Nonparametric Statistics with Applications to Science and Engineering with R, 2nd Edition

7Rank Tests

Each of us has been doing statistics all his life, in the sense that each of us has been busily reaching conclusions based on empirical observations ever since birth.

William Kruskal

All those old basic statistical procedures – the ‐test, the correlation coefficient, and the analysis of variance (ANOVA) – depend strongly on the assumption that the sampled data (or the sufficient statistics) are distributed according to a well‐known distribution, hardly the fodder for a nonparametrics textbook. However, for every classical test, there is a nonparametric alternative that does the same job with fewer assumptions made of the data. Even if the assumptions from a parametric model are modest and relatively non‐constraining, they will undoubtedly be false in the most pure sense. Life, along with your experimental data, is too complicated to fit perfectly into a framework of independently and identically distributed (i.i.d.) errors and exact normal distributions.

Mathematicians have been researching ranks and order statistics since ages ago, but it was not until the 1940s that the idea of rank tests gained prominence in the statistics literature. Hotelling and Pabst (1936) Pabst, M. wrote one of the first papers on the subject, focusing on rank correlations.

There are nonparametric procedures for one sample, for comparing two or more samples, matched samples, bivariate correlation, ...