A Quick Compact Two Sample Test To Duckworth's Specifications

Abstract

A simple test for comparing two samples is proposed. If one sample contains the highest value and the other the lowest value of the two samples combined, the total of two counts is taken as the statistic. These counts are of(i) the number of individuals in the one sample above all individuals in the other, and (ii) the number of individuals in the other below all those in the one. 5%, 1% and 0.1% critical values are roughly 7, 10 and 13 respectively. Precise values for pairs of small and moderate sized samples are given, as are asymptotic critical values. Derivations are included.