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Is it appropriate to use a nonparametric test with a small sample (e.g., less than 65 people) even when data are normally distributed? For example, using the Spearman correlation? Actually my data is ordinal so Spearman is OK.

Also what test should I use when I have one question with binary answers (yes and no) (e.g., 'do you own the iPhone 6?') and the other question with ordinal data? Is the Mann-Whitney U-test OK?

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  • $\begingroup$ For your 2nd question, do you consider one of the variables to be an explanatory variable & one a response variable? If so, which is which? $\endgroup$ Nov 16, 2014 at 0:28
  • $\begingroup$ If the data are ordinal rather than interval, they cannot be normal. However, you can use Spearman's rho with data that are normal, irrespective of sample size. $\endgroup$
    – Glen_b
    Nov 16, 2014 at 0:42

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It is fine to use nonparametric tests with small samples even when your data are normally distributed. If your data are truly normal, and other features of the standard tests apply (e.g., the association is linear for correlations, or there is only a simple location shift for the Mann-Whitney U-test), then you will have less power with a non-parametric test than with the parametric version.

For your correlations, the Spearman correlation is fine, especially since you say your data are ordinal. Be aware that the Pearson correlation is for linear associations, whereas the Spearman correlation is for monotonic associations.

To see if answers differ depending on whether people have an iPhone 6, the Mann-Whitney U-test is OK. Be aware that it can detect differences in the distributions other than just a location shift. (For more on that, see @Glen_b's excellent answer here: What exactly does a non-parametric test accomplish & What do you do with the results?)

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