Checking the Assumptions for T-tests?

Question

I am in the process of checking the assumptions of some data in order to perform a T-Test and had a few questions about how they should be set up. I was able to find the assumptions for a T-test here.

I have one independent variable with two nominal groups, A and B and one dependent variable that is an interval variable as rank does matter.

For the last three assumptions, i.e. Assumption of no outliers, Assumption of Normality, and Assumption of Homogeneity of Variances, should I test each assumption against each independent's group of values? As in test group A for outliers and normality, as well as test group B's outliers and normality?

The reason for my question is because the Normality Assumption is the only one that requires the user to test each independent's group. You cannot check for Homogeneity of Variances of one group as that produces an error.

Should I check group A only for outlier's and normality or should I only test the values of the dependent variable?

Answer 1

I have always seen outliers examined in each group separately. I don't have a citation for this, but it seems to make sense. For instance if the two groups had very different means, then something that was an outlier on one group might not be an outlier on the combined groups and this seems to me to violate the assumptions.

However, rather than formal tests of outliers (which are tricky) I would look at graphs of the two variables. If I had a lot of doubts, I would explore a nonparametric test or a permutation test.

Answer 2

Like one commenter said, it pays to perform regression. There, it is clear that the assumptions relate to errors, and you verify them using residuals. The models are the same so the same assumptions apply.

With an independent samples t-test, this is equivalent to verifying the assumptions by group, or better yet, demeaning the outcome variable using the group means (outcome variable - group mean) then testing all the demeaned data as a whole. By testing, I mean graphical evaluation, same as Peter Flom.

The larger your sample size, the less normality of the demeaned data is relevant for the hypothesis test of the mean difference that normality may affect (CLT). Also, the larger your sample size, the less a single outlying data point can influence your findings, unless you have a cluster or more of outlying data points.

As for homogeneity of variance, don't test it. With the t-test, you already have Welch's adjustment, so just do Welch by default. Unless you have serious sample size imbalance by group coupled with extreme non-normality at small sample size, then you'll be fine using Welch's adjustment. Don't test because we know the tests have their flaws. Additionally, if you choose whether to do t or Welch based on testing homogeneity of variance, the end result on average has problems. Zimmerman's A note on preliminary tests of equality of variances is a good reference on this (https://onlinelibrary.wiley.com/doi/abs/10.1348/000711004849222).