In sections 1.8 and 1.11 of this book, we briefly introduced methods for comparing proportions of “discrete outcomes” or “events.” In this chapter, we will expand on that discussion by introducing odds ratios and relative risk. We will limit the discussion to cases where the outcome is binary. We will also show how one can compare proportions (or odds ratios) of events between two or more groups while adjusting for a set of strata (discrete variables) and/or continuous variables which, if ignored, could influence or bias the inference made about the event proportions or odds ratios. This will be accomplished by the Mantel-Haenszel procedure and logistic regression. Finally, we’ll look at paired binary measurements and discuss methods for quantifying and testing discordance and concordance among those pairs.