Using Bayesian Correspondence Criteria to Compare Results From a Randomized Experiment and a Quasi-Experiment...

Area of Science:

• Statistics
• Causal Inference
• Experimental Design

Background:

• Randomized experiments provide unbiased treatment effect estimates but are not always feasible.
• Researchers seek conditions and criteria for nonrandomized experiments to approximate randomized findings.
• Previous correspondence criteria relied solely on frequentist statistics.

Purpose of the Study:

• To demonstrate how Bayesian correspondence criteria offer more nuanced and informative comparisons than frequentist approaches.
• To introduce the conceptual framework of Bayesian correspondence criteria.
• To illustrate the application of these criteria using a practical example.

Main Methods:

• Described the conceptual foundations of Bayesian correspondence criteria.
• Utilized a comparative analysis between a randomized experiment and a parallel non-equivalent comparison group experiment.
• Incorporated participant self-selection into the nonrandomized design.

Main Results:

• The quasi-experiment, using Bayesian correspondence criteria, reasonably approximated the results of the randomized experiment.
• Bayesian criteria provided more varied and informative assessments compared to traditional frequentist methods.

Conclusions:

• Bayesian correspondence criteria offer significant advantages in computation, interpretation, and policy-relevant estimation.
• The benefits of Bayesian approaches generally outweigh their disadvantages and limitations.
• These criteria enhance the validity of nonrandomized studies when randomization is not possible.