On the relation between the mean and the variance of a diffusion model response time distribution

Eric Jan Wagenmakers, Raoul P.P.P. Grasman, Peter C.M. Molenaar

Research output: Contribution to journalArticle

53 Scopus citations

Abstract

Almost every empirical psychological study finds that the variance of a response time (RT) distribution increases with the mean. Here we present a theoretical analysis of the nature of the relationship between RT mean and RT variance, based on the assumption that a diffusion model (e.g., Ratcliff (1978) Psychological Review, 85, 59-108; Ratcliff (2002). Psychonomic Bulletin & Review, 9, 278-291), adequately captures the shape of empirical RT distributions. We first derive closed-form analytic solutions for the mean and variance of a diffusion model RT distribution. Next, we study how systematic differences in two important diffusion model parameters simultaneously affect the mean and the variance of the diffusion model RT distribution. Within the range of plausible values for the drift rate parameter, the relation between RT mean and RT standard deviation is approximately linear. Manipulation of the boundary separation parameter also leads to an approximately linear relation between RT mean and RT standard deviation, but only for low values of the drift rate parameter.

Original languageEnglish (US)
Pages (from-to)195-204
Number of pages10
JournalJournal of Mathematical Psychology
Volume49
Issue number3
DOIs
StatePublished - Jun 1 2005

All Science Journal Classification (ASJC) codes

  • Psychology(all)
  • Applied Mathematics

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