Propensity Scores

  • Gideon J. MellenberghEmail author


A quasi-experiment is a study, where the researcher manipulates the IV, but participants are not randomly assigned to conditions. Therefore, it is prone to selection bias. The propensity score method reduces the systematic error of selection bias if some conditions are fulfilled. A participant’s propensity score is his or her probability of belonging to the E-condition. The propensity score method consists of two phases. First, the propensity scores are estimated from sample data. A set of auxiliary variables of the participants is measured. These variables are used to estimate participants’ propensity scores. For example, if the IV has two (E- and C-) conditions, the auxiliary variables and logistic regression are applied to estimate a participant’s probability of belonging to the E-condition. Second, effects of the IV on the DV are estimated using the propensity scores to reduce selection bias. For example, groups of participants are matched on their propensity scores, and condition effects are estimated per matched group. The propensity score method corrects for selection bias of the auxiliary variables, but not for bias of variables that are not measured.


Hidden and overt selection bias Logistic regression model Quasi-experimental study Subclassification propensity score method 


  1. Agresti, A. (2002). Categorical data analysis (2nd ed.). Hoboken, NJ: Wiley.Google Scholar
  2. Agresti, A., & Finlay, B. (2009). Statistical methods for the social sciences (4th ed.). London, UK: Pearson Prentice Hall.Google Scholar
  3. Austin, P. C. (2011a). An introduction to propensity score methods for reducing the effects of confounding in observational studies. Multivariate Behavioral Research, 46, 399–424.PubMedPubMedCentralGoogle Scholar
  4. Austin, P. C. (2011b). A tutorial and case study in propensity score analysis: An application to estimating the effect of in-hospital smoking cessation counseling on mortality. Multivariate Behavioral Research, 46, 119–151.PubMedPubMedCentralGoogle Scholar
  5. Cham, H., & West, S. G. (2016). Propensity score analysis with missing data. Psychological Methods, 21, 427–445.PubMedGoogle Scholar
  6. Cochran, W. G. (1968). The effectiveness of adjustment by subclassification in removing bias in observational studies. Biometrics, 24, 295–313.PubMedGoogle Scholar
  7. Cook, T. D., & Steiner, P. M. (2010). Case matching and the reduction of selection bias in quasi-experiments: The relative importance of pretest measures of outcome, of unreliable measurement, and of mode of data analysis. Psychological Methods, 15, 56–68.PubMedGoogle Scholar
  8. D’Agostino, R. B., Jr. (1998). Tutorial in Biostatistics: Propensity score methods for bias reduction in the comparison of a treatment to a non-randomized control group. Statistics in Medicine, 17, 2265–2281.PubMedGoogle Scholar
  9. Everitt, B. S. (1977). The analysis of contingency tables. London, UK: Chapman and Hall.Google Scholar
  10. Imai, K., & van Dijk, D. A. (2004). Causal inference with general treatment regimes: Generalizing the propensity score. Journal of the American Statistical Association, 99, 854–866.Google Scholar
  11. Luellen, J. K., Shadish, W. R., & Clark, M. H. (2005). Propensity scores: An introduction and experimental test. Evaluation Review, 29, 530–558.PubMedGoogle Scholar
  12. Rosenbaum, P. R., & Rubin, D. B. (1983). The central role of the propensity score in observational studies for causal effects. Biometrika, 70, 41–55.Google Scholar
  13. Rosenbaum, P. R., & Rubin, D. B. (1984). Reducing bias in observational studies using subclassification on the propensity score. Journal of the American Statistical Association, 79, 516–524.Google Scholar
  14. Shadish, W. R., Cook, T. D., & Campbell, D. T. (2002). Experimental and quasi-experimental designs for generalized causal inference. New York, NY: Houghton Mifflin.Google Scholar
  15. Steiner, P. M., Cook, T. D., & Shadish, W. R. (2011). On the importance of reliable covariate measurement in selection bias adjustments using propensity scores. Journal of Educational and Behavioral Statistics, 36, 213–236.Google Scholar
  16. Stuart, E. A. (2010). Matching methods for causal inference: A review and a look forward. Statistical Science, 25, 1–21.PubMedPubMedCentralGoogle Scholar
  17. Thoemmes, F. J., & Kim, E. S. (2011). A systematic review of propensity score methods in the social sciences. Multivariate Behavioral Research, 46, 90–118.PubMedGoogle Scholar
  18. van Belle, G. (2002). Statistical rules of thumb. New York, NY: Wiley.Google Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Emeritus Professor Psychological Methods, Department of PsychologyUniversity of AmsterdamAmsterdamThe Netherlands

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