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Does model adequacy checking mean "Checking the normality assumption that $\epsilon_{ij}\sim \mathcal{N}(0,\sigma^2)$"? More specifically, does it mean checking that the residuals, $e_{ij}=y_{ij}−\hat{y}_{ij}$, are distributed in this way?

And is an independence check performed by showing that the mean square due to treatment and mean square due to error independently follow a chi-squared distribution according to Cochran's theorem?

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    $\begingroup$ possible duplicate of ANOVA assumption normality/normal distribution of residuals. Another near duplicate is here. $\endgroup$
    – Macro
    Commented Aug 16, 2013 at 17:02
  • $\begingroup$ I am not understanding the linked page. Can you please explain simply ? $\endgroup$
    – Cynderella
    Commented Aug 16, 2013 at 17:18
  • $\begingroup$ I think the answers on the other page are good answers that only require the minimal background necessary to understand ANOVA. If you do not have that background then that is another issue and suggests you may want to do some studying before trying to do data analysis. If, in the course of your self study, specific questions come up, I encourage you to ask them here. Cheers. $\endgroup$
    – Macro
    Commented Aug 16, 2013 at 17:30
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    $\begingroup$ Why don't you edit (change) your question to that, @Cynderella? I think that's a viable, on-topic, non-duplicate question. $\endgroup$
    – gung - Reinstate Monica
    Commented Aug 17, 2013 at 13:31
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    $\begingroup$ Checking model adequacy involves checking all the assumptions that it's feasible to check. No, the independence assumption is not checked by looking at that. $\endgroup$
    – Glen_b
    Commented Aug 18, 2013 at 5:45

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