P.Mean: T-test with 3 treatment values and 2 controls (created 2008-10-14).

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I received a question about how to run a t-test when one group has 3 observations and the other group has 2 observations? It turns out that you use the same formula/program that you would use with 30 observations in one group and 20 observations in the other group. There are two things, however, that you need to watch out for.

First, the assumptions of normality and equal variances are far more critical with a very small sample size, but you don't have enough data to really check these assumptions effectively. So you need to make a big leap of faith.

Second, the power is extremely poor with such a limited sample size. You need to have a gargantuan difference between the two groups. The largest value in one group would have to be much smaller than the smallest value in the other group. If there is even the slightest bit of overlap between the two groups, then the t-test (or any other test for that matter) will have no hope for achieving statistical significance.

If you are trying to demonstrate that the two groups are equivalent, then you might as well stop now. Any confidence interval that you produce will be too wide to allow any claims of equivalence.

But if you still want to run a t-test for a very small sample size like this, go ahead and do it. Just be sure you are honest with your readers about the serious limitations.

This work is licensed under a Creative Commons Attribution 3.0 United States License. This page was written by Steve Simon and was last modified on 2010-04-01. Need more information? I have a page with general help resources. You can also browse for pages similar to this one at Category: Small sample size issues.