### 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 language | English (US) |
---|---|

Pages (from-to) | 195-204 |

Number of pages | 10 |

Journal | Journal of Mathematical Psychology |

Volume | 49 |

Issue number | 3 |

DOIs | |

State | Published - Jun 1 2005 |

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### All Science Journal Classification (ASJC) codes

- Psychology(all)
- Applied Mathematics

### Cite this

*Journal of Mathematical Psychology*,

*49*(3), 195-204. https://doi.org/10.1016/j.jmp.2005.02.003

}

*Journal of Mathematical Psychology*, vol. 49, no. 3, pp. 195-204. https://doi.org/10.1016/j.jmp.2005.02.003

**On the relation between the mean and the variance of a diffusion model response time distribution.** / Wagenmakers, Eric Jan; Grasman, Raoul P.P.P.; Molenaar, Peter.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On the relation between the mean and the variance of a diffusion model response time distribution

AU - Wagenmakers, Eric Jan

AU - Grasman, Raoul P.P.P.

AU - Molenaar, Peter

PY - 2005/6/1

Y1 - 2005/6/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=17844402252&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=17844402252&partnerID=8YFLogxK

U2 - 10.1016/j.jmp.2005.02.003

DO - 10.1016/j.jmp.2005.02.003

M3 - Article

VL - 49

SP - 195

EP - 204

JO - Journal of Mathematical Psychology

JF - Journal of Mathematical Psychology

SN - 0022-2496

IS - 3

ER -