Constructing a group distribution from individual distributions.

Abstract

A group distribution is a synthesis of a set of individual distributions. To be adequate, a method for creating group distributions should not introduce characteristics that are not present in the individual distributions and preserve those that are present. A method occasionally used is quantile averaging (sometimes called vincentizations), applied generally to response time distributions. However, it is shown here using quantile-quantile plots on empirical response times that this method is inadequate. As shown by Thomas and Ross (1980, Journal of Mathematical Psychology), to solve this problem, quantile averaging can be generalised using an appropriate nonlinear transformation of the data. Here we argue that the correct transformation is the log transform of response times to which the base response time has been removed. Equivalently, the geometric mean of the quantiles can be used. We first propose 4 estimates of the base response times. We next examine empirical data in a same-different task, in a redundant-attribute target detection task and in a visual search task. The results show that this approach is appropriate to construct group distributions. It can be used to aggregate distributions over multiple participants, over multiple sessions of training for a given participant, or both. (PsycINFO Database Record