A Multisample Rank Statistic for Testing the Equality of Distributions

Nonparametric methods are essential in statistical analysis when the underlying distribution of the data cannot be reasonably assumed to follow a specific parametric form. In particular, nonparametric one-way analysis of variance is widely used across scientific fields due to its robustness and minimal distributional assumptions. This paper introduces a novel multisample nonparametric statistic for assessing the equality of distributions across multiple independent samples. To be precise, the statistic of Murakami et al. (2024) is extended to a multisample comparison. To evaluate its performance, we conduct extensive Monte Carlo simulations under various continuous distribution scenarios. The results, supported by both simulation studies and real data applications, demonstrate that the proposed statistic performs competitively compared to existing omnibus statistics and offers distinct advantages in certain settings.