I want to test the effects of different versions of treatment across multiple test groups of a given population. In order to do that, I want to randomly sample my population into, let's say, 4 groups of 2000+ subjects each.
After sampling, I generally try to evaluate each group for equivalence prior to assigning treatment and executing the test.
My question is on how to test for equivalence. In the past I have used ANOVA to evaluate differences of mean on a given attribute (for example, AGE or CHRONIC_CONDITION Y/N), or I have used t-tests to evaluate differences in attribute distribution...remember the goal here is to ensure that my groups are as "equivalent" as possible. However, I feel like there is probably a better way to measure similarity. ANOVA feels too squishy, and T-Tests become unmanageable with each version (for example, 4 groups would require 6 t-tests: AB, AC, AD, BC, BD, CD).
Are there better methods to evaluate sampled group equivalence or similarity? Bonus question: a way to do it in Python?
Note: I've searched the archive but haven't found exactly what I'm looking for. Happy to have another look if someone finds a thread.