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Basically, I have collected sets of data from two demographic groups. One of my demographic groups (say, Male) I have lots and lots of data (N=182). In my other demographic group (say, Female) I have a small data set (N=17). Is it OK to use the unpaired t-test, and does it ever breakdown or become not OK if one condition has very small N?

user2974849
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  • Possible near duplicates - here or here – Glen_b Dec 11 '14 at 10:08
  • Thanks, really useful! I'm not sure though on the best statistical test to use in this case. It it safer to use Welch's t-test in this situation? – user2974849 Dec 11 '14 at 10:29
  • If you're confident the population variances will be very nearly equal, the equal-variance test may tend to do slightly better on average (but there's not much loss in general). Otherwise, yes use the Welch test rather than the equal variance test. If the distribution in the small sample may not be fairly close to normal, you might consider a different test. – Glen_b Dec 11 '14 at 10:33
  • Cheers. Really helpful! – user2974849 Dec 11 '14 at 10:36

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Are you comparing M v. F here?

You can run Welch's t-test if your groups violate the assumption of equal variance.

Jon
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  • Welch test: Use the unequal variance t test, also called the Welch t test. It assumes that both groups of data are sampled from Gaussian populations, but does not assume those two populations have the same standard deviation. If I'm comparing M vs. F, can I not assume that the underlying populations follow a Gaussian distribution and have the same standard deviation? – user2974849 Dec 11 '14 at 10:11
  • Yes. Your samples might violate normality assumptions, but you can probably assume that your populations do not. – Jon Dec 11 '14 at 10:57