One-Way ANOVA, Welch's ANOVA, and Kruskal-Wallis
Checking the three assumptions of ANOVA and routing to Welch's ANOVA or Kruskal-Wallis when assumptions fail.
In this lesson you will learn
- 1Verify the three core assumptions of One-Way ANOVA: independence, residual normality, and homogeneity of variance.
- 2Select Welch's ANOVA with Games-Howell post-hoc tests when data is normal but Levene's test fails (p < .05).
- 3Select the Kruskal-Wallis H test with Dunn's post-hoc procedure when outcomes are skewed or ordinal.
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Assumption Checks & Routing to Welch or Kruskal-Wallis
This section provides the diagnostic routing protocol linking Shapiro-Wilk and Levene's tests to Fisher's ANOVA, Welch's ANOVA, or Kruskal-Wallis.
Applying standard ANOVA and Tukey HSD when group variances differ by 4-fold or when one arm is heavily skewed produces invalid p-values.
Before interpreting a multi-group comparison, check three diagnostic gates in sequence:
- Independence vs Repeated Design: If different patients are in each arm, use a between-groups test. If the same cohort is measured across 3+ timepoints, use Repeated Measures ANOVA or the non-parametric Friedman test.
- Normality Check (Shapiro-Wilk per group): If any group is strongly skewed or ordinal, route to the Kruskal-Wallis H test (reporting
Median [IQR]and Dunn's post-hoc test). - Homogeneity of Variance (Levene's test): If all groups are normal and Levene's
p > .05, use Fisher's One-Way ANOVA + Tukey HSD. If Levene'sp < .05, use Welch's ANOVA + Games-Howell.
Interactive Decision Tree: Pick the Right Statistical Test
Select your clinical objective, sampling structure, and outcome distribution
Two independent groups with normally distributed continuous data and homogeneous variances (Levene's p > .05).
Clinical Example
An emergency department study compares pain relief scores on an ordinal 1–5 Likert scale across 3 analgesic protocols (n = 35 per arm).
Interpretation: Because the outcome is an ordinal 1–5 rating, Kruskal-Wallis compares rank distributions across the three arms, and Dunn's Bonferroni-adjusted test identifies which specific pair differs.
Common Pitfall
Running Tukey HSD post-hoc comparisons after a non-parametric Kruskal-Wallis test instead of using Dunn's rank-based post-hoc test.
Included with Any Analysez AI Study Package
This deep interactive chapter (One-Way ANOVA, Welch's ANOVA, and Kruskal-Wallis) and its clinical simulation labs are unlocked for everyone who has bought any Analysez AI study package.