Gordon, Robert D. On monotonicity of power of two-sample rank tests when testing the alternative \(G\) is stochastically larger than \(F\). (English) Zbl 0384.62031 Commun. Stat., Theory Methods A7, 535-541 (1978). 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. Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page MSC: 62G10 Nonparametric hypothesis testing PDFBibTeX XMLCite \textit{R. D. Gordon}, Commun. Stat., Theory Methods A7, 535--541 (1978; Zbl 0384.62031) Full Text: DOI References: [1] Bell C.B., Ann. Math. Statist 37 pp 133– (1966) · Zbl 0137.12802 · doi:10.1214/aoms/1177699604 [2] Gordon R.D., On rnonotonicity of power of tvo-sairtple rank tests when testing the positive shift alternative (1977) [3] Lehmann E.L., Ann. Math. Statist 22 pp 165– (1951) · Zbl 0045.40903 · doi:10.1214/aoms/1177729639 [4] Lehmann E.L., Testing Statistical Hypotheses (1959) · Zbl 0089.14102 [5] Mann H.B., Ann. Math. Statist 18 pp 50– (1947) · Zbl 0041.26103 · doi:10.1214/aoms/1177730491 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.