# t-test using a sample less than 30 [duplicate]

When I do the two tailed t-test using a sample less than 30, can I use this result? This is because I do also still see the t-test table which has degrees of freedom far less than 30. How further small can the sample size be?

• Is that 30 per group, or 30 total? If the latter, are the groups 15-15? – JAD Jul 27 '17 at 8:29
• One case I have two groups 11-14, the other case I simply have one group to test with sample size less than 30. – Eric Jul 27 '17 at 8:31
• The smallest possible sample sizes for a two-sample equal variance t-test is 1 and 2 (while many packages implement their tests in a way that precludes one of the samples having only one observation there's no good reason that they should do so -- R will do an equal variance t-test with 1 and 2 though, try: t.test(1,c(3.5,3.2),var.equal=TRUE)). Details are covered here. – Glen_b -Reinstate Monica Jul 27 '17 at 9:25
• If you're not fixed on it having to specifically be a t-test, even smaller samples are possible. For example, one can adapt the discussion in whuber's answer here (also see here and comments here) to a two sample test of means with $n_1=n_2=1$ – Glen_b -Reinstate Monica Jul 27 '17 at 9:36
• It's not usually advisable to use such small $n$ but it's not an issue with the test "working" -- it still works as it should. But if your power is very low at anticipated effect sizes, then even if you reject you may have trouble convincing people it's not just a type I error. [Note also that it's not practical to use rank based tests down to sample sizes as low as the $t$ can be used for -- e.g. if you try to do a two-tailed Wilcoxon-Mann-Whitney for n's of 1 & 2 the lowest achievable significance level is $\frac{_2}{^3}$]. – Glen_b -Reinstate Monica Jul 27 '17 at 9:43