Multiple Comparison Tests: Nonparametric and Resampling Approaches

Abstract

Abstract Resampling‐based multiple comparison procedures attempt to circumvent the deleterious effects of nonnormality and/or variance heterogeneity by utilizing empirical rather than theoretical sampling distributions of test statistics. In particular, the original observed data are randomly resampled in order to build an empirical sampling distribution for the test statistic, and the observed test statistic can then be compared to quantiles in this empirical distribution to determine statistical significance or to compute confidence intervals. We present resampling test statistics that can be used to test pairwise and complex contrasts among treatment group trimmed means. Trimmed means are used to circumvent problems due to nonnormality. Moreover, the test statistic is designed to deal with variance heterogeneity. Combining robust estimators (trimmed means) with a heteroscedastic test statistic (e.g., Welch's (1938) two‐sample test) and applying a bootstrap method results in test statistics that should be robust to the combined effects of nonnormality and variance heterogeneity.