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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.

  • student t test is a possible option. – Dave2e Aug 04 '17 at 23:08
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    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 – Glen_b Aug 05 '17 at 03:06
  • ctd.. See [Is normality testing essentially useless?](https://stats.stackexchange.com/questions/2492/is-normality-testing-essentially-useless) -- in particular, I think [this answer](https://stats.stackexchange.com/a/2501/805) 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). – Glen_b Aug 05 '17 at 03:11
  • Thank you, Glen_b! That's what I was asking, is it out to ignore normality tests if they are unlikely to be right. – Katharine Davies Aug 05 '17 at 07:21
  • 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. – Michael R. Chernick Aug 05 '17 at 12:28
  • @Michael Your comment could be misunderstood, because tests are not parametric or nonparametric: *models* are. A parametric model would, by definition, describe all possible distributions using a finite number of real parameters. Thus, it's not enough to suppose normality is *a priori* plausible: one must also be willing to test against a finite-dimensional space of *alternative* distributions--which includes specifying precisely which distributions those might be. – whuber Aug 07 '17 at 16:27

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