Summary: Observational medical studies are becoming more prominent due to interest in using data from current medical practice to help guide treatment selection. We start by reviewing why current analysis strategies for observational data tend to produce findings that fail to replicate. We then argue that there is a real need for simple and objective statistical strategies that yield findings more likely to be dependable. Our proposed way forward is to focus on the empirical distribution of local treatment differences, LTDs, which reveal heterogeneity in effect-sizes. The LTD is the difference in mean outcomes for treated and control patients within a cluster of patients relatively well matched on their observed pretreatment characteristics. Because we focus on only one question (comparing two alternative treatment choices for a given disease or condition) and clustering is nonparametric, our proposed approach is more simple and objective than commonly used statistical analysis strategies. By studying graphical displays of information from an LTD distribution, a doctor and patient not only can see a full picture of current treatment outcomes but also can make a truly well-informed, individualized treatment choice.