Comparison of the power between the Mann Whitney and the Kolmogorov Smirnov Tests and the Chi Square and the Fisher Exact tests on discrete distributions
D'Agostino, Ralph B.
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For the two independent sample problem, when discrete distributions are involved, bow well do the continuous designed tests (the unconditional Mann-Whitney-Wilcoxon test and the unconditional Kolmogorov-Smirnov test) compare in terms of power with the discrete designed tests (the Fisher Exact test and the Chi-Square)? This is the question which the pre ceding attempts to answer. For certain situations some definite results are forthcoming. We have definite results appearing when very small sample situations are being investigated. And also, when structural similarities can be displayed, we have definite results appearing in some large sample situations. From these definite results we indicate some reasonable generalizations which may later prove to be valid in more general situations. Below we shall summarize the different situations which are investigated. The definite results obtained from these situations shall be stated and also stated' shall be t he generalizations which are felt to be indicated by the proven results. Before actually comparing the tests, we have to clarify the notation to be used, the formats (procedures) of the tests and the concepts of "a more powerful" test. The notation and formats of the tests is explained in Sections I.1 to I.4.3. Most of the material presented in these sections is standard. In Section I .5 the concepts of "a more powerful" test are presented. Three "Kinds" of "a more powerful" test are defined. Power Kind 1 refers to the usual concept of a more powerful test. That is test W is more powerful (Kind 1) than test T if the following are satisfied. [TRUNCATED]
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