
Cowan, N., & Chen, Z. (2009). How chunks form in long-term memory and affect short-term
memory limits. In A. Thorn & M. Page (Eds.), Interactions between short-term and
long-term memory in the verbal domain (pp. 86-101). Hove, East Sussex, UK:
Psychology Press.
Cowan, N., Chen, Z., & Rouder, J. N. (2004). Constant capacity in an immediate serial-recall
task: A logical sequel to Miller (1956). Psychological Science, 15(9), 634–640.
Cowan, N., Elliott, E. M., Saults, J. S., Morey, C. C., Mattox, S., Hismjatullina, A., &
Conway, A. R. A. (2005). On the capacity of attention: Its estimation and its role in
working memory and cognitive aptitudes. Cognitive Psychology, 51(1), 42‑100.
Cowan, N., Rouder, J. N., Blume, C. L., & Saults, J. S. (2012). Models of Verbal Working
Memory Capacity: What Does It Take to Make Them Work? Psychological Review,
119(3), 480-499.
Cowan, N., Towse, J. N., Hamilton, Z., Saults, J. S., Elliott, E. M., Lacey, J. F., … Hitch, G.
J. (2003). Children’s working-memory processes: A response-timing analysis. Journal
of Experimental Psychology: General, 132(1), 113.
Craik, F. I., & Lockhart, R. S. (1972). Levels of processing: A framework for memory
research. Journal of Verbal Learning and Verbal Behavior, 11(6), 671–684.
Crannell, C. W., & Parrish, J. M. (1957). A comparison of immediate memory span for digits,
letters, and words. The Journal of Psychology: Interdisciplinary and Applied, 44,
319‑327.
Cumming, N., Page, M., & Norris, D. (2003). Testing a positional model of the Hebb effect.
Memory, 11(1), 43–63.
Daneman, M., & Carpenter, P. A. (1980). Individual differences in working memory and
reading. Journal of Verbal Learning and Verbal Behavior, 19(4), 450–466.
68
Daneman, M., & Merikle, P. M. (1996). Working memory and language comprehension: A
meta-analysis. Psychonomic Bulletin & Review, 3(4), 422–433.
Davelaar, E. J. (2013). Short-term memory as a working memory control process. Frontiers in
Psychology, 4,13.
De Groot, A. D., & Gobet, F. (1996). Perception and memory in chess: Studies in the
heuristics of the professional eye. Assen, Netherlands: Van Gorcum.
Dieguez, S., Wagner-Egger, P., & Gauvrit, N. (in press). “Nothing happens by accident”, or
does it? A low prior for randomness does not explain belief in conspiracy theories.
Psychological Science.
Delahaye, J.-P., & Zenil, H. (2012). Numerical evaluation of algorithmic complexity for short
strings: A glance into the innermost structure of randomness. Applied Mathematics
and Computation, 219(1), 63–77.
Dixon, P., LeFevre, J.-A., & Twilley, L. C. (1988). Word knowledge and working memory as
predictors of reading skill. Journal of Educational Psychology, 80(4), 465.
Duncan, J. (2006). EPS Mid-Career Award 2004: Brain mechanisms of attention. The
Quarterly Journal of Experimental Psychology, 59(1), 2‑27.
Duncan, J., Schramm, M., Thompson, R., & Dumontheil, I. (2012). Task rules, working
memory, and fluid intelligence. Psychonomic Bulletin & Review, 19(5), 864–870.
Ehrlich, M.-F., & Delafoy, M. (1990). La mémoire de travail: structure, fonctionnement,
capacité. L'Année Psychologique, 90(3), 403–427.
Engle, R. W. (2002). Working memory capacity as executive attention. Current Directions in
Psychological Science, 11(1), 19–23.
69
Engle, R. W., Tuholski, S. W., Laughlin, J. E., & Conway, A. R. (1999). Working memory,
short-term memory, and general fluid intelligence: a latent-variable approach. Journal
of Experimental Psychology: General, 128(3), 309.
Ericsson, K. A., Chase, W. G., & Faloon, S. (1980). Acquisition of a memory skill. Science,
208(4448), 1181–1182.
Ericsson, K. A., & Kintsch, W. (1995). Long-term working memory. Psychological Review,
102(2), 211.
Farrell, S. (2008). Multiple roles for time in short-term memory: Evidence from serial recall
of order and timing. Journal of Experimental Psychology: Learning, Memory, and
Cognition, 34(1), 128.
Farrell, S. (2012). Temporal clustering and sequencing in short-term memory and episodic
memory. Psychological Review, 119(2), 223.
Feigenson, L., & Halberda, J. (2008). Conceptual knowledge increases infants’ memory
capacity. Proceedings of the National Academy of Sciences, 105(29), 9926–9930.
Fernández, A., Ríos-Lago, M., Abásolo, D., Hornero, R., Álvarez-Linera, J., Paul, N., …
Ortiz, T. (2011). The correlation between white-matter microstructure and the
complexity of spontaneous brain activity: a diffusion tensor imaging-MEG study.
Neuroimage, 57(4), 1300–1307.
Fernández, A., Zuluaga, P., Abásolo, D., Gómez, C., Serra, A., Méndez, M. A., & Hornero, R.
(2012). Brain oscillatory complexity across the life span. Clinical Neurophysiology,
123(11), 2154–2162.
French, R. M., Addyman, C., & Mareschal, D. (2011). TRACX: a recognition-based
connectionist framework for sequence segmentation and chunk extraction.
Psychological Review, 118(4), 614.
70
Fukuda, K., Vogel, E., Mayr, U., & Awh, E. (2010). Quantity, not quality: The relationship
between fluid intelligence and working memory capacity. Psychonomic Bulletin &
Review, 17(5), 673–679.
Gauvrit, N., Singmann, H., Soler-Toscano, F., & Zenil, H. (2015). Algorithmic complexity for
psychology: A user-friendly implementation of the coding theorem method. Behavior
Research Methods, 1-16.
Gauvrit, N., Soler-Toscano, F., & Zenil, H. (2014). Natural scene statistics mediate the
perception of image complexity. Visual Cognition, 22(8), 1084-1091.
Gauvrit, N., Zenil, H., Delahaye, J.-P., & Soler-Toscano, F. (2014). Algorithmic complexity
for short binary strings applied to psychology: a primer. Behavior Research Methods,
46(3), 732‑744.
Gendle, M. H., & Ransom, M. R. (2006). Use of the electronic game SIMON® as a measure
of working memory span in college age adults. Journal of Behavioral and
Neuroscience Research, 4, 1‑7.
Gilbert, A. C., Boucher, V. J., & Jemel, B. (2014). Perceptual chunking and its effect on
memory in speech processing: ERP and behavioral evidence. Frontiers in Psychology,
5.
Gilchrist, A. L., Cowan, N., & Naveh-Benjamin, M. (2008). Working memory capacity for
spoken sentences decreases with adult ageing: Recall of fewer but not smaller chunks
in older adults. Memory, 16(7), 773–787.
Gobet, F., & Simon, H. A. (1996). Recall of rapidly presented random chess positions is a
function of skill. Psychonomic Bulletin & Review, 3(2), 159–163.
Gray, J. R., Chabris, C. F., & Braver, T. S. (2003). Neural mechanisms of general fluid
intelligence. Nature Neuroscience, 6(3), 316–322.
71
Guida, A., Gobet, F., & Nicolas, S. (2013). Functional cerebral reorganization: a signature of
expertise? Reexamining Guida, Gobet, Tardieu, and Nicolas’(2012) two-stage
framework. Frontiers in Human Neuroscience, 7.
Guida, A., Gobet, F., Tardieu, H., & Nicolas, S. (2012). How chunks, long-term working
memory and templates offer a cognitive explanation for neuroimaging data on
expertise acquisition: a two-stage framework. Brain and Cognition, 79(3), 221–244.
Guida, A., Tardieu, H., & Nicolas, S. (2009). The personalisation method applied to a
working memory task: Evidence of long-term working memory effects. European
Journal of Cognitive Psychology, 21(6), 862–896.
Haarmann, H. J., Davelaar, E. J., & Usher, M. (2003). Individual differences in semantic
short-term memory capacity and reading comprehension. Journal of Memory and
Language, 48(2), 320–345.
Hanten, G., & Martin, R. C. (2000). Contributions of phonological and semantic short-term
memory to sentence processing: Evidence from two cases of closed head injury in
children. Journal of Memory and Language, 43(2), 335–361.
Hitch, G. J., Towse, J. N., & Hutton, U. (2001). What limits children’s working memory
span? Theoretical accounts and applications for scholastic development. Journal of
Experimental Psychology: General, 130(2), 184.
Humes, L. E., & Floyd, S. S. (2005). Measures of working memory, sequence learning, and
speech recognition in the elderly. Journal of Speech, Language, and Hearing
Research, 48(1), 224–235.
Hutter, M. (2005). Universal artificial intelligence. Berlin, Germany: Springer-Verlag.
James, W. (1890). The methods and snares of psychology. In The principles of psychology,
Vol I (p. 183‑198). New York, NY: Henry Holt and Co.
72
Johnson, N. F. (1969). Chunking: Associative chaining versus coding. Journal of Verbal
Learning and Verbal Behavior, 8(6), 725–731.
Kane, M. J., Hambrick, D. Z., & Conway, A. R. (2005). Working memory capacity and fluid
intelligence are strongly related constructs: comment on Ackerman, Beier, and Boyle
(2005). Psychological Bulletin, 131(1), 66–71.
Kane, M. J., Hambrick, D. Z., Tuholski, S. W., Wilhelm, O., Payne, T. W., & Engle, R. W.
(2004). The generality of working memory capacity: a latent-variable approach to
verbal and visuospatial memory span and reasoning. Journal of Experimental
Psychology: General, 133(2), 189.
Kane, M. J., & Miyake, T. M. (2007). The validity of « conceptual span » as a measure of
working memory capacity. Memory & Cognition, 35(5), 1136–1150.
Karpicke, J., & Pisoni, D. B. (2000). Memory span and sequence learning using multimodal
stimulus patterns: Preliminary findings in normal-hearing adults. Research on Spoken
Language Processing.
Kempe, V., Gauvrit, N., & Forsyth, D. (2015). Structure emerges faster during cultural
transmission in children than in adults. Cognition, 136, 247-254.
Kibbe, M. M., & Feigenson, L. (2014). Developmental origins of recoding and decoding in
memory. Cognitive Psychology, 75, 55–79.
Klapp, S. T., Marshburn, E. A., & Lester, P. T. (1983). Short-term memory does not involve
the « working memory » of information processing: The demise of a common
assumption. Journal of Experimental Psychology: General, 112(2), 240.
Kolmogorov, A. N. (1965). Three approaches to the quantitative definition of information.
Problems of Information Transmission, 1(1), 1–7.
Krumm, S., Schmidt-Atzert, L., Buehner, M., Ziegler, M., Michalczyk, K., & Arrow, K.
(2009). Storage and non-storage components of working memory predicting
73
reasoning: A simultaneous examination of a wide range of ability factors. Intelligence,
37(4), 347-364.
Lewandowsky, S., Oberauer, K., Yang, L.-X., & Ecker, U. K. (2010). A working memory test
battery for MATLAB. Behavior Research Methods, 42(2), 571–585.
Li, M., & Vitányi, P. M. (2009). An introduction to Kolmogorov complexity and its
applications. New York, NY: Springer Verlag.
Logan, G. D. (2004). Working memory, task switching, and executive control in the task span
procedure. Journal of Experimental Psychology: General, 133(2), 218.
Luck, S. J., & Vogel, E. K. (1997). The capacity of visual working memory for features and
conjunctions. Nature, 390(6657), 279–281.
Machado, B. S., Miranda, T. B., Morya, E., Amaro Jr, E., & Sameshima, K. (2010).
Algorithmic complexity measure of EEG for staging brain state. Clinical
Neurophysiology, 121, S249–S250.
Majerus, S., Martinez Perez, T., & Oberauer, K. (2012). Two distinct origins of long-term
learning effects in verbal short-term memory. Journal of Memory and Language,
66(1), 38–51.
Martin, R. C., & Romani, C. (1994). Verbal working memory and sentence comprehension: A
multiple-components view. Neuropsychology, 8(4), 506.
Martínez, K., Burgaleta, M., Román, F. J., Escorial, S., Shih, P. C., Quiroga, M. Á., & Colom,
R. (2011). Can fluid intelligence be reduced to ‘simple’short-term storage?.
Intelligence, 39(6), 473-480.
Mathy, F., & Feldman, J. (2012). What’s magic about magic numbers? Chunking and data
compression in short-term memory. Cognition, 122(3), 346–362.
Mathy, F., & Varré, J.-S. (2013). Retention-error patterns in complex alphanumeric serialrecall tasks. Memory, 21(8), 945–968.
74
Maybery, M. T., Parmentier, F. B., & Jones, D. M. (2002). Grouping of list items reflected in
the timing of recall: Implications for models of serial verbal memory. Journal of
Memory and Language, 47(3), 360–385.
Miller, G. A. (1956). The magical number seven, plus or minus two: some limits on our
capacity for processing information. Psychological Review, 63(2), 81.
Moher, M., Tuerk, A. S., & Feigenson, L. (2012). Seven-month-old infants chunk items in
memory. Journal of Experimental Child Psychology, 112(4), 361–377.
Naveh-Benjamin, M., Cowan, N., Kilb, A., & Chen, Z. (2007). Age-related differences in
immediate serial recall: Dissociating chunk formation and capacity. Memory &
Cognition, 35(4), 724–737.
Ng, H. L., & Maybery, M. T. (2002). Grouping in short-term verbal memory: Is position
coded temporally? The Quarterly Journal of Experimental Psychology: Section A,
55(2), 391–424.
Oakes, L. M., Ross-Sheehy, S., & Luck, S. J. (2006). Rapid development of feature binding in
visual short-term memory. Psychological Science, 17(9), 781–787.
Oberauer, K. (2002). Access to information in working memory: exploring the focus of
attention. Journal of Experimental Psychology: Learning, Memory, and Cognition,
28(3), 411.
Oberauer, K., Farrell, S., Jarrold, C., Pasiecznik, K., & Greaves, M. (2012). Interference
between maintenance and processing in working memory: The effect of item–
distractor similarity in complex span. Journal of Experimental Psychology: Learning,
Memory, and Cognition, 38(3), 665.
Oberauer, K., & Lange, E. B. (2009). Activation and binding in verbal working memory: A
dual-process model for the recognition of nonwords. Cognitive Psychology, 58(1),
102–136.
75
Oberauer, K., Lange, E., & Engle, R. W. (2004). Working memory capacity and resistance to
interference. Journal of Memory and Language, 51(1), 80–96.
Oberauer, K., Lewandowsky, S., Farrell, S., Jarrold, C., & Greaves, M. (2012). Modeling
working memory: an interference model of complex span. Psychonomic Bulletin &
Review, 19(5), 779–819.
Osaka, M., Nishizaki, Y., Komori, M., & Osaka, N. (2002). Effect of focus on verbal working
memory: Critical role of the focus word in reading. Memory & Cognition, 30(4), 562–
571.
Pelli, D. G. (1997). The VideoToolbox software for visual psychophysics: Transforming
numbers into movies. Spatial Vision, 10(4), 437–442.
Perfetti, C. A., & Lesgold, A. M. (1977). Discourse comprehension and sources of individual
differences. In M.A. Just & P.A. Carpenter (Eds), Cognitive processes in
comprehension. Hillsdale, NJ: Erlbaum.
Perlman, A., Pothos, E. M., Edwards, D. J., & Tzelgov, J. (2010). Task-relevant chunking in
sequence learning. Journal of Experimental Psychology: Human Perception and
Performance, 36(3), 649.
Perruchet, P., & Pacteau, C. (1990). Synthetic grammar learning: Implicit rule abstraction or
explicit fragmentary knowledge? Journal of Experimental Psychology: General,
119(3), 264.
Rabinovich, M. I., Varona, P., Tristan, I., & Afraimovich, V. S. (2014). Chunking dynamics:
heteroclinics in mind. Frontiers in Computational Neuroscience, 8, 22.
Raven, J. C. (1962). Advanced progressive matrices: Sets I and II. HK Lewis.
Robinet, V., Lemaire, B., & Gordon, M. B. (2011). MDLChunker: a MDL-based cognitive
model of inductive learning. Cognitive Science, 35(7), 1352–1389.
76
Ryabko, B., Reznikova, Z., Druzyaka, A., & Panteleeva, S. (2013). Using ideas of
Kolmogorov complexity for studying biological texts. Theory of Computing Systems,
52(1), 133–147.
Saito, S., & Miyake, A. (2004). On the nature of forgetting and the processing–storage
relationship in reading span performance. Journal of Memory and Language, 50(4),
425–443.
Salthouse, T. A., & Babcock, R. L. (1991). Decomposing adult age differences in working
memory. Developmental Psychology, 27(5), 763.
Schroeder, P. J., Copeland, D. E., & Bies-Hernandez, N. J. (2012). The influence of story
context on a working memory span task. The Quarterly Journal of Experimental
Psychology, 65(3), 488–500.
Shipstead, Z., Redick, T. S., & Engle, R. W. (2012). Is working memory training effective?
Psychological Bulletin, 138(4), 628.
Soler-Toscano, F., Zenil, H., Delahaye, J.-P., & Gauvrit, N. (2013). Correspondence and
independence of numerical evaluations of algorithmic information measures.
Computability, 2(2), 125–140.
Soler-Toscano, F., Zenil, H., Delahaye, J.-P., & Gauvrit, N. (2014). Calculating Kolmogorov
complexity from the output frequency distributions of small Turing machines. PloS
One, 9(5), e96223.
Solway, A., Diuk, C., Córdova, N., Yee, D., Barto, A. G., Niv, Y., & Botvinick, M. M.
(2014). Optimal hehavioral hierarchy. PLoS Computational Biology, 10(8), e1003779.
Stahl, A. E. & Feigenson, L. (2014). Social knowledge facilitates chunking in infancy. Child
Development, 85(4), 1477-1490.
Steiger, J. H. (1980). Tests for comparing elements of a correlation matrix. Psychological
Bulletin, 87(2), 245.
77
Szmalec, A., Page, M., & Duyck, W. (2012). The development of long-term lexical
representations through Hebb repetition learning. Journal of Memory and Language,
67(3), 342–354.
Thomas, J. G., Milner, H. R., & Haberlandt, K. F. (2003). Forward and Backward Recall
Different Response Time Patterns, Same Retrieval Order. Psychological Science,
14(2), 169–174.
Towse, J. N., Cowan, N., Hitch, G. J., & Horton, N. J. (2008). The recall of information from
working memory: Insights from behavioral and chronometric perspectives.
Experimental Psychology, 55(6), 371.
Towse, J. N., Hitch, G. J., Horton, N., & Harvey, K. (2010). Synergies between processing
and memory in children’s reading span. Developmental Science, 13(5), 779–789.
Tulving, E., & Patkau, J. E. (1962). Concurrent effects of contextual constraint and word
frequency on immediate recall and learning of verbal material. Canadian Journal of
Psychology, 16(2), 83.
Turner, M. L., & Engle, R. W. (1989). Is working memory capacity task dependent? Journal
of Memory and Language, 28(2), 127–154.
Unsworth, N., & Engle, R. W. (2006). Simple and complex memory spans and their relation
to fluid abilities: Evidence from list-length effects. Journal of Memory and Language,
54(1), 68–80.
Unsworth, N., & Engle, R. W. (2007a). On the division of short-term and working memory:
an examination of simple and complex span and their relation to higher order abilities.
Psychological Bulletin, 133(6), 1038.
Unsworth, N., & Engle, R. W. (2007b). The nature of individual differences in working
memory capacity: active maintenance in primary memory and controlled search from
secondary memory. Psychological Review, 114(1), 104.
78
Unsworth, N., Redick, T. S., Heitz, R. P., Broadway, J. M., & Engle, R. W. (2009). Complex
working memory span tasks and higher-order cognition: A latent-variable analysis of
the relationship between processing and storage. Memory, 17(6), 635–654.
Wang, T., Ren, X., Li, X., & Schweizer, K. (2015). The modeling of temporary storage and
its effect on fluid intelligence: Evidence from both Brown–Peterson and complex span
tasks. Intelligence, 49, 84-93.
Wechsler, D. (2008). Wechsler adult intelligence scale–Fourth Edition (WAIS–IV). San
Antonio, TX: NCS Pearson.
Wheeler, M. E., & Treisman, A. M. (2002). Binding in short-term visual memory. Journal of
Experimental Psychology: General, 131(1), 48.
Yagil, G. (2009). The structural complexity of DNA templates—Implications on cellular
complexity. Journal of Theoretical Biology, 259(3), 621–627.
79