ANOVA (Analysis of Variance) Simulation

Understanding ANOVA

Analysis of Variance (ANOVA) tests whether there are statistically significant differences between the means of three or more independent groups.

Key Concepts:

• Null Hypothesis (H₀): All group means are equal (μ₁ = μ₂ = μ₃ = ...)
• Alternative Hypothesis (H₁): At least one group mean differs from the others
• F-statistic: Ratio of between-group variance to within-group variance
• Effect Size (η²): Proportion of total variance explained by group differences
• Post-hoc tests: If ANOVA is significant, these identify which specific groups differ

ANOVA Assumptions:

• Independence of observations
• Normality within each group
• Homogeneity of variance (equal variances across groups)

When to Use ANOVA:

• Comparing means of 3+ groups (for 2 groups, use t-test)
• One continuous dependent variable
• One categorical independent variable (factor)