Dear Professor Mean, Are there problems with a very small sample? Can the t-test be used with a sample of just three subjects? – Anxious Abdelwahab
It sounds like you got your funding from the Jack Benny Research Foundation.
You can use the t-test, but the question is should you? If you want your power to be 80%, a sample size of 3 is only capable of detecting a 2.3 standard deviation difference (paired test). The situation is even worse for the two-sample t-test. To give some perspective, most effect sizes seen in published research range from 0.2 to 0.8 standard deviations.
Unless you know for a fact that the differences you are likely to see are huge (and I mean Godzilla sized differences), then you should not run the experiment. You will almost certainly accept the null hypothesis, and you won’t know if it is because of your small sample size or the fact that there really is no difference. In other words, the experiment will not provide any useful information.
You can find an earlier version of this page on my original website.