# Paired t-test assumptions

I would like to perform some paired t-test by using Wilcoxon tests. I am trying to figure out which one should be the assumptions that I need to make from before. From what I found so far I need to respect the following:

• The two groups need to be independent.
• The differences between the two samples need to be normally distributed.
• The variables need to be measured at either the interval or ratio level of measurement.

My question is what exactly should I do for the two last bullets? Also, should I consider checking the constant variance? Is it also an assumption for paired t-tests?

1. If you're doing a paired t-test, then the two groups most definitely should be related, often by measuring a before and after on the same subject.

2. This would be an assumption of the paired t-test. When this assumption is violated, the Wilcoxon signed-rank test is a viable nonparametric alternative. (This isn't quite true, because of the central limit theorem, but it's close enough for now.)

3. This makes sense to me, though I am open to being wrong.

I am not sure, however, that you're using the terminology that you intend to use. The paired t-test is a one-sample test; your sample is composed of the differences between pairs (such as after minus before). I think you have two samples that you want to compare, not paired samples. Please leave a comment with your setup.

• My scenario is that I have two population performing a test, for example, a bachelor and master students playing a game and I want to figure out whether their time and performance is significantly different. When I perform t-test it shows that their mean is significantly different but I guess also I need to have some assumptions like the one I mentioned before I am to perform the tests. Jul 2, 2019 at 15:56
• As I suspected, you're not doing a paired test. A paired test would be something like evaluating the performance on a test of Brad, Ronald, and John before starting their master's degrees and then again after. You're doing two-sample testing. Yes, if you want to use the t-test, you should examine your data to make sure the assumptions are met. (Some have said that it's improper to examine your data, since that examination could be wrong, though relying on prior knowledge or intuition instead of examining the data doesn't seem practical.)
– Dave
Jul 2, 2019 at 16:43
• Then what exactly the constant variance means in that case. Should both population have similar variance? Jul 3, 2019 at 8:56
• @JoseRamon Both populations should have the same variance. The Welch test, which is the default "t-test" in R software, accounts for unequal variance.
– Dave
Jul 3, 2019 at 12:34