Track C – Chapter 19 Problem Set (Non-Parametric Statistics)

This problem set practices the core ideas of non-parametric statistics and chi-square tests:

When assumptions fail (non-normality, ordinal data, heavy skew, outliers)
Categorical outcomes (counts and contingency tables)

You will practice:

Chi-square goodness-of-fit (does the observed distribution match an expected one?)
Chi-square independence (are two categorical variables related?)
Mann–Whitney U (2-group alternative to the independent t-test)
Kruskal–Wallis (k-group alternative to one-way ANOVA)

Run the worked solutions

make psych-ch19-problems

Run only the tests

make test-psych-ch19-problems

Files and outputs

The solution script writes:

Synthetic datasets: data/synthetic/
Summaries + plots: outputs/track_c/

Exercises

Exercise 1 — Chi-square goodness-of-fit

A 4-category variable is sampled. The expected distribution is uniform, but the observed counts are biased. You should see a significant GOF test.

Exercise 2 — Chi-square independence

Two categorical variables (condition and outcome) are associated. You should see a significant chi-square test of independence and a non-trivial effect size.

Exercise 3 — Mann–Whitney U and Kruskal–Wallis

Skewed (lognormal) data are generated for groups A, B, and C. You should see:

a significant Mann–Whitney U difference between A and B
a significant Kruskal–Wallis difference across A, B, and C