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Statistics
Non-parametric Methods
1. Introduction to Non-parametric Statistics
2. Fundamental Concepts and Tools
3. One-Sample Tests
4. Two-Sample Tests
5. Multiple Sample Tests
6. Measures of Association
7. Non-parametric Regression and Smoothing
8. Advanced Resampling Methods
9. Survival Analysis Methods
10. Multivariate Non-parametric Methods
11. Practical Implementation
12. Advanced Topics and Extensions
6.
Measures of Association
6.1.
Rank Correlation Coefficients
6.1.1.
Spearman's Rank Correlation
6.1.1.1.
Definition and Calculation
6.1.1.2.
Relationship to Pearson Correlation
6.1.1.3.
Hypothesis Testing
6.1.1.4.
Confidence Intervals
6.1.1.5.
Handling Tied Observations
6.1.2.
Kendall's Tau
6.1.2.1.
Concordant and Discordant Pairs
6.1.2.2.
Tau-a Coefficient
6.1.2.3.
Tau-b Coefficient
6.1.2.4.
Tau-c Coefficient
6.1.2.5.
Hypothesis Testing
6.1.2.6.
Comparison with Spearman's Rho
6.1.3.
Partial Rank Correlation
6.1.3.1.
Definition and Calculation
6.2.
Association in Contingency Tables
6.2.1.
Chi-Square Test of Independence
6.2.1.1.
Test Setup and Assumptions
6.2.1.2.
Expected Frequency Calculation
6.2.1.3.
Test Statistic Construction
6.2.1.4.
Degrees of Freedom
6.2.2.
Measures of Association Strength
6.2.2.1.
Phi Coefficient
6.2.2.2.
Cramer's V
6.2.2.3.
Contingency Coefficient
6.2.3.
Ordinal Association Measures
6.2.3.1.
Goodman and Kruskal's Gamma
6.2.3.2.
Somers' d
6.2.3.3.
Kendall's Tau-b for Tables
6.2.4.
Exact Tests for Small Samples
6.2.4.1.
Fisher's Exact Test
6.2.4.2.
Freeman-Halton Extension
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5. Multiple Sample Tests
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7. Non-parametric Regression and Smoothing