In many papers that consider treatments and outcomes, I see tables (usually “table 1”) of what might be called nuisance variables (often demographics, sometimes medical conditions) with tests of significance and text such as “the groups were broadly similar, there were no significant differences on XXXXX, see Table”. So the clear goal is to show that the groups assigned to different treatments are similar.
However, this seems to me like it could be “accepting the null” and that what we should be doing (or demanding be done) is tests of equivalence.
This could apply to randomized trials or to observational studies.
Am I missing something here?