A test statistic with a ranking method based on the Jeffreys divergence measure

Nonparametric two-sample tests are important statistical procedures in many scientific fields. The test statistic has been derived from the Kullback-Liebler divergence between two empirical distribution functions. This study modifies a nonparametric two-sample test statistic using a ranking method. The modified test statistic is shown to be based on the Jeffreys divergence measure. The exact critical value of the proposed test statistic is derived for small sample sizes. Simulations are used to investigate the power of the proposed test statistic for the location alternative and for any difference between distributions, with various population distributions, for small sample sizes.