ANOVA Assumptions
Classical ANOVA rests on three assumptions: residuals are normally distributed, group variances are equal (homoscedasticity), and observations are independent. Each assumption has a standard check, and each has a fallback when it fails.
Normality of residuals
ANOVA assumes the within-group residuals (not the raw data) are normal. Use the Shapiro-Wilk test on the residuals for small to medium samples, Anderson-Darling for emphasis on the tails, or a Q-Q plot for a visual check. Mild non-normality is not fatal, especially with balanced designs and moderate n, because the F statistic is robust. Severe non-normality calls for a transformation (Box-Cox for positive responses, arcsine-square-root for proportions) or a nonparametric alternative (Kruskal-Wallis).
Homogeneity of variances
Levene's test (Brown-Forsythe with median centring is the robust default) checks whether group variances are equal. Bartlett's test is more powerful when residuals are normal but very sensitive to non-normality, so do not use Bartlett unless you have already accepted normality. If equal-variance is rejected, use Welch's ANOVA with Games-Howell post-hoc instead of classical ANOVA with Tukey.
Independence and design
Independence is the strongest assumption. It cannot be tested from the data alone; it follows from the experimental design. Repeated measures on the same subject violate independence: use repeated-measures ANOVA or a mixed-effects model. Spatial correlation in the field violates independence: use a blocked design or fit a spatial covariance structure. If observations are clearly clustered (students within classes, plants within plots), use a linear mixed-effects model.