Confidence intervals for an effect size measure based on the Mann-Whitney statistic. Part 1: general issues and tail-area-based methods

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 sampl...

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Bibliographic Details
Published in:Statistics in medicine 2006-02, Vol.25 (4), p.543-557
Main Author: Newcombe, Robert G.
Format: Article
Language:English
Subjects:
Confidence Intervals
Craniocerebral Trauma
Data Interpretation, Statistical
Disruptive, Impulse Control, and Conduct Disorders
effect size
generalized Mann-Whitney statistic
Humans
Male
Normal distribution
Random variables
ROC Curve
Sample Size
Statistics
Statistics, Nonparametric
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Summary: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.
ISSN:0277-6715
1097-0258
DOI:10.1002/sim.2323