Mirah
I love you
My brain feels floppy and needs a workout:
ON A TEST OF WHETHER ONE OF TWO RANDOM VARIABLES IS STOCHASTICALLYLA RGERT HAN THE OTHER BY H. B. MANN AND D. R. WHITNEY Ohio State University 1. Summary. Letx and ybe two random variableswith continuous cumulative distribution functions f and g. A statistic U depending on the relative ranks of the x's and y's is proposed for testing the hypothesisf = g. Wilcoxon proposed an equivalent test in the Biometrics Bulletin, December, 1945, but gave only a few points of the distribution of his statistic. Under the hypothesis f = g the probability of obtaining a given U in a sample of n x's and m y's is the solution of a certain recurrence relation involving n and m. Using this recurrence relation tables have been computed giving the probability of U for samples up to n = m = 8. At this point the distribution is almost normal. From the recurrence relation explicit expressions for the mean, variance, and fourth moment are obtained. The 2rth moment is shown to have a certain form which enabled us to prove that the limit distribution is normal if m, n go to infinity in any arbitrary manner. The test is shown to be consistent with respect to the class of alternatives f(x) > g(x) for every x.
ON A TEST OF WHETHER ONE OF TWO RANDOM VARIABLES IS STOCHASTICALLYLA RGERT HAN THE OTHER BY H. B. MANN AND D. R. WHITNEY Ohio State University 1. Summary. Letx and ybe two random variableswith continuous cumulative distribution functions f and g. A statistic U depending on the relative ranks of the x's and y's is proposed for testing the hypothesisf = g. Wilcoxon proposed an equivalent test in the Biometrics Bulletin, December, 1945, but gave only a few points of the distribution of his statistic. Under the hypothesis f = g the probability of obtaining a given U in a sample of n x's and m y's is the solution of a certain recurrence relation involving n and m. Using this recurrence relation tables have been computed giving the probability of U for samples up to n = m = 8. At this point the distribution is almost normal. From the recurrence relation explicit expressions for the mean, variance, and fourth moment are obtained. The 2rth moment is shown to have a certain form which enabled us to prove that the limit distribution is normal if m, n go to infinity in any arbitrary manner. The test is shown to be consistent with respect to the class of alternatives f(x) > g(x) for every x.
