ANOVA Assumptions

Statistics · Axiom Academy

Understanding the foundational requirements for valid ANOVA inference 1. Independence of Observations The fundamental assumption: Each observation must be independent of all other observations. This means that the value of one observation should not influence or be influenced by any other observation. Avoid repeated measures from same subjects Check for temporal or spatial clustering Consider experimental design carefully 2. Normality Within Each Group The normality assumption: Within each group, the dependent variable should follow a normal distribution. More precisely, the residuals (deviations from group means) should be normally distributed. Q-Q plots (quantile-quantile plots) Shapiro-Wilk test (formal test) Equal variance assumption: The variance of the dependent variable should be approximately equal across all groups. This is also called "homoscedasticity." Levene's test (robust to non-normality) Bartlett's test (assumes normality) Residual plots (look for funnel shapes) Rule of thumb: largest variance should be less than 4x smallest variance 4. Checking Assumptions with Residual Plots Residual analysis: The most practical way to check assumptions is through examining residual plots. Residuals are the differences between observed values and their group means. Residuals vs. Fitted Values (check for equal spread) Q-Q Plot of Residuals (check normality) Residuals vs. Group (check variance equality) Residuals vs. Order (check independence over time)

This is the written version of the interactive lesson above. See the full Statistics course.