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Confidence intervals for an effect size measure based on the Mann–Whitney statistic. Part 1: general issues and tail‐area‐based methods
Author(s) -
Newcombe Robert G.
Publication year - 2005
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.2323
Subject(s) - mathematics , confidence interval , statistics , statistic , mann–whitney u test , measure (data warehouse) , generalization , sample size determination , test statistic , gaussian , discretization , u statistic , random variable , statistical hypothesis testing , mathematical analysis , computer science , physics , mean squared error , minimum variance unbiased estimator , quantum mechanics , database
For two random variables X and Y , θ =Pr[ Y > X ] + ½Pr[ Y = X ] is advocated as a general measure of effect size to characterize the degree of separation of their distributions. It is estimated by U / mn , a generalization of the Mann–Whitney U statistic, derived by dividing U by the product of the two sample sizes. It is equivalent to the area under the receiver operating characteristic curve. It is readily visualized in terms of two Gaussian distributions with appropriately separated peaks. The effect of discretization of a continuous variable is explored. Tail‐area‐based confidence interval methods are developed which can be applied to very small samples or extreme outcomes. Copyright © 2005 John Wiley & Sons, Ltd.