Assumptions of ANOVA

• Independence: the observations should be independent between groups and within each group.
• Normality
  • Normality assumption applies to the residuals.
    • Plot the standardized residuals to see if they are normal and centered around zero
  • If there is only few groups and each group has many values, check normality separately for each group.
  • If you have many groups (a 2x2x3 ANOVA has 12 groups) or if there are few observations per group, check them all together.
  • If you have a continuous covariate in the model as well, you CANNOT check per group.
  • For small samples, normality check is a must.
  • For large samples (usually n≥30 in each group/sample), normality is not required (central limit theorem)
• Outliers: There should be no significant outliers in any group.
• Homoscedasticity

Homoscedasticity aka are variances are equal

• Bartlett test when your data are normally distributed and sample sizes are similar,
• Levene test when data are non-normally distributed or if outliers are suspected.