Using the cross-match test to appraise covariate balance in matched Pairs

Ruth Heller*, Paul R. Rosenbaum, Dylan S. Small

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Having created a tentative matched design for an observational study, diagnostic checks are performed to see whether observed covariates exhibit reasonable balance, or alternatively whether further effort is required to improve the match. We illustrate the use of the cross-match test as an aid to appraising balance on high-dimensional covariates, and we discuss its close logical connections to the techniques used to construct matched samples. In particular, in addition to a significance level, the cross-match test provides an interpretable measure of high-dimensional covariate balance, specifically a measure defined in terms of the propensity score. An example from the economics of education is used to illustrate. In the example, imbalances in an initial match guide the construction of a better match. The better match uses a recently proposed technique, optimal tapered matching, that leaves certain possibly innocuous covariates imbalanced in one match but not in another, and yields a test of whether the imbalances are actually innocuous.

Original languageEnglish
Pages (from-to)299-309
Number of pages11
JournalAmerican Statistician
Issue number4
StatePublished - Nov 2010
Externally publishedYes


FundersFunder number
Faculty of Industrial Engineering and Management
Technion—Israel Institute of Technology, Haifa, Israel
U.S.–Israel Binational Science Foundation
National Science FoundationBSF 2008049
Henry and Marilyn Taub FoundationSES-0961971, SES-0849370


    • Multivariate matching
    • Observational study
    • Propensity score
    • Seemingly innocuous confounding
    • Tapered matching


    Dive into the research topics of 'Using the cross-match test to appraise covariate balance in matched Pairs'. Together they form a unique fingerprint.

    Cite this