Comparing Two Independent Groups Via a Quantile Generalization of the Wilcoxon-Mann-Whitney Test

Comparing Two Independent Groups Via a Quantile Generalization of the Wilcoxon-Mann-Whitney Test

An improved ranked set two-sample Mann-Whitney-Wilcoxon test

The authors present an improved ranked set two-sample Mann-Whitney-Wilcoxon test for a location shift between samples from two distributions F and G. They define a function that measures the amount of information provided by each observation from the two samples, given the actual joint ranking of all the units in a set. This information function is used as a guide for improving the Pitman effic...

Optimizing Classi er Performance Via the Wilcoxon-Mann-Whitney Statistic

Cross entropy and mean squared error are typical cost functions used to optimize classi er performance. The goal of the optimization is usually to achieve the best correct classi cation rate. However, for many two-class real-world problems, the ROC curve is a more meaningful performance measure. We demonstrate that minimizing cross entropy or mean squared error does not necessarily maximize the...

Combinatorics, Computer Algebra and Wilcoxon-mann-whitney Test

We show the combinatorics behind the Wilcoxon-Mann-Whitney two-sample test. This yields new combinatorial proofs of recurrences for its null distribution given recently by Brus and Chang, as well as new recurrences. It is shown how to convert these recurrences into generating functions. These generating functions are used to obtain closed expressions for the null distribution when one of the sa...

Exploiting the Link Between the Wilcoxon-Mann-Whitney Test and a Simple Odds Statistic

Over a quarter-century ago, Alan Agresti (Biometrics, 1980) proposed using the generalized odds ratio (genOR) to summarize the association between two ordinal variables. Unfortunately, genOR is still largely unknown, even though it is elegantly straightforward and fills key voids in the working statistician’s toolbox. An extension of it, a statistic we are calling “WMWodds,” is an ideal effect-...