Statistics

  1. Non-Parametric Statistics
    1. Introduction to Non-Parametric Methods
      1. Distribution-Free Methods
      2. When to Use Non-Parametric Tests
        1. Assumptions Violated in Parametric Tests
          1. Non-Normal Distributions
            1. Unequal Variances
              1. Small Sample Sizes
              2. Types of Data Suitable
                1. Ordinal Data
                  1. Skewed Distributions
                    1. Outlier-Prone Data
                  2. Advantages and Disadvantages
                    1. Fewer Assumptions
                      1. Lower Power
                        1. Robustness
                        2. Sign Test
                          1. Purpose
                            1. Testing Median
                              1. Paired Data Analysis
                              2. Assumptions
                                1. Minimal Requirements
                                2. Procedure
                                  1. Sign Assignment
                                    1. Binomial Distribution
                                  2. Wilcoxon Rank-Sum Test (Mann-Whitney U Test)
                                    1. Purpose
                                      1. Comparing Two Independent Groups
                                        1. Alternative to t-test
                                        2. Assumptions
                                          1. Independent Samples
                                            1. Ordinal or Continuous Data
                                            2. Procedure
                                              1. Ranking Process
                                                1. Test Statistic Calculation
                                                2. Normal Approximation
                                                  1. Large Sample Correction
                                                3. Wilcoxon Signed-Rank Test
                                                  1. Purpose
                                                    1. Paired Sample Analysis
                                                      1. Alternative to Paired t-test
                                                      2. Assumptions
                                                        1. Symmetric Differences
                                                        2. Procedure
                                                          1. Difference Calculation
                                                            1. Ranking Absolute Differences
                                                              1. Sign Assignment
                                                            2. Kruskal-Wallis Test
                                                              1. Purpose
                                                                1. Comparing Multiple Groups
                                                                  1. Alternative to One-Way ANOVA
                                                                  2. Assumptions
                                                                    1. Independent Groups
                                                                      1. Ordinal Data
                                                                      2. Procedure
                                                                        1. Overall Ranking
                                                                          1. Test Statistic Calculation
                                                                          2. Post-Hoc Comparisons
                                                                          3. Spearman's Rank Correlation Coefficient
                                                                            1. Purpose
                                                                              1. Monotonic Relationships
                                                                                1. Alternative to Pearson Correlation
                                                                                2. Calculation
                                                                                  1. Ranking Variables
                                                                                    1. Correlation of Ranks
                                                                                    2. Interpretation
                                                                                      1. Strength of Monotonic Relationship
                                                                                      2. Tied Ranks
                                                                                        1. Handling Procedures

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                                                                                    13. Experimental Design