Multiple inference - comparing many "things" simultaneously - is common in social science. Behavioral scientists regularly compare the effects of many behavioral interventions, personality psychologists study individual differences by comparing many people, and diversity researchers compare the impact of policies on many demographic groups, to name only a few examples. Unfortunately, it is difficult to perform multiple inference correctly, and many social scientists do not. As a result, social scientists often draw unfounded or misleading conclusions from their data. This thesis addresses the problem of multiple inference, especially in social science. Chapter 1 describes several of the best-performing multiple inference techniques - including several new techniques developed in later chapters - and shows how applying them to social science datasets can lead to substantially different conclusions compared to traditional statistics. Chapters 2 and 3 describe the new multiple inference techniques introduced in Chapter 1 (inference after ranking, Bayesian ranking, and Bayesian selection) in greater detail. Importantly, we provide an open-source statistics package so that social scientists and other researchers can apply correct multiple inference techniques in a few lines of code.