## The Annals of Mathematical Statistics

### On the Asymptotic Efficiency of Certain Nonparametric Two-Sample Tests

A. M. Mood

#### 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.

#### Article information

Source
Ann. Math. Statist., Volume 25, Number 3 (1954), 514-522.

Dates
First available in Project Euclid: 28 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177728719

Digital Object Identifier
doi:10.1214/aoms/1177728719

Mathematical Reviews number (MathSciNet)
MR63628

Zentralblatt MATH identifier
0057.11603

JSTOR