17.5 Nonparametric Tests (Pro Only)

Paired-Sample Wilcoxon Signed Rank Test

The Paired-Sample Wilcoxon Signed Rank Test is a nonparametric alternative method to the paired sample t-test. Paired samples are presumed to be drawn, at random, from a single population. Differences between paired samples are assumed to be distributed symmetrically about the median.

Paired Sample Sign Test

The Paired-Sample Sign Test is a simple, nonparametric alternative to the paired sample t-test. It tests tallies (+) and (-) differences between paired samples and tests whether the two are present in equal numbers. While not considered a statistically powerful test, the only requirement that need to be met is that the differences between paired samples are independent such that differences exist within the same continuous population and measurements exist along some scale by which they can be judged to be greater, equal to, or less than each other.

Mann-Whitney Test

The Mann-Whitney Test (M-W) is a useful nonparametric alternative to the two-sample t-test. Because the M-W test is nearly as powerful as a two-sample t-test yet nonparametric, it is considered as a more useful test in certain scenarios.

The M-W test frequently produces a similar result to the two-sample Kolmogorov-Smirnov test but the two tests show differences in sensitivities to changes in location and distribution

Two-Sample Kolmogorov-Smirnov Test

The Two-Sample Kolmogorov-Smirnov test (K-S) is a nonparametric alternative to the two-sample t-test. In general, the K-S test uses the unsigned differences between two samples to determine whether the two are drawn from the same continuous distribution.

The K-S test and the Mann-Whitney Test (M-W) can be used in similar analyses. Whereas, K-S is less powerful, it is considered more comprehensive because it tests both shape and location of distributions

Kruskal-Wallis ANOVA

Kruskal-Wallis (K-W) ANOVA is a nonparametric alternative to the one-way analysis of variance (ANOVA) test. The K-W ANOVA uses rank sums to determine whether three or more independent samples are taken from the same distribution (when comparing two samples, the Mann-Whitney test is more often used). When K-W test results are significant, post-hoc tests between pairs of samples can be used to determine which pairs show significant differences.

Mood's Median Test

The Mood's Median Test is a nonparametric alternative to one-way analysis of variance (ANOVA). Mood's Median tests the likelihood that the median values of two samples are equal and, therefore, are drawn from the same population. Mood's Median only accounts for the number of variates that are larger or smaller than the median value and does not take into account their actual differences from the median. Hence, it is regarded as a less powerful alternative to the Kruskal-Wallis ANOVA. Nevertheless, it is more robust in cases where the dataset contains extreme outliers.