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Current statistical theory provides little useful guidance about how to reduce the sensitivity of analyses of reaction time data to aberrant observations and violations of statistical assumptions, either because robust methods, which are very inviting, are insufficiently understood, or because aspects of the data are not characterized fully enough to permit devising theoretically justifiable analyses. In this report we suggest an empirical approach, in which one applies the same criteria to the problem of selecting a statistical method as those that one uses to select among alternative experimental procedures. We define six such criteria, and then describe five tests based on a set of about 36,000 observations in which we compare ordinary least-squares multiple regression as a way of characterizing the data with Hubers robust iteratively reweighted least-squares method. Results favor the robust method. Results favor the robust method. Keywords: Psychology, Perception, Visual, Statistics, Mathematics, Reaction time, Memory.