Introduction to Nonparametric Tests

Nonparametric tests make fewer assumptions about the distribution of the data compared to parametric tests like the t-Test. Nonparametric tests do not rely on the estimation of parameters such as the mean or the standard deviation. They are sometimes called distribution-free tests.

Nonparametric tests use Medians and Ranks, thus they are robust to outliers in the data. If, however, the data are normal and free of outliers, nonparametric tests are less powerful than normal based tests to detect a real difference when one exists.

Nonparametric tests should be used when the data are non-normal, data cannot be readily transformed to normality, and sample size is small (n < 30). If the sample sizes are large, the Central Limit Theorem says that parametric tests are robust to non-normality.

1 Sample Sign and 1 Sample Wilcoxon

2 Sample Mann-Whitney

Kruskal-Wallis and Mood’s Median Test

Kruskal-Wallis and Mood’s include a graph of Group Medians and 95% Median Confidence Intervals

Runs Test