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My data set is very small (n=16) which according to a Shapiro-wilk test is normally distributed (p=0.82), despite the histogram looking questionable. When I split the data into my two categories there are only 8 samples in each group. In this case should a parametric test like an lm be used to analyse the difference between the 2 groups or should a nonparametric test like a Wilcox-mann-whitney U be used?

Sorry if this is a repost.

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  • $\begingroup$ student t test is a possible option. $\endgroup$
    – Dave2e
    Commented Aug 4, 2017 at 23:08
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    $\begingroup$ Your opening sentence is incorrect. Failure to reject normality (especially at small sample size!) doesn't mean you do have normality, it means you didn't detect non-normality. Since power won't be great at low sample size, failure to detect it doesn't necessarily tell you much; it's a bit like tossing a coin twice, getting two tails and concluding that with this coin you're safe from the possibility of heads. On the other hand at large sample sizes, you can reject even fairly trivial deviations from normality, ones that won't affect your inference at all. ...ctd $\endgroup$
    – Glen_b
    Commented Aug 5, 2017 at 3:06
  • $\begingroup$ ctd.. See Is normality testing essentially useless? -- in particular, I think this answer gets to the heart of the matter. The most important thing to start with is a clear statement of what you really wanted to find out (ignoring any issues of sample size or distribution shape to start with). $\endgroup$
    – Glen_b
    Commented Aug 5, 2017 at 3:11
  • $\begingroup$ Thank you, Glen_b! That's what I was asking, is it out to ignore normality tests if they are unlikely to be right. $\endgroup$
    – Katharine Davies
    Commented Aug 5, 2017 at 7:21
  • $\begingroup$ Glen_b addressed the appropriateness of concluding normality with a small sample size. But suppose you have a good apriori reason to believe normality. Then a nonparametric test would have less power and would not overcome the small sample size issue. $\endgroup$
    – Michael R. Chernick
    Commented Aug 5, 2017 at 12:28

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