A nonparametric test for a two-sample scale problem based on subsample medians

A nonparametric test for the two-sample scale problem is proposed by considering the subsample medians of three observations. The proposed statistic has the advantage of not requiring the two distribution functions to have a common median, but rather requiring them to have any common quantile of order [alpha],0<=[alpha]<=1 (not necessarily 1/2), which is assumed to be known. Pitman efficiency considerations indicate that the proposed test performs well relative to tests already existing in the literature for heavy tailed distributions.