Asymptotic Relative Efficiency of Mood's and Massey's Two Sample Tests Against Some Parametric Alternatives

Abstract

In [2], the exact power of Mood's and Massey's two-sample tests for discriminating between two populations was derived. Two types of alternatives were considered--change in the location of an exponential distribution and change in the location and scale of a rectangular distribution. The asymptotic relative efficiency of Mood's test based on the median against an alternative of change in location of a normal distribution was shown ([1], [8]) to be $2/\pi$. A limited comparison of powers of the tests based on the median, on the first quartile and the median and on the likelihood-ratio against the exponential alternative is given in [3]. In this paper, the asymptotic relative efficiencies of Mood's test based on the median and Massey's test based on the first quartile and the median are shown to be zero, when these tests are compared against the likelihood-ratio test appropriate for detecting a shift in location of an exponential distribution. Massey's test is found to be about three times as efficient as Mood's test, for exponential distribution. But so also is the test based on the first quartile alone. If the order of the fractile is lowered, the efficiency of the test based on it is increased. Similar comparisons are also made for the normal distribution.