Skip to main content

Capacity estimates in working memory: Reliability and interrelationships among tasks

Abstract

The concept of capacity has become increasingly important in discussions of working memory (WM), in so far as most models of WM conceptualize it as a limited-capacity mechanism for maintaining information in an active state, and as capacity estimates from at least one type of WM task—complex span—are valid predictors of real-world cognitive performance. However, the term capacity is also often used in the context of a distinct set of WM tasks, change detection, and may or may not refer to the same cognitive capability. We here develop maximum-likelihood models of capacity from each of these tasks—as well as from a third WM task that places heavy demands on cognitive control, the self-ordered WM task (SOT)—and show that the capacity estimates from change detection and complex span tasks are not correlated with each other, although capacity estimates from change detection tasks do correlate with those from the SOT. Furthermore, exploratory factor analysis confirmed that performance on the SOT and change detection load on the same factor, with performance on our complex span task loading on its own factor. These findings suggest that at least two distinct cognitive capabilities underlie the concept of WM capacity as it applies to each of these three tasks.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2

Notes

  1. 1.

    Although Rouder et al. (2008) did not spell out the MLE procedure used, the approach taken here was to treat each trial as a Bernoulli trial with a probability determined by the formulae above and to use a brute-force search of possible values for all three parameters.

  2. 2.

    Although Efron and Tibshirani (1993) did not provide a means of directly calculating p values for BCa, this can be done by determining α for the (1 – α)% CI that would have its upper or lower bound at exactly the null-hypothesis value being tested. Thus, one simply observes the proportion of the bootstrap distribution falling below the null-hypothesis value of the statistic and applies the function inverse {i.e., given the function f(x), the function inverse of f(x) is f –1(x), such that f –1[f(x)] = x} of the BCa correction given for CIs to this proportion.

References

  1. Benjamini, Y., & Hochberg, Y. (1995). Controlling the false discovery rate: A practical and powerful approach to multiple testing. Journal of the Royal Statistical Society, Series B, 57, 289–300.

    Google Scholar 

  2. Chein, J. M., Moore, A. B., & Conway, A. R. A. (2011). Domain-general mechanisms of complex working memory span. NeuroImage, 54, 550–559. doi:10.1016/j.neuroimage.2010.07.067

    PubMed  Article  Google Scholar 

  3. Conway, A. R. A., Cowan, N., Bunting, M. F., Therriault, D., & Minkoff, S. (2002). A latent variable analysis of working memory capacity, short term memory capacity, processing speed, and general fluid intelligence. Intelligence, 30, 163–183.

    Article  Google Scholar 

  4. Conway, A. R. A., 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. Pyschonomic Bulletin & Review, 12, 769–786. doi:10.3758/BF03196772

    Article  Google Scholar 

  5. Cowan, N. (2001). The magical number 4 in short-term memory: A reconsideration of mental storage capacity. Behavioral and Brain Sciences, 24, 87–114. doi:10.1017/S0140525X01003922. disc. 114–185.

    PubMed  Article  Google Scholar 

  6. 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, 42–100. doi:10.1016/j.cogpsych.2004.12.001

    PubMed Central  PubMed  Article  Google Scholar 

  7. Curtis, C. E., Zald, D. H., & Pardo, J. V. (2000). Organization of working memory within the human prefrontal cortex: A PET study of self-ordered object working memory. Neuropsychologia, 38, 1503–1510.

    PubMed  Article  Google Scholar 

  8. Efron, B., & Tibshirani, R. J. (1993). An introduction to the bootstrap. New York, NY: Chapman & Hall/CRC.

    Book  Google Scholar 

  9. Gibson, B., Wasserman, E., & Luck, S. J. (2011). Qualitative similarities in the visual short-term memory of pigeons and people. Psychonomic Bulletin & Review, 18, 979–984. doi:10.3758/s13423-011-0132-7

    Article  Google Scholar 

  10. Gold, J. M., Fuller, R. L., Robinson, B. M., McMahon, R. P., Braun, E. L., & Luck, S. J. (2006). Intact attentional control of working memory encoding in schizophrenia. Journal of Abnormal Psychology, 115, 658–673. doi:10.1037/0021-843X.115.4.658

    PubMed  Article  Google Scholar 

  11. Hayton, J. C., Allen, D. G., & Scarpello, V. (2004). Factor retention decisions in exploratory factor analysis: A tutorial on parallel analysis. Organizational Research Methods, 7, 191–205.

    Article  Google Scholar 

  12. Johnson, M. K., McMahon, R. P., Robinson, B. M., Harvey, A. N., Britta, H., Leonard, C. J., . . . Gold, J. M. (2013). The relationship between working memory capacity and broad measures of cognitive ability in healthy adults and people with schizophrenia. Neuropsychology, 27, 220–229.

    Google Scholar 

  13. Kyllingsbæk, S., & Bundesen, C. (2009). Changing change detection: Improving the reliability of measures of visual short-term memory capacity. Psychonomic Bulletin & Review, 16, 1000–1010. doi:10.3758/PBR.16.6.1000

    Article  Google Scholar 

  14. Lin, P.–. H., & Luck, S. J. (2012). Proactive interference does not meaningfully distort visual working memory capacity estimates in the canonical change detection task. Frontiers in Psychology, 3, 42.

    PubMed Central  PubMed  Article  Google Scholar 

  15. Luck, S. J., & Vogel, E. K. (1997). The capacity of visual working memory for features and conjunctions. Nature, 390, 279–281. doi:10.1038/36846

    PubMed  Article  Google Scholar 

  16. Osaka, N., Osaka, M., Kondo, H., Morishita, M., Fukuyama, H., & Shibasaki, H. (2004). Theneural basis of executive function in working memory: An fMRI study based on individual differences. NeuroImage, 21, 623–631. doi:10.1016/j.neuroimage.2003.09.069

    PubMed  Article  Google Scholar 

  17. Pashler, H. (1988). Familiarity and visual change detection. Perception & Psychophysics, 44, 369–378. doi:10.3758/BF03210419

    Article  Google Scholar 

  18. Rouder, J. N., Morey, R. D., Cowan, N., Zwilling, C. E., Morey, C. C., & Pratte, M. S. (2008). An assessment of fixed-capacity models of visual working memory. Proceedings of the National Academy of Sciences, 105, 5975–5979. doi:10.1073/pnas.0711295105

    Article  Google Scholar 

  19. Shipstead, Z., Redick, T. S., Hicks, K. L., & Engle, R. W. (2012). The scope and control of attention as separate aspects of working memory. Memory, 20, 608–628. doi:10.1080/09658211.2012.691519

    PubMed  Article  Google Scholar 

  20. Smith, E. E., Geva, A., Jonides, J., Miller, P., Reuter-Lorenz, P., & Koeppe, R. A. (2001). The neural basis of task-switching in working memory: Effects of performance and aging. Proceedings of the National Academy of Sciences, 98, 2095–2100.

    Article  Google Scholar 

  21. Smith, E. E., & Van Snellenberg, J. X. (2011). Capacity and processing deficits in working memory in schizophrenia. Schizophrenia Bulletin, 37, 228.

    Google Scholar 

  22. Todd, J. J., & Marois, R. (2004). Capacity limit of visual short-term memory in human posterior parietal cortex. Nature, 428, 751–754. doi:10.1038/nature02466

    PubMed  Article  Google Scholar 

  23. Todd, J. J., & Marois, R. (2005). Posterior parietal cortex activity predicts individual differences in visual short-term memory capacity. Cognitive, Affective, & Behavioral Neuroscience, 5, 144–155. doi:10.3758/CABN.5.2.144

    Article  Google Scholar 

  24. Unsworth, N., & Engle, R. W. (2007). The nature of individual differences in working memory capacity: Active maintenance in primary memory and controlled search from secondary memory. Psychological Review, 114, 104–132. doi:10.1037/0033-295X.114.1.104

    PubMed  Article  Google Scholar 

  25. Unsworth, N., Heitz, R. P., Schrock, J. C., & Engle, R. W. (2005). An automated version of the operation span task. Behavior Research Methods, 37, 498–505. doi:10.3758/BF03192720

    PubMed  Article  Google Scholar 

  26. Van Snellenberg, J. X. (2012). An investigation of the neural correlates of working memory in healthy individuals and individuals with schizophrenia. PhD dissertation, Columbia University. Retrieved from http://hdl.handle.net/10022/AC:P:13157

  27. Van Snellenberg, J. X., Girgis, R. R., Read, C., Thompson, J. L., Weber, J., Wager, T. D., … Smith, E. E. (2013). Individuals with schizophrenia fail to show normative inverted-U activation in response to fine-grained working memory load manipulation [Abstract]. Schizophrenia Bulletin, 39, S251–S252.

  28. Van Snellenberg, J. X., Slifstein, M., Read, C., Weber, J., Thompson, J. L., Wager, T. D., … Smith, E. E. (2013). Dynamic shifts in brain network activation during working memory task performance. Manuscript submitted for publication.

  29. Van Snellenberg, J. X., Wager, T. D., Abi-Dargham, A., Urban, N., & Smith, E. E. (2010). Parametric variation in working memory demand in patients with schizophrenia: A behavioral and neuroimaging pilot study [Abstract]. Biological Psychiatry, 67, 158S.

    Google Scholar 

  30. Vogel, E. K., & Machizawa, M. G. (2004). Neural activity predicts individual differences in visual working memory capacity. Nature, 428, 748–751. doi:10.1038/nature02447

    PubMed  Article  Google Scholar 

  31. Xu, Y., & Chun, M. M. (2006). Dissociable neural mechanisms supporting visual short-term memory for objects. Nature, 440, 91–95. doi:10.1038/nature04262

    PubMed  Article  Google Scholar 

Download references

Author note

E.E.S. (deceased August 17, 2012) was heavily involved throughout the preliminary and intermediate phases of the study reported in this article. He saw early versions of the analyses presented here, but passed away before the maximum likelihood models were fully developed. However, he had seen and approved of earlier analyses that broadly parallel those presented here. This work was supported by NIMH Grant No. 5P50 MH086404. The authors thank Melanie Pincus for her assistance in setting up the study protocol, and Debbie Fraser, Mona Griffin, and Serena di Stefani for their assistance in running participants.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Jared X. Van Snellenberg.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Van Snellenberg, J.X., Conway, A.R.A., Spicer, J. et al. Capacity estimates in working memory: Reliability and interrelationships among tasks. Cogn Affect Behav Neurosci 14, 106–116 (2014). https://doi.org/10.3758/s13415-013-0235-x

Download citation

Keywords

  • Working memory
  • Short-term memory
  • Cognitive control