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Cited by 473Cognitive Abilities and TestingNeural and Behavioral Psychology StudiesCognitive Functions and Memory

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What is working memory capacity, and how can we measure it?

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Wilhelm, Oliver, Hildebrandt, Andrea, Oberauer, Klaus·2013·Frontiers in Psychology
DOI 10.3389/fpsyg.2013.00433PMC PMC3721021
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Abstract

A latent variable study examined whether different classes of working-memory tasks measure the same general construct of working-memory capacity (WMC). Data from 270 subjects were used to examine the relationship between Binding, Updating, Recall-N-back, and Complex Span tasks, and the relations of WMC with secondary memory measures, indicators of cognitive control from two response-conflict paradigms (Simon task and Eriksen flanker task), and fluid intelligence. Confirmatory factor analyses support the concept of a general WMC factor. Results from structural-equation modeling show negligible relations of WMC with response-conflict resolution, and very strong relations of WMC with secondary memory and fluid intelligence. The findings support the hypothesis that individual differences in WMC reflect the ability to build, maintain and update arbitrary bindings.

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Figures

Figure 1 Schematic outline of the constructs investigated (ovals), their indicators (rectangles), and their relations (arrows). The relations are color-coded (see legend in upper left corner) to indicate which relation is postulated by which of the three theories of WMC discussed in the text (relations drawn in black are theoretically non-controversial). Relations not coded in the color of a theory might be compatible with the theory in question but are not explicitly assumed in that theory. Indicators and constructs not measured in the present study are drawn with broken lines. Gf, fluid intelligence; EA, executive attention; PM, primary memory; WMC, working-memory capacity; SM, secondary memory; Swi, task switching/shifting; Inhib, inhibition; Upd, working-memory updating; FR, free recall; PA, paired-associates recall; Rec, recognition.
Figure 1 Schematic outline of the constructs investigated (ovals), their indicators (rectangles), and their relations (arrows). The relations are color-coded (see legend in upper left corner) to indicate which relation is postulated by which of the three theories of WMC discussed in the text (relations drawn in black are theoretically non-controversial). Relations not coded in the color of a theory might be compatible with the theory in question but are not explicitly assumed in that theory. Indicators and constructs not measured in the present study are drawn with broken lines. Gf, fluid intelligence; EA, executive attention; PM, primary memory; WMC, working-memory capacity; SM, secondary memory; Swi, task switching/shifting; Inhib, inhibition; Upd, working-memory updating; FR, free recall; PA, paired-associates recall; Rec, recognition.CC BY · PubMed Central
Figure 2 Schematic representations of tasks. (A) Schematic representations of complex span tasks (rotation span). (B) Schematic representations of updating tasks (updating verbal). (C) Schematic representations of recall 1-back tasks (numerical recall 1-back). (D) Schematic representations of binding tasks (verbal-numerical binding). See task descriptions for details.
Figure 2 Schematic representations of tasks. (A) Schematic representations of complex span tasks (rotation span). (B) Schematic representations of updating tasks (updating verbal). (C) Schematic representations of recall 1-back tasks (numerical recall 1-back). (D) Schematic representations of binding tasks (verbal-numerical binding). See task descriptions for details.CC BY · PubMed Central
Figure 3 Confirmatory factor analysis of updating, Recall 1-back (RNb) and Complex Span (Cspan) Tasks (Model 1). The model postulates a verbal-numerical nested factor (VN that is orthogonal to task class specific factors). _v, verbal indicators; _n, numerical indicators; _f, figural indicators.
Figure 3 Confirmatory factor analysis of updating, Recall 1-back (RNb) and Complex Span (Cspan) Tasks (Model 1). The model postulates a verbal-numerical nested factor (VN that is orthogonal to task class specific factors). _v, verbal indicators; _n, numerical indicators; _f, figural indicators.CC BY · PubMed Central
Figure 4 Confirmatory factor analysis of Binding, Updating, Recall 1-back (RNb) and Complex Span (Cspan) Tasks (Model 2). The common variance of the task factors is accounted for by the higher-order Working Memory (WM) factor. The loadings of the Binding and Updating factors on WM were set to 1, the disturbance term of these factors was constrained to zero. _v, verbal indicators; _n, numerical indicators; _f, figural indicators; _lc, letter-color; _wn, word-number; _ll, location-letter; CS, Cspan indicators; VN, Verbal-numerical content factor.
Figure 4 Confirmatory factor analysis of Binding, Updating, Recall 1-back (RNb) and Complex Span (Cspan) Tasks (Model 2). The common variance of the task factors is accounted for by the higher-order Working Memory (WM) factor. The loadings of the Binding and Updating factors on WM were set to 1, the disturbance term of these factors was constrained to zero. _v, verbal indicators; _n, numerical indicators; _f, figural indicators; _lc, letter-color; _wn, word-number; _ll, location-letter; CS, Cspan indicators; VN, Verbal-numerical content factor.CC BY · PubMed Central
Figure 5 Structural equation model of WMC and Secondary Memory (SM) (Model 3). The measurement model of WMC is identical with the one depicted in Figure 3, postulating a higher order model for WMC with four first order factors: Binding, Updating, Recall 1-back (RNb) and Complex Span (Cspan). The VN (Verbal-Numerical Content) factor is maintained from Model 2. SM, Secondary Memory; PAsso, Learning Paired-Associations; _v, verbal indicators; _n, numerical indicators; _f, figural indicators; _lc, letter-color; _wn, word-number; _ll, location-letter; CS, Cspan indicators.
Figure 5 Structural equation model of WMC and Secondary Memory (SM) (Model 3). The measurement model of WMC is identical with the one depicted in Figure 3, postulating a higher order model for WMC with four first order factors: Binding, Updating, Recall 1-back (RNb) and Complex Span (Cspan). The VN (Verbal-Numerical Content) factor is maintained from Model 2. SM, Secondary Memory; PAsso, Learning Paired-Associations; _v, verbal indicators; _n, numerical indicators; _f, figural indicators; _lc, letter-color; _wn, word-number; _ll, location-letter; CS, Cspan indicators.CC BY · PubMed Central
Figure 6 Measurement Model of Response Inhibition (Model 4a). The model postulates two general factors (E and S); which account for individual variation in the number of correctly solved items per second (inverted latencies) during the Eriksen Flanker task and the Simon task, respectively. Additionally, for each paradigm we specified a factor to capture variation in response inhibition, and another factor for repetition priming (E RI, E Rep, and S RI and S Rep). Indicators were built to reflect sequence modulations of performance; cC, compatible trials following compatible trials; iC, compatible trials preceded by incompatible trials; cI, incompatible trials following compatible trials; iI, incompatible trials preceded by incompatible trials; _id, identical (stimulus repetition, relative to preceding trial); _ni, non-identical (stimulus change, relative to preceding trial).
Figure 6 Measurement Model of Response Inhibition (Model 4a). The model postulates two general factors (E and S); which account for individual variation in the number of correctly solved items per second (inverted latencies) during the Eriksen Flanker task and the Simon task, respectively. Additionally, for each paradigm we specified a factor to capture variation in response inhibition, and another factor for repetition priming (E RI, E Rep, and S RI and S Rep). Indicators were built to reflect sequence modulations of performance; cC, compatible trials following compatible trials; iC, compatible trials preceded by incompatible trials; cI, incompatible trials following compatible trials; iI, incompatible trials preceded by incompatible trials; _id, identical (stimulus repetition, relative to preceding trial); _ni, non-identical (stimulus change, relative to preceding trial).CC BY · PubMed Central
Figure 7 Structural Equation Model testing the relationship of WM, SM and Response Inhibition un the Simon task (Model 4b). Binding, Updating, Recall 1-back (RNb) and Complex Span (Cspan); VN, Verbal-Numerical Content Factor; SM, Secondary Memory; PAsso, Learning Paired-Associations; _v, verbal indicators; _n, numerical indicators; _f, figural indicators; _lc, letter-color; _wn, word-number; _ll, location-letter; CS, Cspan indicators; S, General RT performance during the Simon task; S RI, Response Inhibition effect in the Simon task, S Rep, Repetition Priming during the Simon task; cC, compatible trials following compatible trials; iC, compatible trials preceded by incompatible trials; cI, incompatible trials following compatible trials; iI, incompatible trials preceded by incompatible trials; _id, identical (Repetition Priming); _ni, non-identical (Unprimed).
Figure 7 Structural Equation Model testing the relationship of WM, SM and Response Inhibition un the Simon task (Model 4b). Binding, Updating, Recall 1-back (RNb) and Complex Span (Cspan); VN, Verbal-Numerical Content Factor; SM, Secondary Memory; PAsso, Learning Paired-Associations; _v, verbal indicators; _n, numerical indicators; _f, figural indicators; _lc, letter-color; _wn, word-number; _ll, location-letter; CS, Cspan indicators; S, General RT performance during the Simon task; S RI, Response Inhibition effect in the Simon task, S Rep, Repetition Priming during the Simon task; cC, compatible trials following compatible trials; iC, compatible trials preceded by incompatible trials; cI, incompatible trials following compatible trials; iI, incompatible trials preceded by incompatible trials; _id, identical (Repetition Priming); _ni, non-identical (Unprimed).CC BY · PubMed Central
Figure 8 Structural Equation Model testing the relationship of WM, SM and Gf (Model 5). Binding, Updating, Recall 1-back (RNb) and Complex Span (Cspan); VN, Verbal-Numerical Content Factor; SM, Secondary Memory; PAsso, Learning Paired-Associations; Gf, Fluid Intelligence; _v, verbal indicators; _n, numerical indicators; _f, figural indicators; _lc, letter-color; _wn, word-number; _ll, location-letter; CS, Cspan indicators.
Figure 8 Structural Equation Model testing the relationship of WM, SM and Gf (Model 5). Binding, Updating, Recall 1-back (RNb) and Complex Span (Cspan); VN, Verbal-Numerical Content Factor; SM, Secondary Memory; PAsso, Learning Paired-Associations; Gf, Fluid Intelligence; _v, verbal indicators; _n, numerical indicators; _f, figural indicators; _lc, letter-color; _wn, word-number; _ll, location-letter; CS, Cspan indicators.CC BY · PubMed Central
Figure 9 A first structural model estimating explained variance in Gf by means of binding and secondary memory indicators (Model 6a). Gf, Fluid Intelligence; VN, Verbal-Numerical Content Factor; _v, verbal indicator; _n, numerical indicator; _f, figural indicator; _lc, letter-color; _wn, word-number; _ll, location-letter.
Figure 9 A first structural model estimating explained variance in Gf by means of binding and secondary memory indicators (Model 6a). Gf, Fluid Intelligence; VN, Verbal-Numerical Content Factor; _v, verbal indicator; _n, numerical indicator; _f, figural indicator; _lc, letter-color; _wn, word-number; _ll, location-letter.CC BY · PubMed Central
Figure 10 A second structural model estimating explained variance in Gf by means of binding and secondary memory indicators (Model 6b). SM+,Secondary Memory for Paired Associations; Gf, Fluid Intelligence; VN, Verbal-Numerical Content Factor; _v, verbal indicator; _n, numerical indicator; _f, figural indicator; _lc, letter-color; _wn, word-number; _ll, location-letter; the residual variance of the SM_n indicator was fixed to zero.
Figure 10 A second structural model estimating explained variance in Gf by means of binding and secondary memory indicators (Model 6b). SM+,Secondary Memory for Paired Associations; Gf, Fluid Intelligence; VN, Verbal-Numerical Content Factor; _v, verbal indicator; _n, numerical indicator; _f, figural indicator; _lc, letter-color; _wn, word-number; _ll, location-letter; the residual variance of the SM_n indicator was fixed to zero.CC BY · PubMed Central

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Research works printed but not linked: 2

  1. Allison P. D. (2001). Missing Data. Thousand Oaks, CA: Sage Publications
  2. Keye D. Wilhelm O. Oberauer K. van Ravenzwaaij D. (2010). Erratum. Individual differences in conflict-monitoring: testing means and covariance hypothesis about the Simon and the Eriksen Flanker task. Psychol. Res. 74, 237– 238 10.1007/s00426-008-0188-9 19034502 · DOI

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Metadata

Authors
Wilhelm, O., Hildebrandt, A., & Oberauer, K.
Affiliations
  • Universität Ulm (DE)
  • Humboldt-Universität zu Berlin (DE)
  • University of Zurich (CH)
Corresponding author
Wilhelm, Oliver
ORCID
Venue
Frontiers in Psychology
Publisher
Frontiers Media SA
Published
2013
Volume
4
Pages
433-433
ISSN
1664-1078 (ISSN-L)
DOI
10.3389/fpsyg.2013.00433
PMC
PMC3721021
OpenAlex
W2115768836
Cited by
468
References
78
Citations by year
2026: 23 · 2025: 38 · 2024: 46 · 2023: 40 · 2022: 46 · 2021: 56 · 2020: 47 · 2019: 43 · 2018: 50 · 2017: 33 · 2016: 22 · 2015: 11 · 2014: 11 · 2013: 2
FWCI
20.77
Type
journal article
Language
en
Open access
Licence
cc-by
Locations
  • Frontiers in Psychology (publishedVersion, cc-by)
  • Europe PMC (PubMed Central) (publishedVersion, cc-by)
  • PubMed Central (publishedVersion, cc-by)
  • PubMed (publishedVersion)
  • Zurich Open Repository and Archive (University of Zurich) (acceptedVersion, cc-by)
  • OPen Access Repositorium der Universität Ulm (OPARU) (Ulm University) (submittedVersion, other-oa)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
  • edoc Publication server (Humboldt University of Berlin) (submittedVersion, cc-by)
  • Zurich Open Repository and Archive (University of Zurich) (submittedVersion, cc-by)
  • Universität Ulm, Kommunikations- und Informationszentrum (kiz) (cc-by)
  • Zurich Open Repository and Archive (University of Zurich)
Funders
Deutsche Forschungsgemeinschaft
Topics
  • Social Sciences › Psychology › Experimental and Cognitive Psychology › Cognitive Abilities and Testing
  • Life Sciences › Neuroscience › Cognitive Neuroscience › Neural and Behavioral Psychology Studies
  • Social Sciences › Psychology › Experimental and Cognitive Psychology › Cognitive Functions and Memory
Keywords
working memory capacity, latent constructs, binding, updating, complex span, secondary memory, cognitive control, response conflict, Simon task, flanker task, fluid intelligence, individual differences

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