On the Asymptotic Efficiency of Certain Nonparametric Two-Sample Tests

Abstract

In this paper the following asymptotic efficiencies are computed for the given two-sample tests against normal alternatives to the null hypothesis: $\text{rank test for location}\ldots\ldots\ldots\ldots 3/\pi \cong 95{\tt\%}$ $\text{median test for location}\ldots\ldots\ldots\ldots 2/\pi \cong 64{\tt\%}$ $\text{run test for location}\ldots\ldots\ldots \ldots 0$ $\text{run test for dispersion}\ldots\ldots\ldots\ldots 0$ $\text{square rank test for dispersion}\ldots\ldots\ldots\ldots 15/2\pi^2 \cong 76{\tt\%}$ Also, general expressions for means and variances of some of these test criteria are found for distributions alternative to the null hypothesis.