Some notes on biasedness and unbiasedness of two-sample Kolmogorov-Smirnov test

TL;DR

This paper investigates the bias properties of the two-sample Kolmogorov-Smirnov test, identifying conditions under which it is biased or unbiased depending on sample sizes and significance levels.

Contribution

It provides new insights into the biasedness of the test and identifies specific conditions where the test remains unbiased.

Findings

Most biased distribution identified for certain significance levels

Existence of sample size and significance level combinations where the test is unbiased

Analysis of the biasedness behavior across different scenarios

Abstract

This paper deals with two-sample Kolmogorov-Smirnov test and its biasedness. This test is not unbiased in general in case of different sample sizes. We found out most biased distribution for some values of significance level $\alpha$. Moreover we discovered that there exists number of observation and significance level $\alpha$ such that this test is unbiased at level $\alpha$.