A simple nonparametric test of the difference of location of two populations

Abstract

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Šidák-type tests for the two-sample problem based on precedence and exceedance statistics

“…Reasonable values of ρ are between 0 and 1/2. For ρ = 0, it is equivalent to Šidák's statistic [3]. ρ > 0 determines a part from the ordered samples that are skipped before the threshold is specified.…”

“…However, it does not take a simpler expression. For the simplest case when ρ = 0, Šidák and Vondráček [3] presented the formula…”

“…For the V 0 -test, Šidák and Vondráček [3] presented tables up to m = 26 and n = 26 at the 5% and 1% levels of significance.…”

“…For the V 0 -test, Šidák and Vondráček [3] presented tables of approximate critical values for 5% and 1% levels of significance. As m/n → 1, the right tail probability of the test statistic is asymptotically equivalent to c + 2 2 c+1 , where c is the corresponding critical value.…”

“…The test based on the sum of these two quantities is mentioned as the earliest work of Šidák on nonparametric statistics; see [2]. The null distribution of this test statistic was studied by Šidák and Vondráček [3] and tables of critical values were produced by these authors. A slight modification of the test statistic based on the sum became popular as Tukey's Quick Test (see [4] and [5]).…”