Non parametric combination methodology for comparing multiple samples under heteroscedasticity

Abstract.: Comparing heteroscedastic samples is a common statistical task across various fields. However, assuming equal error variances may not always be straightforward, leading to significant real-world implications. While parametric tests have been extensively studied, the assumption of normality and variance homogeneity can be unrealistic, especially in scenarios with small sample sizes. Recently, four parametric bootstrap test procedures were introduced to assess treatment homogeneity in a one-way design characterized by unequal variances. This article introduces a permutation-based approach exploiting the non parametric combination (NPC) methodology. We conduct an extensive simulation study focusing on critical scenarios characterized by small and unbalanced sample sizes and extend it to a multivariate framework. In particular, we evaluate various data distributions, including normal and several non normal and asymmetric distributions. The application of the NPC methodology demonstrates advantages across different scenarios. Moreover, it appears to be suitable for application in situations characterized by high dimensionality, even with small sample sizes, which are common in real-world applications.