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Do we assume that the population distributions are normal, or that the sample distributions are normal, or that the sampling distribution is normal? If the latter, what do we mean by sampling distribution in this context?

Why do we need to assume this?

Does the normality of these things entail or suggest the normality of others?

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  • $\begingroup$ The distribution of residuals. See en.wikipedia.org/wiki/Anova#Assumptions_of_ANOVA and stats.stackexchange.com/questions/6350/… $\endgroup$
    – nico
    Commented Jul 25, 2014 at 9:28
  • $\begingroup$ @nico Although you are correct, your reply is far too restrictive. The need for assumptions depends on how ANOVA will be used and for many purposes it suffices that the sampling distributions of the means depart not too badly from Normality. Note that further on in the Wikipedia article you reference it flatly states "there are no necessary assumptions for ANOVA in its full generality." $\endgroup$
    – whuber ♦
    Commented Jul 25, 2014 at 13:36
  • $\begingroup$ User1205901 you ask several questions here and answers to them all can be found elsewhere on our site. Among many others, please see stats.stackexchange.com/questions/78466 for sampling distributions and stats.stackexchange.com/questions/16381 for linear regression assumptions (ANOVA is a form of linear regression). $\endgroup$
    – whuber ♦
    Commented Jul 25, 2014 at 13:37

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