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On monotonicity of power of two-sample rank tests when testing the alternative \(G\) is stochastically larger than \(F\). (English) Zbl 0384.62031

Summary: We consider the problem of testing the equality of two continuous distribution functions \(F\) and \(G\) against the alternative \(G\) is stochastically larger than \(F\) on the basis of two independent random samples. For testing \(H:F\equiv G\) against \(K: F(x)\ge G(x), F\not\equiv\G\), we say a test is monotone in power if its power function is a nondecreasing function of sample size for all levels of significance and all pairs of continuous distribution functions \((F,G)\) such that \(G(x)\le F(x)\) for all \(x\). Examples are given to show that the Wilcoxon, normal scores and Van der Waerden tests, or more generally tests based on two-sample rank statistics of a particular form lack the monotonicity of power property. In addition, the examples illustrate some types of undesirable power function behavior which may occur when considering the power function as a function of sample size.

MSC:

62G10 Nonparametric hypothesis testing
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References:

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