Group reaction time distributions and an analysis of distribution statistics.

Abstract

A method of obtaining an average reaction time distribution for a group of subjects is described. The method is particularly useful for cases in which data from many subjects are available but there are only 10-20 reaction time observations per subject cell. Essentially, reaction times for each subject are organized in ascending order, and quantiles are calculated. The quantiles are then averaged over subjects to give group quantiles (cf. Vincent learning curves). From the group quantiles, a group reaction time distribution can be constructed. It is shown that this method of averaging is exact for certain distributions (i.e., the resulting distribution belongs to the same family as the individual distributions). Furthermore, Monte Carlo studies and application of the method to the combined data from three large experiments provide evidence that properties derived from the group reaction time distribution are much the same as average properties derived from the data of individual subjects. This article also examines how to quantitatively describe the shape of reaction time distributions. The use of moments and cumulants as sources of information about distribution shape is evaluated and rejected because of extreme dependence on long, outlier reaction times. As an alternative, the use of explicit distribution functions as approximations to reaction time distributions is considered. Despite the recent popularity of reaction time research, the use of reaction time distributions for both model testing and model development has been largely ignored. This is surprising in view of the fact that properties of distributions can prove decisive in discriminating among models i(Sternberg, Note 1) and can falsify models that quite adequately describe the behavior of mean reaction time (Ratcliff & Murdock, 1976). Two methods have been used to obtain distributional or shape information. One

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