QANOVA: Quantile-based Permutation Methods For General Factorial Designs

TL;DR

QANOVA introduces permutation-based methods for robust analysis of factorial designs focusing on medians and quantiles, extending traditional mean-based approaches to handle heteroscedasticity and non-normal data.

Contribution

It develops asymptotically valid permutation procedures for quantile-based effects in factorial designs, addressing robustness and heteroscedasticity issues.

Findings

Effective control of Type I error in simulations

Robust analysis of medians and IQR in complex layouts

Application to children's height and weight data

Abstract

Population means and standard deviations are the most common estimands to quantify effects in factorial layouts. In fact, most statistical procedures in such designs are built towards inferring means or contrasts thereof. For more robust analyses, we consider the population median, the interquartile range (IQR) and more general quantile combinations as estimands in which we formulate null hypotheses and calculate compatible confidence regions. Based upon simultaneous multivariate central limit theorems and corresponding resampling results, we derive asymptotically correct procedures in general, potentially heteroscedastic, factorial designs with univariate endpoints. Special cases cover robust tests for the population median or the IQR in arbitrary crossed one-, two- and higher-way layouts with potentially heteroscedastic error distributions. In extensive simulations we analyze their small sample properties and also conduct an illustrating data analysis comparing children's height and weight from different countries.