## Why there's no such thing as an ordinal test

A lot of health data is ordinal: even if the measurement process is interval or ratio level, a 10mmHg blood pressure difference doesn't mean the same thing at different starting points. Tests that only used the ordinal structure of the data would seem to be valuable. However, nearly all rank tests turn out to have the 'rock-paper-scissors' property: they need not be transitive. I discovered this while trying to work out what the Wilcoxon rank-sum test really meant, in order to explain it in an introductory statistics course. I will explain why non-transitivity happens, and why it is just an extreme case of a more general problem. The fact that rank tests compare distributions without relying on interval-level or ratio-level scores looks like a feature. I will argue that it is a bug, especially in health research. This talk will assume no more than simple undergraduate statistics, although there will be cameo appearances by bits of higher mathematics.