U-statistic hierarchical clustering

A monotone invariant method of hierarchical clustering based on the Mann-Whitney U-statistic is presented. The effectiveness of the complete-link, single-link, and U-statistic methods in recovering tree structures from error perturbed data are evaluated. The U-statistic method is found to be consistently more effective in recovering the original tree structures than either the single-link or complete-link methods.     

A note on analyzing ordered alternatives

A general method of devising stepwise multiple testing procedures with fixed experimentwise error is applied to the problem of non-parametric randomized block design with ordered alternatives. In addition, the method is applied to other models with ordered alternatives.The author wishes to thank the referees for helpful suggestions.     

Distribution-free tests of stochastic dominance for small samples

One variable is said to “stochastically dominate” another if the probability of observations smaller than x is greater for one variable than the other, for all x. Inferring stochastic dominance from data samples is important for many applications of econometrics and experimental psychology, but little is known about the performance of existing inferential methods. Through simulation, we show that three of the most widely used inferential methods are inadequate for use in small samples of the size commonly encountered in many applications (up to 400 observations from each distribution). We develop two new inferential methods that perform very well in a limited, but practically important, case where the two variables are guaranteed not to be equal in distribution. We also show that extensions of these new methods, and an improved version of an existing method, perform quite well in the original, unlimited case.     

A note on moran's measure of multiple rank correlation

A measure of multiple rank correlation,T _y.12 ², is proposed for the situation with no tied observations in the variables. The measure is a weighted average of two squared Kendall taus. It is shown thatT _y.12 ² is equivalent to a statistic previously proposed by Moran and thus a new interpretation is given to Moran's statistic.The author wishes to thank Nancy Anderson, Willard Larkin, and Kent Norman for their helpful comments.     

A still further note on freeman's measure of association

This article demonstrates that Freeman's theta, a measure of association between a nominal variable and an ordinal variable, has a sampling distribution identical with the sampling distribution of Mann-Whitney'sU.     

aPRIDIT Unsupervised Classification with Asymmetric Valuation of Variable Discriminatory Worth

Abstract

Sometimes one needs to classify individuals into groups, but there is no available grouping information due to social desirability bias in reporting behavior like unethical or dishonest intentions or unlawful actions. Assessing hard-to-detect behaviors is useful; however it is methodologically difficult because people are unlikely to self-disclose bad actions. This paper presents an unsupervised classification methodology utilizing ordinal categorical predictor variables. It allows for classification, individual respondent ranking, and grouping without access to a dependent group indicator variable. The methodology also measures predictor variable worth (for determining target behavior group membership) at a predictor variable category-by-category level, so different variable response categories can contain different amounts of information about classification. It is asymmetric in that a “0” on a binary predictor does not have a similar impact toward signaling “membership in the target group” as a “1” has for signaling “membership in the non-target group.” The methodology is illustrated by identifying Spanish consumers filing fraudulent insurance claims. A second illustration classifies Portuguese high school student’s propensity to alcohol abuse. Results show the methodology is useful when it is difficult to get dependent variable information, and is useful for deciding which predictor variables and categorical response options are most important.     

A note on ROC analysis and non-parametric estimate of sensitivity

In the signal detection paradigm, the non-parametric index of sensitivity A′, as first introduced by Pollack and Norman (1964), is a popular alternative to the more traditional d′ measure of sensitivity. Smith (1995) clarified a confusion about the interpretation of A′ in relation to the area beneath proper receiver operating characteristic (ROC) curves, and provided a formula (which he called A′′) for this commonly held interpretation. However, he made an error in his calculations. Here, we rectify this error by providing the correct formula (which we call A) and compare the discrepancy that would have resulted. The corresponding measure for bias b is also provided. Since all such calculations apply to “proper” ROC curves with non-decreasing slopes, we also prove, as a separate result, the slope-monotonicity of ROC curves generated by likelihood-ratio criterion.This revised article was published online in August 2005 with the PDF paginated correctly.