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Behaviour of the Zaremba test for small sample sizes. (English) Zbl 0609.62068

Let \(X_ 1,X_ 2,...,X_ n\) and \(Y_ 1,Y_ 2,...,Y_ m\) be independent random samples from populations with continuous distribution functions F and G respectively. We consider the problem of testing the hypothesis H: P(X\(<Y)=1/2\) against the alternative \(K_ 1: P(X<Y)>1/2\) or \(K_ 2: P(X<Y)\neq 1/2\). S. K. Zaremba [Monatsh. Math. 66, 359–370 (1962; Zbl 0212.21901)] proposed a test for H based on the Mann- Whitney-Wilcoxon statistic. The main purpose of this paper is to compare the behaviour of the Zaremba test with some other tests (Wilcoxon, Student) for small samples under the hypothesis H and under the alternative \(K_ 1\).

MSC:

62G10 Nonparametric hypothesis testing
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