Despite the widespread and nonsensical claim, that "logistic regression is not a regression", it constitutes one of the key regression and hypothesis testing tools used in the experimental research (like clinical trials).
Let me show you how the logistic regression (with a few extensions) can be used to test hypotheses about fractions (%) of successes, repacling the classic "test for proportions". Namely, it can replicate the results of:
- the Wald's (normal approximation) z test for 2 proportions with non-pooled standard errors (common in clinical trials) via LS-means on the prediction scale or AME (average marginal effect)
- the Rao's score (normal appr.) z test for 2 proportions with pooled standard errors (just what the
prop.test()
does in R) - the z test for multiple (2+) proportions
- ANOVA-like (joint) test for multiple caterogical predictors (n-way ANOVA). Also (n-way) ANCOVA if you employ numerical covariates.
- [the **Cochran-Mantel-Haenszel