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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 Aug 16 '13 at 17:02
  • $\begingroup$ I am not understanding the linked page. Can you please explain simply ? $\endgroup$ – Cynderella Aug 16 '13 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 Aug 16 '13 at 17:30
  • $\begingroup$ What about the answers on the linked page don't you understand, @Cynderella? If this question were to stay open in its current form, you would just get more answers like those. So if you can clearly specify what you don't understand in what's been posted already, this question can stay open & you might get answers that would be useful for you; if not, this question may be closed. $\endgroup$ – gung Aug 16 '13 at 17:35
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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 Aug 17 '13 at 13:31

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