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Propensity Scores

A propensity score is the probability that an individual received a particular treatment, given a set of researcher-identified variables related to self-selected treatment participation. The use of propensity scores is grounded in the logic of the counterfactual: To know the true effect of a treatment on the outcome, a researcher must also know what the outcome would have been had participants not received treatment. However, this is not something researchers will ever know. Accounting for the propensity for treatment, given a set of variables related to self-selection into that treatment, can increase precision in estimating the effect of the treatment on the outcome.

In the context of educational and social sciences research, treatment typically refers to a course, intervention, or program. Propensity scores are used in observational or quasi-experimental studies, in which researchers are unable to randomly assign participants to conditions, making accurate evidence-based causal claims challenging. Instead, students typically self-select or choose to participate in educational programs. Propensity scores provide a means of accounting for variables related to self-selection bias, allowing the researcher to create matched, or balanced, treatment and comparison groups. Propensity scores can also be used to adjust, or assign weight to, outcome analyses to account for self-selection bias, thereby mimicking a randomized controlled study.

Example

As an illustration, perhaps education researchers are interested in implementing a new afterschool program and then comparing the academic performance of students in the program with the performance of students who did not attend it. Because students are not randomly assigned to the new afterschool program (i.e., the treatment), the researchers are conducting an observational or quasi-experimental research study. In order to make claims about the impact of the new afterschool program, educational researchers need to take into account variables related to the students’ self-selection into the program. Such variables may include the incoming interest, motivation, or prior ability of the students, and they may be related to the outcome of interest to the program (e.g., a test score). Once self-selection variables are identified, the researcher computes the probability that a given student was enrolled in the afterschool program, taking into account each student’s levels on those variables.

When the self-selection variables (i.e., the covariates) are properly identified, propensity scores can be used to control for bias related to self-selection into treatment. In the afterschool program example, propensity scores could be used to form a matched comparison group of students with similar levels of interest, motivation, and prior ability. The performance of the two matched groups can then be compared. Alternatively, researchers could compute propensity scores and use them as weights to examine differences in performance between the students who attended the program and those who did not. It is for situations such as this example that propensity scores were developed.

Calculation of Propensity Scores

There are numerous methods of estimating propensity scores; however, logistic regression is the most common. Although logistic regression is usually considered a statistical inference technique, in this case, it is used simply for the purpose of computing propensity scores. Variables related to self-selection into the program, the covariates, serve as predictors of treatment participation. From the logistic regression analysis, propensity scores are the probability that an individual participated in treatment, given the set of covariates. Individuals with the same propensity scores have similar distributions on the covariates, regardless of whether they were in the treatment group. Consequently, matching nonparticipants to participants with similar propensity scores provides a means of creating a comparison group that is balanced with the treatment group on the covariates.

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