Non-parametric Methods

  1. One-Sample Tests
    1. Tests for Location
      1. Sign Test
        1. Hypotheses for Population Median
          1. Test Statistic Construction
            1. Exact p-value Calculation
              1. Normal Approximation
                1. Confidence Interval for Median
                  1. Power and Sample Size
                  2. Wilcoxon Signed-Rank Test
                    1. Assumptions and Hypotheses
                      1. Signed Rank Calculation
                        1. Test Statistic Construction
                          1. Exact Distribution
                            1. Normal Approximation
                              1. Confidence Interval Construction
                                1. Handling Zero Differences
                                  1. Handling Tied Observations
                                2. Tests for Goodness-of-Fit
                                  1. Chi-Square Goodness-of-Fit Test
                                    1. Test Setup and Assumptions
                                      1. Expected Frequency Calculation
                                        1. Test Statistic Construction
                                          1. Degrees of Freedom
                                            1. Critical Values and p-values
                                              1. Limitations and Alternatives
                                              2. Kolmogorov-Smirnov One-Sample Test
                                                1. Test Setup and Assumptions
                                                  1. Test Statistic Calculation
                                                    1. Critical Values
                                                      1. p-value Computation
                                                        1. Lilliefors Test for Normality
                                                          1. Anderson-Darling Test
                                                            1. Cramér-von Mises Test
                                                          2. Tests for Randomness
                                                            1. Runs Test
                                                              1. Definition of Runs
                                                                1. Test Setup and Hypotheses
                                                                  1. Test Statistic Construction
                                                                    1. Exact Distribution
                                                                      1. Normal Approximation
                                                                        1. Applications to Time Series
                                                                        2. Turning Points Test
                                                                          1. Definition and Setup
                                                                            1. Test Statistic Construction

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                                                                        2. Fundamental Concepts and Tools

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                                                                        4. Two-Sample Tests