Non-parametric Methods

  1. Two-Sample Tests
    1. Independent Samples
      1. Wilcoxon Rank-Sum Test
        1. Test Setup and Assumptions
          1. Ranking Procedure
            1. Test Statistic Construction
              1. Exact Distribution
                1. Normal Approximation
                  1. Confidence Interval for Location Difference
                    1. Handling Tied Observations
                    2. Mann-Whitney U Test
                      1. Relationship to Wilcoxon Test
                        1. U Statistic Construction
                          1. Equivalence of Test Statistics
                          2. Kolmogorov-Smirnov Two-Sample Test
                            1. Test Setup and Assumptions
                              1. Test Statistic Construction
                                1. Critical Values
                                  1. p-value Calculation
                                    1. One-sided vs. Two-sided Tests
                                    2. Median Test
                                      1. Test Setup Using Contingency Table
                                        1. Test Statistic Construction
                                          1. Chi-square Approximation
                                            1. Limitations and Alternatives
                                            2. Wald-Wolfowitz Runs Test
                                              1. Test for Identical Distributions
                                                1. Test Statistic Construction
                                              2. Dependent Samples
                                                1. Sign Test for Paired Data
                                                  1. Test Setup and Assumptions
                                                    1. Test Statistic Construction
                                                      1. Exact p-value Calculation
                                                        1. Normal Approximation
                                                        2. Wilcoxon Signed-Rank Test for Pairs
                                                          1. Application to Paired Differences
                                                            1. Test Statistic Construction
                                                              1. Confidence Interval Construction
                                                              2. McNemar's Test
                                                                1. Test for Paired Proportions
                                                                  1. Test Setup Using 2×2 Table
                                                                    1. Test Statistic Construction
                                                                      1. Continuity Correction
                                                                        1. Exact Test for Small Samples

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                                                                    3. One-Sample Tests

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                                                                    5. Multiple Sample Tests