A $k$-Sample Slippage Test for an Extreme Population

Abstract

A test is proposed for deciding whether one of $k$ populations has slipped to the right of the rest, under the null hypothesis that all populations are continuous and identical. The procedure is to pick the sample with the largest observation, and to count the number of observations $r$ in it which exceed all observations of all other samples. If all samples are of the same size $n, n$ large, the probability of getting $r$ or more such observations, when the null hypothesis is true, is about $k^{1-r}$. Some remarks are made about kinds of errors in testing hypothesies.