WOWWWWWWWWWW!!!

THANKS Trinker and other guys

In all these years, this is the first time I am hearing normality test of ANOVA and t-test depends on the distribution of residuals (not sample distribution), which really shocked me. It was never recommended (or done) by any statistician or requested by any journal statisticians or reviewers to revise the statistics and redo the normality test on the error terms, not sample distribution. I have never seen any articles in which the authors have justified the usage or exclusion of an ANOVA by means of checking the normality of residuals. All of them, I mean all!, had checked sample distribution. So, an ANOVA can be applied to non-normal data, if the residuals are still normally distributed (as I remember was accentuated by Dason as the real assumption for linear regression)?

Could somebody please tell me how to find the residuals in an ANOVA output? In regression, SPSS plots the residuals so its very easy to check them, but I have never seen any option for plotting residuals in ANOVA, nor have I seen any easy articles talking about slopes in ANOVA or at least calculating them (except some tutorials about fitting slopes in ANCOVA). Is the answer again R?!

Maybe I should do it independently using a q-q plot first.

But again I don't know why I haven't been asked or corrected in any research project of mine, to actually look for normal distribution of residuals in an ANOVA rather than normal distribution of sample?

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No, not basically after an ANOVA, but it can draw a q-q plot.

Edit:

I tested it. It works quite fine. Thanks

But again why our or journals' statisticians don't know this?! Why they always perform a KS test and

**incorrectly** rely on it without noticing the

**residuals**' distribution?

Edit 2:

I guess perhaps since the KS test itself uses residuals to check the normality of sample and perhaps if it reports a non-normal

**sample** (P<0.05), it is actually implying a non-normal distribution of

**residuals**. So when a sample is normally distributed, its residuals might fit the normal curve in a way that the q-q plot gets smooth and in line. So statisticians might know and do it without wanting to confuse medical researchers by statistical details which are usually frightening to them.

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Residuals are just the actual value minus the predicted value. In the case of the t-test the predicted value is just the group mean so your residuals just reduce down to the observation minus the group mean.

Could you please kindly tell what is the predicted value in ANOVA? For example I can draw a q-q plot and check it with normal or other types of distributions, but should I check it against something else in an ANOVA? Again, is it the mean?

AFAK, in linear regression, residuals are checked in terms of being normally distributed; does it apply to ANOVA too? If so, again the normality of sample might tell the normality of residuals.