Nonparametric statistics
Undergraduate · Statistics
Syllabus focus
Standard syllabus · STEM / applied
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Topics typically covered
Standard syllabus
One- and two-sample methods
- Sign test and Wilcoxon signed-rank test
- Wilcoxon rank-sum (Mann–Whitney) test
- Permutation tests: principles and examples
- Bootstrap hypothesis tests (introduction)
- Rank correlation: Spearman and Kendall
K-sample and related methods
- Kruskal–Wallis test
- Friedman test for repeated measures
- Kolmogorov–Smirnov tests
- Nonparametric regression: kernel smoothing (intro)
- Runs tests and goodness-of-fit (overview)
Density and smoothing
- Empirical distribution functions
- Kernel density estimation
- Bandwidth selection (introduction)
- Comparison to parametric alternatives
STEM / applied
Applied nonparametric analysis
- Choosing parametric vs nonparametric tests
- Analyzing ordinal survey data
- Nonparametric methods in R (coin, wilcox.test)
- Case studies with heavy-tailed or censored data
- Reporting effect sizes for rank tests
- Robustness checks in applied research papers
Additional applied practice
- Reviewing assumptions with domain experts
- Documenting analysis choices for reproducibility
- Sensitivity analyses for key modeling decisions
- Connecting results to the original research or business question
Notes
Provides alternatives when parametric assumptions fail. Applied sections emphasize correct use in small samples and skewed data.