Common Variance Assumption in ANOVA
The common variance assumption says that the errors have the same variance in every treatment group:
$$ \varepsilon_{ij} \overset{\text{iid}}{\sim} (0, \sigma^2). $$Equivalently, the within-group variability is assumed to be the same across treatments.
This assumption is commonly checked with a residuals-versus-fitted plot. Large funnel shapes or obvious changes in spread are warning signs.