# Independent samples t-test with unequal sample sizes

I have two independent groups: from one I have drawn a sample of size less than 30 due to its small population, while the second group has sample size 100.

Is it appropriate to use an independent samples t-test in this case?

• Do you want to compare the means of the two groups? If so, yes a t-test is appropriate, notwithstanding the unequal sample sizes. Oct 3, 2015 at 13:27
– Dave
May 13, 2020 at 2:50

The two-sample t-test makes no assumption about equal sample sizes. However, if you have $$2n$$ observations, the best allocation of them is into two groups, each with $$n$$ observations. This is part of the experimental design; if you already have your observations, then you don’t get to allocate them into groups. (They either got the coronavirus miracle drug or a placebo, for instance, but if you’re designing the study, the best allocation of 10 patients would be into 5 treatment subjects and 5 placebo subjects, at least as far as statistical power goes.)