## 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.

#### Prof. Thomas Lumley

Thomas Lumley is Professor of Biostatistics at the University of Auckland. He studied mathematics at Monash, applied statistics at Oxford, and biostatistics at the University of Washington. Thomas spent twelve years on the staff of the Biostatistics department at the University of Washington before moving to Auckland in 2010. His main applied research is in cardiovascular epidemiology and genomics, and his main statistical research is in analysis of complex samples and related issues in semiparametrics. He is a member of the R Core Development Team, and a Fellow of the American Statistical Association.

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Presentation slides.pdf | 1.73 MB |