Nonparametric Methods

Basic Concepts

A brief introduction to what we're going to discuss in later chapters.

Fundamentals of Nonparametric Methods

Some basic tools such as the permutation test and the binomial test. We also introduce order statistics and ranks, which will come in handy in later chapters.

Location Inference for Single Samples

The Wilcoxin signed rank test explained.

Other Single Sample Inferences

Explore whether the sample is consistent with a specified distribution at the population level. Kolmogorov's test, Lilliefors test and Shapiro-Wilk test are introduced, as well as tests for runs or trends.

Methods for Paired Samples

An obvious extension of the one-sample procedures.

Two Independent Samples

With two independent samples, we may ask about the centrality of the population distribution and see if there's a shift. Wilcoxon-Mann-Whitney is here!

Basic Tests for Three or More Samples

Nonparametric analogues of the one-way classification ANOVA and the simplest two-way classifications, namely the Kruskal-Wallis test, the Jonckheere-Terpstra test, and the Friedman test.

Correlation and Concordance

Measures for the strength of relationships between variables (two or more). The Spearman rank correlation coefficient, Kendall's tau and Kendall's W are introduced.

Categorical Data

Dealing with contingency tables. Fisher's exact test comes back, together with Chi-squared test and likelihood-ratio test. We also talk about testing goodness-of-fit.

Bootstrap

The procedure and applications of the nonparametric bootstrap.