A Rank Test on Equality of Population Medians

The Kruskal-Wallis test is a non-parametric test for the equality of K population medians. The test statistic involved is a measure of the overall closeness of the K average ranks in the individual samples to the average rank in the combined sample. The resulting acceptance region of the test however may not be the smallest region with the required acceptance probability under the null hypothesis. Presently an alternative acceptance region is constructed such that it has the smallest size, apart from having the required acceptance probability. Compared to the Kruskal-Wallis test, the alternative test is found to have larger average power computed from the powers along the evenly chosen directions of deviation of the medians