Overview

This session introduces Analysis of Variance (ANOVA) as a principled way to compare locations (means) across two or more groups, building on hypothesis testing, p-values, and multiple-comparisons control. We cover Student’s and Welch’s t-tests, the Mann–Whitney–Wilcoxon test, Fisher’s one-way ANOVA, Welch’s ANOVA (unequal variances), and the Kruskal–Wallis test (rank-based alternative), with emphasis on assumptions, diagnostics, and effect sizes.

Because we discuss both two-sample and multi-sample scenarios, this class bridges t-tests and ANOVA within a unified inferential framework.

Today’s objectives

The objectives of this class are to:

• Review core concepts: hypotheses, errors (Type I/II), p-values, and power
  
• Understand when to use Student’s t-test, Welch’s t-test, or the Mann–Whitney–Wilcoxon test for two groups
  
• Understand when to use Fisher’s ANOVA, Welch’s ANOVA, or the Kruskal–Wallis test for multiple groups
  
• Assess key assumptions: normality, variance homogeneity, and independence
  
• Apply multiple testing corrections using Bonferroni and Dunn–Šidák methods
  
• Perform and report analyses in Python clearly and effectively

Slides

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