A Trimean and Asymmetry-Based Statistical Permutation Test for Group Comparisons

Abstract

Statistical multiple comparison tests are methods used to detect differences between several groups and to assess whether these differences are statistically significant. Typically, parametric tests like ANOVA (Analysis of Variance) or non-parametric tests like Kruskal-Wallis are employed for this purpose. In this study, we propose a new statistical permutation test based on the trimean and Bowley’s measure of asymmetry as an alternative to conventional multiple comparison tests. The proposed method is compared with ANOVA and Kruskal-Wallis tests in terms of reliability and statistical power. The analyses demonstrate that the proposed test yields statistically significant and effective results comparable to traditional methods. The findings reveal that the new test provides reliable outcomes especially for heterogeneous groups, skewed distributions, and small sample sizes. Overall, the proposed method can be considered a viable alternative in statistical analysis.