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A GENERAL UPPER BOUND ON THE VARIANCE OF THE WILCOXON‐MANN‐WHITNEY U ‐STATISTIC FOR SYMMETRIC DISTRIBUTIONS WITH SHIFT ALTERNATIVES
Author(s) -
Ury Hans K.,
Wiggins Alvin D.
Publication year - 1976
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1111/j.2044-8317.1976.tb00719.x
Subject(s) - mathematics , upper and lower bounds , statistic , statistics , sample size determination , variance (accounting) , combinatorics , wilcoxon signed rank test , mann–whitney u test , mathematical analysis , accounting , business
Using Johnson's (1975) sharp upper bound on the variance of the Wilcoxon‐Mann‐Whitney U ‐statistic for the case of continuous symmetric distributions and shift alternatives, an upper bound depending only on the sample sizes is obtained for this case. The new bound is smaller than the corresponding bound given by van Dantzig (1951) for a more general model. The decrease is smallest for equal sample sizes, in which case it ranges from 16 to 29 percent as the sample sizes increase.