Percentile rank pooling: A simple nonparametric method for comparing group reaction time distributions with few trials
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Percentile rank pooling: A simple nonparametric method for comparing group reaction time distributions with few trials Jeff Miller 1
# The Psychonomic Society, Inc. 2020
Abstract Although many studies of reaction time (RT) focus on a single measure of central tendency such as the mean RT, a more detailed picture of the underlying processes can be gained by looking at full distributions of RTs. Unfortunately, for practical reasons it is sometimes difficult to obtain enough trials per participant in a condition of interest to construct such a distribution with existing methods. The purpose of this article is to propose a method of forming group RT distributions that can be used to compare the full distributions of RTs even in an infrequent condition with only a few trials per participant. In brief, the percentile ranks of each participant’s infrequent-condition RTs are scored relative to a larger pool including that participant’s RTs in other conditions, and a histogram of the infrequent-condition’s percentile ranks is then formed by pooling across participants. The resulting histogram of infrequent-condition RT ranks shows where the RTs in that condition tend to fall relative to the other conditions, and this histogram can reveal systematic patterns in the infrequent-condition’s RT distribution. To illustrate the method, I present histograms of the ranks of infrequent error RTs (~ 5% of trials), ranked relative to correct responses, in real data sets from Simon and lexical decision tasks. Keywords Group reaction time distributions . Infrequent conditions
Psychologists have increasingly turned to the study of the distributional properties of the reaction times (RTs) observed in cognitive tasks. A major reason for this trend is that distributional properties can provide useful information beyond what is available in mean RTs (e.g., Luce, 1986). For example, between-condition comparisons of the estimated parameters for specific RT distribution models (e.g., the ex-Gaussian) provide a more nuanced description of experimental effects than a simple comparison of mean RTs (e.g., Balota & Yap, 2011; Heathcote, Popiel, & Mewhort, 1991). Comparisons of RT distributions have also been used extensively to study the time course of experimental effects (e.g., De Jong, Liang, & Lauber, 1994; Reingold, Reichle, Glaholt, & Sheridan, 2012) and to test distributional predictions of RT models (e.g., Miller, 1982; Ratcliff & McKoon, 2008; Ruthruff, 1996). Because distributional comparisons allow a more in-depth examination of results, several techniques have been developed for the analysis of RT distributions. All of these start by * Jeff Miller [email protected] 1
Department of Psychology, University of Otago, PO Box 56, Dunedin 9054, New Zealand
estimating the simple or cumulative distributions of RTs in each single condition (e.g., Van Zandt, 2000), after which it is possible to compare conditions using delta plots (e.g., De Jong et al., 1994), quantile-quantile plots (e.g., Myerson, Adams, Hale, & Jenkins, 2003), estimated
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