7 - Nonparametric Methods

Summary

This chapter covers nonparametric tests of two classes: goodness of fit tests and rank based hypothesis tests. The former begins with the little-used likelihood ratio test for a multinomial distribution that is more general than its widely used, but less accurate, asymptotic approximation, Pearson’s chi square test. The Kolmogorov-Smirnov and Anderson-Darling tests for data distribution assessment are then reviewed, and the Jarque-Bera test for Gaussianity is summarized. Rank-based nonparametric tests are typically permutation tests applied to the data ranks. Such tests are less sensitive to distributional assumptions, and work better than parametric tests with small samples. The sign, signed rank and rank sum tests are described and illustrated. The Ansari-Bradley test for dispersion is summarized. A pair of nonparametric tests for correlation, the Spearman rank correlation and Kendall’s tau, are then described. The chapter closes with a description of meta-analysis that allows p-values from separate studies to be combined.