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Expressions for the exact power of th«?two-sample Mann-Whitney Wilcoxon U test procedure against alternatives of exponential and rectangular populations have been derived. Several examples for total sample sizes of 11 and 15 have been compared with Mood'a median test. Mood » s test is more powerful than the U test in all instances in which the number of observations from the null population exceeds the number from the alternative population. The converse is true when the number of observations from the null population is less than the number from the alternative. Expressions for the asymptotic efficiency of the Mann-Whitney-Wilcoxon Ü test relative to Mood's and Massey's tests and the like-lihood ratio test have been derived for exponential populations. The asymptotic efficiency of the U test relative to the likelihood ratio test is zero. Mood's and Massey's test procedures for two samples have been extended to the case of discriminating among c populations on the basis of c ordered samples. Expressions for the exact power have been derived for Mood's test with exponential and rectangular popu-lations and for Massey's test with exponential populations. With exponential translation alternatives,the tests are biased. The exact null distributions of goodness of fit tests for one-way and two-way contingency tables indicate that even for samples as small as ten, the exact distribution is closely approximated; by a chi-square distribution with the appropriate degrees of freedom. ■ ' i iA •--> '■■■--v. {j —:xa