Comparison of the student two-sample test and the Wilcoxon-Mann-Whitney test for normal distributions with unequal variances
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Abstract
The two-sample problem is one of the important problems examined in the theory of testing hypotheses. Stated briefly, the problem is to test whether the distribution functions F(t) and G(t) of two random variables may be considered identical.
The type of test used depends on the alternative hypothesis considered. Two of the most popular two-sample tests, Student's t and the Wilcoxon-Mann-Whitney test, are used with the alternative hypothesis that the two distributions differ in the location parameter. This alternative implies equal variances for the two distributions.
In this dissertation, the properties of the two tests are investigated for two normal distributions with unequal variances. F(t) is assumed to have mean zero and standard deviation one, and G(t) is assumed to have mean theta (>0) and standard deviation sigma(.5< sigma < 2). A sample of size m is taken from F(t) and a sample of size n from G(t). Asymptomatic power functions are calculated from an Edgeworth expansion using the first four moments. The results of these calculations are checked with an experimental analysis based on 4000 replications for m + n = 8; 2000 replications for m + n = 16; and 1000 replications for m + n = 32. In addition, exact power functions are calculated for the Mann-Whitney test for m + n = 8. All calculations are compared with the asymptotoc analyses performed by Wetherill and van der Vaart for similar problems [TRUNCATED]
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Thesis (Ph.D.)--Boston University
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