Statistics Quest

Comparing Groups and Categorical Data

Compare several groups and analyse counts and tables.

Contingency tables, chi-square tests, one-way and two-way ANOVA, post-hoc comparisons, repeated measures foundations, and nonparametric alternatives (Mann–Whitney, Wilcoxon, Kruskal–Wallis) — and how to choose among them.

Lessons

  1. 1Contingency tablesBuild a contingency table for two categorical variables and read its joint, marginal and conditional distributions correctly.25 minFree
  2. 2Chi-square test of independenceTest whether two categorical variables are associated with the chi-square test, check its conditions, and measure the strength of the association with Cramér's V.35 minMembers
  3. 3Chi-square goodness of fitTest whether the counts of one categorical variable are consistent with a claimed distribution, including a fitted model whose parameters are estimated from the data.30 minMembers
  4. 4One-way ANOVATest whether several group means differ with one-way ANOVA, explain the F ratio as between- versus within-group variation, check its assumptions and report η² and ω².40 minMembers
  5. 5Post-hoc comparisonsExplain why many unadjusted t-tests inflate the false-positive rate, and use Tukey's HSD (and Bonferroni/Holm adjustments) to find which group means differ after an ANOVA.35 minMembers
  6. 6Two-way ANOVA foundationsSeparate the main effects of two factors from their interaction in a balanced two-way ANOVA, read an interaction plot, and know when main effects stop being meaningful.40 minMembers
  7. 7Repeated measures foundationsAnalyse a within-subject design with one-way repeated-measures ANOVA, explain why removing subject-to-subject variation increases power, and describe the sphericity assumption and its corrections.35 minMembers
  8. 8Mann–Whitney U testCompare two independent groups with the Mann–Whitney U test, compute U from ranks, and state correctly what the test does — and does not — show.35 minMembers
  9. 9Wilcoxon signed-rank testAnalyse paired data without assuming normal differences using the Wilcoxon signed-rank test, handle zeros and ties, and choose between it, the sign test and the paired t-test.30 minMembers
  10. 10Kruskal–Wallis testCompare three or more independent groups with the Kruskal–Wallis test, follow it up with adjusted pairwise rank tests, and interpret the result without over-claiming.30 minMembers
  11. 11Choosing a testChoose an appropriate test for comparing groups from the study design, the type of outcome, the number of groups and the plausibility of the assumptions — and justify the choice.30 minMembers