Early and Late Buzzards: Comparing Different Approaches for Quantile-based Multiple Testing in Heavy-Tailed Wildlife Research Data

In medical, ecological and psychological research, there is a need for methods to handle multiple testing, for example to consider group comparisons with more than two groups. Typical approaches that deal with multiple testing are mean or variance based which can be less effective in the context of heavy-tailed and skewed data. Here, the median is the preferred measure of location and the interquartile range (IQR) is an adequate alternative to the variance. Therefore, it may be fruitful to formulate research questions of interest in terms of the median or the IQR. For this reason, we compare different inference approaches for two-sided and non-inferiority hypotheses formulated in terms of medians or IQRs in an extensive simulation study. We consider multiple contrast testing procedures combined with a bootstrap method as well as testing procedures with Bonferroni correction. As an example of a multiple testing problem based on heavy-tailed data we analyse an ecological trait variation in early and late breeding in a medium-sized bird of prey.