Normality

... a racist as Darwin today, that person would be in an extreme, but it was normal at that time. Within every movement of people there is a range of normality that most people stay within. That is what Darwin did as far as racism is concerned, though he challenged society with his science.

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and before applying T-test or ANOVA, it is indeed good to test for normality. And if you have a non normal distribution you will have to use non parametric tests like U-test

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... sample size. They look “OK” to my eye—but I warn you: what I am willing to accept and what your prof is willing to accept for deviations from normality may not be the same. You’d better take your lead from your prof, not from me, though you can have my opinion, for what it’s worth. I notice ...

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... assume an underlying normal distribution with random error. Chi-squared and t-statistics, in particular, can be strongly biased by departures from normality. F-tests, on the other hand, are fairly robust toward “deviant” behavior. Non-parametric tests like the Wilcoxan don’t assume a normal distribution ...

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... there is no assumption about the nature of the underlying distribution, non-parametric statistics can be used in cases where the assumption of normality doesn’t hold. When the assumption of normality holds, both U and t should lead to similar conclusions. As with testing for the equality of ...

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