Matched samples are usually created to aid in the design of a study to assess the causal effect of some active treatment or intervention relative to some control treatment, based on nonrandomized observational data. Consequently, this summary of advice on matching will also offer some general suggestions for the design of such studies based on my four decades of work on them. The theoretical perspective for this advice, the “Rubin Causal Model” (RCM – Holland, 1986b; Rubin, 2006), has two essential parts: the definition of the scientific situation using “potential outcomes” to define causal effect estimands, and the formulation of a real or hypothetical “assignment mechanism”; and a third optional part, the modeling of the science to produce imputations of missing potential outcomes. Matched sampling is focused on the second step. As stated in the initial introduction, a full-length textbook from this perspective is Imbens and Rubin (2006b); and recent summaries of the RCM appear in Imbens and Rubin (2006a) and Rubin (2006a).

The first part of the RCM implies that we should always start by carefully defining all causal estimands in terms of potential outcomes, which are all values that could be observed in some real or hypothetical experiment comparing the results under an active treatment to the results under a control treatment. That is, causal effects are defined by a comparison of (a) the values that would be observed if the active treatment were applied and (b) the values that would be observed if instead the control treatment were applied.