Nonparametric Statistics for Exam MAS-I

Rank-Based Tests

Nonparametric tests avoid assumptions about the underlying distribution. The Wilcoxon signed-rank test replaces the paired t-test, using ranks of absolute differences. The Mann-Whitney U test (Wilcoxon rank-sum) compares two independent samples by ranking all observations together. The Kruskal-Wallis test extends Mann-Whitney to k groups, serving as a nonparametric ANOVA. These tests are based on ranks rather than actual values, making them robust to outliers and applicable to ordinal data.

Other Nonparametric Methods

The sign test is the simplest nonparametric test for paired data, using only the signs of differences. The runs test checks for randomness in a sequence. The Spearman rank correlation measures monotonic association using ranks. The Kolmogorov-Smirnov test compares an empirical distribution to a theoretical one or two empirical distributions to each other. Kernel density estimation provides nonparametric density estimates. Exam MAS-I tests when to use nonparametric methods (small samples, non-normality, ordinal data), how to compute test statistics, and interpretation of results.