A nonparametric multiple comparison test for differences in scale parameters

A nonparametric multiple comparison test for differences in scale parameters is suggested The asymptotic distribution of the test statistic is derived. A modification of the test when the location parameters are unknown and unequal is suggested. This modified test is not asymptotically distribution free for all underlying location-scale families; however, we give sufficient conditions on the families under which the test is asymptotically distribution free.