, Volume 70, Issue 3, pp 405–425 | Cite as

Combining speed and accuracy to assess error-free cognitive processes

  • Mark E. GlickmanEmail author
  • Jeremy R. Gray
  • Carlos J. Morales


Both the speed and accuracy of responding are important measures of performance. A well-known interpretive difficulty is that participants may differ in their strategy, trading speed for accuracy, with no change in underlying competence. Another difficulty arises when participants respond slowly and inaccurately (rather than quickly but inaccurately), e.g., due to a lapse of attention. We introduce an approach that combines response time and accuracy information and addresses both situations. The modeling framework assumes two latent competing processes. The first, the error-free process, always produces correct responses. The second, the guessing process, results in all observed errors and some of the correct responses (but does so via non-specific processes, e.g., guessing in compliance with instructions to respond on each trial). Inferential summaries of the speed of the error-free process provide a principled assessment of cognitive performance reducing the influences of both fast and slow guesses. Likelihood analysis is discussed for the basic model and extensions. The approach is applied to a data set on response times in a working memory test.


competing risks reaction times speed/accuracy tradeoff time-to-event model working memory tasks 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Berger J.O., Sun D. (1993) Bayesian analysis for the poly-Weibull distribution. Journal of the American Statistical Association 88:1412–1418Google Scholar
  2. Berger J.O., Sun D. (1996) Bayesian inference for a class of poly-Weibull distributions. In: Berry D.A., Chaloner K.M., Geweke J.K. (eds) Bayesian Analysis in Statistics and Econometrics. Wiley, New York, pp 101–113Google Scholar
  3. Dempster A.P., Laird N.M., Rubin D.B. (1977) Maximum likelihood estimation from incomplete data via the EM algorithm (with discussion). Journal of the Royal Statistical Society, Series B 39:1–38Google Scholar
  4. Dickman S.J., Meyer D.E. (1988) Impulsivity and speed-accuracy tradeoffs in information processing. Journal of Personality and Social Psychology 54:274–290Google Scholar
  5. Gray J.R. (1999) A bias toward short-term thinking in threat-related negative emotional states. Personality and Social Psychology Bulletin 25:65–75Google Scholar
  6. Gray J.R. (2001) Emotional modulation of cognitive control: Approach-withdrawal states double-dissociate spatial from verbal two-back task performance. Journal of Experimental Psychology – General 130:436–452Google Scholar
  7. Heathcote A., Popiel S.J., Mewhort D.J.K. (1991) Analysis of response time distributions: An example using the Stroop task. Psychological Bulletin 109:340–347Google Scholar
  8. Lavric A., Rippon G., Gray J.R. (2003) Threat-evoked anxiety disrupts spatial working memory performance: An attentional account. Cognitive Therapy & Research 27:489–504Google Scholar
  9. Lindsey J.K., Lambert P. (1995) Dynamic generalized linear models and repeated measurements. Journal of Statistical Planning and Inference 47:129–139Google Scholar
  10. Louis T.A. (1982) Finding the observed information matrix when using the EM algorithm. Journal of the Royal Statistical Society, Series B 44:226–233Google Scholar
  11. Luce R.D. (1986) Response Times. Oxford University Press, New YorkGoogle Scholar
  12. Meng X.L., Rubin D.B. (1993) Maximum likelihood estimation via the ECM algorithm: A general framework. Biometrika 80:267–278Google Scholar
  13. Meyer D.E., Irwin D.E., Osman A.M., Kounios J. (1988) The dynamics of cognition and action: Mental processes inferred from speed-accuracy decomposition. Psychological Review 95:183–237Google Scholar
  14. Nádas A. (1970) On estimating the distribution of a random vector when only the smallest coordinate is observable. Technometrics 12:923–924Google Scholar
  15. Ollman R. (1966) Fast guesses in choice reaction time. Psychonomic Science 6:155–156Google Scholar
  16. Ratcliff R. (1979) Group RT distributions and an analysis of distribution statistics. Psychological Bulletin 86:446–461Google Scholar
  17. Ratcliff R., Rouder J. (1998) Modeling response times for two-choice decisions. Psychological Science 9:347–356Google Scholar
  18. Ratcliff R., Rouder J. (2000) A diffusion model account of masking in two-choice letter identification. Journal of Experimental Psychology: Human Perception & Performance 26:127–140Google Scholar
  19. Ratcliff R., Thapar A., McKoon G. (2001) The effects of aging on reaction time in a signal detection task. Psychology & Aging 16:323–341Google Scholar
  20. Ratcliff R., Tuerlinckx F. (2002) Estimating parameters of the diffusion model: Approaching to dealing with contaminant reaction and parameter variability. Psychonomic Bulletin & Review 9:438–481Google Scholar
  21. Ratcliff R., Van Zandt T., McKoon G. (1999) Connectionist and diffusion models of reaction time. Psychological Review 106:261–300Google Scholar
  22. Smith R.W., Kounios J., Osterhout L. (1997) The robustness and applicability of speed-accuracy decomposition, a technique for measuring partial information. Psychological Methods 2:95–120Google Scholar
  23. Sternberg S. (1969) The discovery of processing stages: Extensions of Donder’s method. Acta Psychologica 30:276–315Google Scholar
  24. Townsend J.T., Ashby F.G. (1983) Stochastic Modeling of Elementary Psychological Processes. Cambridge, LondonGoogle Scholar
  25. Wickelgren W.A. (1977) Speed-accuracy tradeoff and information processing dynamics. Acta Psychologica 41:67–85Google Scholar
  26. Yellott J.I. (1971) Correction for fast guessing and the speed-accuracy tradeoff in choice reaction time. Journal of Mathematical Psychology 8:159–199Google Scholar

Copyright information

© The Psychometric Society 2005

Authors and Affiliations

  • Mark E. Glickman
    • 1
    • 4
    Email author
  • Jeremy R. Gray
    • 2
  • Carlos J. Morales
    • 3
  1. 1.Boston University School of Public HealthUSA
  2. 2.Yale UniversityUSA
  3. 3.Worcester Polytechnic InstituteUSA
  4. 4.Center for Health Quality, Outcomes & Economics ResearchEdith Nourse Rogers Memorial Hospital (152)BedfordUSA

Personalised recommendations