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I have read that for a one way ANOVA, you should check that the model residuals are normally distributed. If the variance of each group is homogeneous then this implies that the residuals with each group being compared are also normally distributed

So let's say we are doing an ANOVA to compare the means for two groups. Data for each group resembles a skewed distribution and both have approximately equal variance but one group is positively skewed, and a the other is negatively skewed. A histogram or QQ plot of model residuals would probably indicate normality of residuals, and therefore normality of each group. However this is clearly not the case. So my question is what am I missing?

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  • $\begingroup$ Good edits to both your question and my answer, thanks. $\endgroup$
    – Glen_b
    Commented Mar 16, 2013 at 5:24
  • $\begingroup$ JVR, please visit our help page to merge your two accounts $\endgroup$
    – chl
    Commented Mar 16, 2013 at 8:23

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If you think there's any chance that the subgroups are non-normal in ways that will make the whole set of residuals look normal you should check all of the subgroups individually.

Please note that Q-Q plots don't imply normality. They can be consistent with it, or they can be inconsistent with it. But no matter how consistent with normality they are, they aren't telling you that the data are normal, indeed, that doesn't even suggest the data are normal - since the data may also be consistent with all manner of other distributions. Countless numbers of them.

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