Analogs of the Wilcoxon-Mann-Whitney Test When There is a Covariate

When t-tests or Wilcoxon-Mann-Whitney tests won't do.

t-Tests are widely used by researchers to compare the average values of a numeric outcome between two groups. If there are doubts about the suitability of the data for the requirements of a t-test, most notably the distribution being non-normal, the Wilcoxon-Mann-Whitney test may be used instead. However, although often applied, both tests may be invalid when discrete and/or extremely skew data...

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...

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...

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

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-...