Robust measures of central tendency: weighting as a possible alternative to trimming in response-time data analysis

In this paper, a problem with the robustness of measures of central tendency is analyzed in the context of studies on the speed of information processing. Within these studies, the raw data of each participant always includes a set of response times, and a single estimate of the location of individual response-time distribution has to be calculated as a measure of individual performance in a speed task. This paper consists of three sections. In the first section, the measures of central tendency are reviewed. Special attention is paid to the measures that are based on trimming, as they are commonly recommended in modern statistics as the most robust to distribution skewness and the presence of outliers. Another possible approach to obtaining a robust measure of central tendency, which is based on data weighting, is discussed; two weighted estimators of central tendency are introduced. The second section, based on the results of an empirical study and a computer simulation, demonstrates how the choice of which measure of central tendency is used for calculating individual response time in a speed task can affect conclusions on the significance of the association between response time and an external variable. In the third section, the measures of central tendency are compared in a computer simulation study, which mimics empirical response-time data. The R code for computing the measures of central tendency that are under consideration is presented in the appendix.