Conditions for ANOVA

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Mine Cetinkaya-Rundel

Associate Professor of the Practice, Duke University

Conditions for ANOVA

Independence:
- within groups: sampled observations must be independent
- between groups: the groups must be independent of each other (non-paired)
Approximate normality: distribution of the response variable should be nearly normal within each group
Equal variance: groups should have roughly equal variability

Independence

Within groups: Sampled observations must be independent of each other
- Random sample / assignment
- Each $n_j$ less than 10% of respective population always important, but sometimes difficult to check
Between groups: Groups must be independent of each other
- Carefully consider whether the groups may be dependent

Approximately normal

Distribution of response variable within each group should be approximately normal
Especially important when sample sizes are small
Check with visuals

Constant variance

Variability should be consistent across groups (homoscedasticity)
Especially important when sample sizes differ between groups

Let's practice!

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