Motivation
NXV began with protecting human rights in hospitals, though it is a general test for any type of work and I am not promoting it using any claim to medical expertise. I was working on reducing the use of restraint in care, and building two tools to help: PROD-ALERT, a measure, and the L-test, which looks for patterns in data. When I looked for the statistical test those tools needed, the standard one wasn't precise for the data they would see, so I thought about it and developed NXV.
The standard test is Mann–Whitney U, the usual way to compare two groups when the data are ranks or scores rather than measurements you can average. NXV is for rating scales and counts over small samples. Mann–Whitney U's exact p-values assume that no two people share a score. That holds for continuous measurements, like blood pressure or temperature or height, which can have decimal points, but clinical rating scales have only a handful of points, so in many studies or audits, tied scores are guaranteed.
Take the Clinical Global Impression scale (CGI), which scores a patient from 1 to 7. Rate eight people on it. There are only seven possible scores, so at least two of the eight must share one: a tied score is unavoidable before anyone has been assessed. This is the pigeonhole principle, eight pigeons and seven holes. Rate twenty people with CGI and at least fourteen of them must share their score with someone else in the sample, and that breaks Mann–Whitney U's exact p-values, and would have blurred PROD-ALERT and L-test a little in my case, and, in general, makes Mann–Whitney U results a bit unreliable in this important field.
The usual fixes are midranks plus a correction to a normal approximation. They are approximations, and they are weakest exactly where rating-scales might be used: small groups, coarse scales, many tied scores. The result can be a p-value on the wrong side of a decision threshold, with nothing in the output to warn you. NXV replaces the approximation with exact counting. It counts every way the scores, tied and untied, could fall between the two groups, and gives the exact probability of a result at least as extreme as yours. The method was published in Frontiers in Applied Mathematics and Statistics in January 2026. This site makes it usable without writing code, for groups of up to 20 each. The name NXV contains a joke, also. NXV is MWU (for "Mann–Whitney U"), moved on one in the alphabet: M -> N, W -> X, U -> V.