Distribution-Free Confidence Intervals for Pr(X 1 &lt; X 2 )

143

137

Several asymptotic confidence interval methods for U/mn, the Mann-Whitney U statistic divided by the product of the two sample sizes, are developed and evaluated alongside published methods. Novel methods derived from Gaussian and beta models perform well, though overall a modification of the Hanley-McNeil approach (method 5 in this evaluation) performed better and is recommended for calculating confidence intervals for U/mn for continuously distributed data.

Section: Definitions Of 8 Asymptotic Methodsmentioning

confidence: 99%

Confidence intervals for an effect size measure based on the Mann–Whitney statistic. Part 2: asymptotic methods and evaluation

Newcombe

2005

143

137

“…Also, some work has been developed in nonparametric settings. Here, we should cite Birnbaum and McCarty [12] for confidence intervals for using Kolmogorov-Smirnov statistics, Sen [13,14] and Hilgers [15] for asymptotic normality of the Studentized Wilcoxon-Mann-Whitney statistics, Cheng and Chao [16] for comparison of the various types of confidence intervals, Halperin et al [17] and Feigin et al [18] for interval estimations based on pivotal quantities. See also Hanley and McNeil [19], Mee [20] and the most recent comprehensive papers by Newcombe [21,22].…”

Section: W Zhoumentioning

confidence: 99%

“…Although others suggest several competitive estimators of 2 , (see Chapter 5 of Kotz et al [11]), there is no further development in approximating the distribution of the Studentizedˆ . See Cheng and Chao [16], Halperin et al [17].…”

mentioning

confidence: 99%

Statistical inference for P(X<Y)

Wang

2007

“…Subjects were rated for impulsivity using the Monroe dyscontrol scale (RDS) [23,24] that can range from 0 to 54. Scores for the 19 subjects were 4*, 5,8,12,14,16,18,19,23,24,28,29,35, 36*, 38*, 39*, 39, 44* and 45*. Scores for 6 subjects with history of head injury leading to loss of consciousness for over 48 hours are asterisked.…”

Section: An Examplementioning

confidence: 99%

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

Newcombe¹

2005

150

111

For two random variables X and Y, theta = Pr[Y > X] + (1/2)Pr[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.