FAQ/DOC: hypothesis testing: what are the maintained assumptions

[josef-pkt]

hypothesis test generally specify H0 and H1.

Additionally, it would be useful if we could also point out "maintained assumptions". In general, what are the "maintained assumptions" is or might be difficult to specify, in some cases it might point to simple important restrictions for the applicability of a test.

e.g. "common variance" for t-test (when not using the unequal variance option), sphericity or similar for repeated measures or manova, or common covariance. likelihood ratio tests assume either correctly specified loglike or correctly specified up to scaling (in GLM, RLM?)

related: I added a sentence to the OLS summary() comments about the robustness of the cov_params

It should be possible to get to a more consistent doc string pattern for hypothesis test, beyond formal (numpy) docstring standard.

(I don't know how easy this will be to add to the docstrings. Often we might have not be aware of the crucial maintained assumptions.)

"maintained assumption" shouldn't be everything, it should cover the major deviations against which a test is not robust. e.g. t-test is pretty robust to distributional assumption, except for heavy tailed distributions and outliers, but it will usually not be robust to correlation across observations.