Permutation Tests with Transformations Enhance Power in Percentile Comparisons.

Percentiles are widely used in scientific research; for example, in geology to predict petroleum reserves and in traffic engineering to analyze travel times. However, statistical inference for percentiles or their differences has received far less attention than inference for means. This study aims to improve the power of hypothesis tests for comparing percentile differences between two independent samples using permutation tests with transformations. Motivated by prior work showing that transformations can enhance permutation tests for means and medians, we extend this idea to percentiles. Simulation studies based on Beta-distributed data demonstrate that the Box–Cox transformation improves power compared with untransformed methods. We conclude by discussing the strengths and limitations of the proposed approach.