Nonparametric Statistics Course

Lesson 1 • Hypothesis Testing Review

Refreshes null and alternative hypothesis logic, p-values, and error types. Anchors nonparametric inference within the general hypothesis-testing framework.

Lesson 2 • Measurement Scales and Data Types

Covers nominal, ordinal, interval, and ratio scales and their analytic implications. Links scale type to appropriate test selection throughout the course.

Lesson 3 • Parametric Versus Nonparametric Frameworks

Contrasts distributional assumptions underlying each framework. Establishes the chapter's core rationale for choosing nonparametric methods.

Lesson 4 • Assessing Distributional Assumptions

Teaches graphical and formal tools for checking normality and homogeneity. Equips students to diagnose when nonparametric methods are warranted.

Lesson 1 • Kolmogorov-Smirnov One-Sample Test

Uses the empirical cumulative distribution function to test distributional fit. Offers a continuous-data alternative to the chi-square goodness-of-fit approach.

Lesson 2 • The Sign Test

Introduces the simplest one-sample nonparametric test based on binomial logic. Establishes the concept of testing a population median without distributional assumptions.

Lesson 3 • Selecting and Reporting One-Sample Tests

Guides decision-making among one-sample nonparametric options based on data characteristics. Covers APA-style reporting conventions for test results.

Lesson 4 • Chi-Square Goodness-of-Fit Test

Tests whether observed frequencies match a specified theoretical distribution. Connects categorical data analysis to the broader nonparametric toolkit.

Lesson 1 • Mann-Whitney U Test

Tests whether two independent samples come from the same population using rank sums. Serves as the nonparametric counterpart to the independent-samples t-test.

Lesson 2 • Effect Size and Practical Significance

Introduces rank-biserial correlation and related measures for two-sample tests. Bridges statistical significance and real-world meaningfulness of findings.

Lesson 3 • Wilcoxon Signed-Rank for Paired Data

Applies the signed-rank procedure to matched-pair or repeated-measures designs. Reinforces the distinction between independent and dependent sample structures.

Lesson 4 • Two-Sample Kolmogorov-Smirnov Test

Compares the full empirical distributions of two independent samples. Detects differences in location, spread, and shape simultaneously.

Lesson 1 • Kruskal-Wallis Test

Generalises the Mann-Whitney test to k independent groups via overall rank analysis. Serves as the nonparametric analog to one-way ANOVA.

Lesson 2 • Jonckheere-Terpstra Trend Test

Detects ordered alternatives across k independent groups when a directional trend is hypothesised. Adds directional power beyond the omnibus Kruskal-Wallis test.

Lesson 3 • Choosing Among K-Sample Procedures

Synthesises decision criteria for selecting among omnibus and trend tests. Reinforces correct test choice based on design type and research question.

Lesson 4 • Post-Hoc Pairwise Comparisons

Controls familywise error rate when following up a significant Kruskal-Wallis result. Covers Dunn's test and Bonferroni-type adjustments for multiple comparisons.

Lesson 1 • Measures for Categorical Association

Covers chi-square-based measures including Cramer's V and contingency coefficient. Extends association analysis to nominal and ordinal categorical variables.

Lesson 2 • Spearman Rank Correlation

Measures monotonic association by correlating ranks of two variables. Provides the foundational rank-based alternative to Pearson correlation.

Lesson 3 • Reporting and Visualising Associations [d9c35] Rank scatterplot construction

Covers scatterplots, rank plots, and formatted tables for association results. Ensures students communicate findings clearly and accurately.

Lesson 4 • Partial and Multiple Rank Correlations

Controls for confounding variables within rank-based correlation frameworks. Bridges nonparametric association to multivariate analytic thinking.

Lesson 1 • Two-Way Contingency Tables

Constructs and interprets r × c tables for two categorical variables. Establishes the structural foundation for all chi-square-based tests in this chapter.

Lesson 2 • Cochran's Q Test

Extends McNemar's test to three or more related binary measurements. Provides the categorical analog to the Friedman test for dichotomous outcomes.

Lesson 3 • Trend Tests for Ordinal Categories

Applies Cochran-Armitage and related tests to detect linear trend across ordered categories. Adds directional sensitivity beyond omnibus chi-square tests.

Lesson 4 • McNemar's Test for Paired Proportions

Tests change in binary outcomes for matched or repeated-measures categorical data. Complements the Wilcoxon signed-rank test for dichotomous response variables.

Lesson 1 • Bootstrap for Correlation and Regression

Bootstraps Spearman rho and regression coefficients to assess stability and uncertainty. Extends resampling methods to association and prediction contexts.

Lesson 2 • Practical Considerations in Resampling

Addresses iteration count, computational cost, and software implementation of resampling. Prepares students to apply these methods reliably in real analytic workflows.

Lesson 3 • Permutation Tests for Two Samples

Applies permutation logic to mean, median, and rank-sum differences between groups. Reinforces two-sample concepts from Chapter 3 with a resampling perspective.

Lesson 4 • Permutation Test Principles

Derives the null distribution by exhaustive or random permutation of observed data. Establishes the logical foundation for all resampling-based inference.

Lesson 1 • Kaplan-Meier Survival Analysis

Estimates survival functions from censored time-to-event data nonparametrically. Introduces the foundational tool for nonparametric analysis of survival outcomes.

Lesson 2 • Log-Rank and Related Survival Tests

Compares survival curves across groups using rank-based test statistics. Connects survival analysis to the broader nonparametric comparison framework.

Lesson 3 • Nonparametric Regression and Smoothing

Fits flexible regression curves using local polynomial and spline methods. Extends regression analysis to nonlinear relationships without functional form assumptions.

Lesson 4 • Kernel Density Estimation

Estimates continuous probability densities without assuming a parametric form. Provides flexible distributional description beyond histograms and box plots.