What is model adequacy checking in anova?

Cynderella

New Member
In anova, we assume that the random error term $$\epsilon_{ij}$$ is independent and identically distributed with mean $$0$$ and variance $$\sigma^2$$

How can I check the normality assumption and independence assumption?

Does model adequacy checking mean "Checking the normality assumption that $$\epsilon_{ij}\sim N(0,\sigma^2)$$"?More specifically checking the residual, $$e_{ij}=y_{ij}-\hat y_{ij}$$?And is independence check performed by showing Mean square due to treatment and Mean square due to error independently follow chi-square distribution according to Cochran theorem ?