Hansen, Ben. 2004. "Full Matching in an Observational Study of Coaching for the SAT." Journal of the American Statistical Association, 99:609-618.
Among matching techniques for observational studies, full matching is in principle the best, in the sense that its alignment of comparable treated and control subjects is as good as that of any alternate method, and potentially much better. This article evaluates the practical performance of full matching for the first time, modifying it in order to minimize variance as well as bias and then using it to compare coached and uncoached takers of the SAT. In this new version, with restrictions on the ratio of treated subjects to controls within matched sets, full matching makes use of many more observations than does pair matching, but achieves far closer matches than does matching with k greater than or equal to 2 controls. Prior to matching, the coached and uncoached groups are separated on the propensity score by 1.1 SDs. Full matching reduces this separation to 1% or 2% of an SD. In older literature comparing matching and regression, Cochran expressed doubts that ani method of adjustment could substantially reduce observed bias of this magnitude. To accommodate missing data, regression-based analyses by ETS researchers rejected a subset of the available sample that differed significantly from the subsample they analyzed. Full matching on the propensity score handles the same problem simply and without rejecting observations. In addition, it eases the detection and handling of nonconstancy of treatment effects, which the regression-based analyses had obscured, and it makes fuller use of covariate information. It estimates a somewhat larger effect of coaching on the math score than did ETS's methods.