A new permutation test statistic for complete block designs

TL;DR

This paper introduces a new nonparametric permutation test statistic for complete block designs, demonstrating improved accuracy and power over classical methods in certain non-Gaussian scenarios.

Contribution

It proposes a novel permutation test statistic, analyzes its properties, and shows its advantages over the classical F-statistic in non-Gaussian models.

Findings

Improved accuracy and power in non-Gaussian models

Saddlepoint approximations are effective within the interior region

Performance matches classical F-statistic in Gaussian case

Abstract

We introduce a nonparametric test statistic for the permutation test in complete block designs. We find the region in which the statistic exists and consider particularly its properties on the boundary of the region. Further, we prove that saddlepoint approximations for tail probabilities can be obtained inside the interior of this region. Finally, numerical examples are given showing that both accuracy and power of the new statistic improves on these properties of the classical $F$-statistic under some non-Gaussian models and equals them for the Gaussian case.