In studies of public health, outcome measures such as the odds ratio, rate ratio, or efficacy are often estimated across strata to assess the overall effect of active treatment versus control treatment. Patients may be partitioned into such strata or blocks by experimental design, or, in non-randomized studies, patients may be partitioned into subclasses based on key covariates or estimated propensity scores to improve observed covariate balance across treatment groups. In finite samples, there exist tests and intervals for these estimands that can be more powerful than tests and intervals created with Cochran-Mantel-Haenszel or analogous procedures . The proposed methods multiply impute missing potential outcomes within the Rubin Causal Model so that estimands can be directly estimated. The assumptions underlying these typically more powerful methods are appropriate in many circumstances, especially when the strata are based on covariates highly predictive of treatment decisions and outcomes. When used to draw inferences about a population from which the patients in the study are considered a random sample, and the sample is large, these methods are extremely similar to the classical methods. The proposed approach is particularly relevant when assessing the safety of a new treatment relative to a standard one because, under typical conditions, the tests are more powerful and the intervals are shorter, thereby detecting smaller differences.