Testing race models by estimating the smaller of two true mean or true median reaction times: an analysis of estimation bias.

Abstract

Researchers testing certain race models of reaction time sometimes want to estimate the smaller of the true mean (or median) reaction times in two experimental conditions. Standard practice is to collect a number of observations in each condition, and then take the smaller of the observed mean reaction times as the estimate of the smaller of the two true means. Unfortunately, this is a biased procedure, tending in the long run to underestimate the smaller of the two true means. This article presents computer simulations that investigate the size of this bias as a function of sample size, variance and shape of RT distributions, and separation between the true means of the two conditions. The amount of bias is directly related to the standard errors of the mean reaction times and inversely related to the separation between the true means. Bias can exceed 50 msec under some conditions that might be found in an actual experimental setting. Several other estimators were also examined in the simulations, and some had much smaller, though still nonnegligible, bias. By using estimators that are biased in opposite directions, it is possible to construct a conservative interval estimate of the true value being sought. Implications for testing race models are discussed.