RANK ORDER PROBABILITIES: TWO-SAMPLE NORMAL SHIFT ALTERNATIVES.
MINNESOTA UNIV MINNEAPOLIS DEPT OF STATISTICS
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Let Z denote a random vector of mn zeros and ones where the i-th component of Z is 01 if the i-th order statistic of the independent random variables X sub 1,...,X sub m, Y sub 1,...,Y sub n is an XY and the XsYs are normally distributed with mean OD and variance 1. Values of the probability of the rank order z, are tabulated to 9 decimal places for all z for 1nm7 and n1, m8112 D0.21,1.5,2,3. These tables are used to find the exact power of the Wilcoxon, c sub 1, median, and Kolmogorov-Smirnov two-sample tests for location against the normal shift alternative for sample sizes 1nm7 and for one-sided and two-sided tests at nominal levels of significance .25, .10, .05, .025, .01, .005. Selected power and efficiency comparisons are made among these tests and with the two-sample Students t-test. The most powerful rank test is also considered. Sequential two-sample rank tests based on the likelihood ratios of the probabilities of the vector z and of the rank sum are described, extending the work of Wilcoxon et al Biometrics, 1963 to the case of the normal shift hypothesis. Tables are presented which facilitate the use of these tests, and values of the OC and ASN functions are given. A multiple decision or ranking procedure is considered for selecting a subset of s populations from among k normal populations with common variance o2 such that at least c of the t populations with largest means are among the s populations selected. Author
- Statistics and Probability