Things which are equivalent to t-tests


Cameron Patrick


16 December, 2019

If you have a continuous measurement and two groups you’d like to compare based on that measurement, what’s the first statistical test that comes to mind? Chances are it’s the two-sample t-test, sometimes known as Student’s t-test. It’s typically the first statistical test taught in an introductory statistics course, it’s well known and understood, and it has good theoretical properties—so if a t-test answers your research question, you should probably use it. (Actually, in practice, you should probably use Welch’s t-test which doesn’t assume equal variance within groups. For the rest of the post, I’m only going to consider the equal variance case.)

Every now and again, I find a client in this situation who has done something which is… not a t-test. Here are some other ways to do the same thing which turn out to be identical to the two-sample t-test: