Beyond “Treatment Versus Control”: How Bayesian Analysis Makes Factorial Experiments Feasible in Education Research

Beyond “Treatment Versus Control”: How Bayesian Analysis Makes Factorial Experiments Feasible in Education Research

Published: Jan 10, 2019
Publisher: Evaluation Review (online ahead of print)
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Associated Project

In the School Choice Era, Making Shopping for Schools Easier

Time frame: 2015-2018

Prepared for:

U.S. Department of Education, Institute of Education Sciences

The Walton Family Foundation

Authors

Daniel Kassler

Mariel Finucane

Background

Researchers often wish to test a large set of related interventions or approaches to implementation. A factorial experiment accomplishes this by examining not only basic treatment–control comparisons but also the effects of multiple implementation “factors” such as different dosages or implementation strategies and the interactions between these factor levels. However, traditional methods of statistical inference may require prohibitively large sample sizes to perform complex factorial experiments.

Objectives

We present a Bayesian approach to factorial design. Through the use of hierarchical priors and partial pooling, we show how Bayesian analysis substantially increases the precision of estimates in complex experiments with many factors and factor levels, while controlling the risk of false positives from multiple comparisons.

Research Design

Using an experiment we performed for the U.S. Department of Education as a motivating example, we perform power calculations for both classical and Bayesian methods. We repeatedly simulate factorial experiments with a variety of sample sizes and numbers of treatment arms to estimate the minimum detectable effect (MDE) for each combination.

Results

The Bayesian approach yields substantially lower MDEs when compared with classical methods for complex factorial experiments. For example, to test 72 treatment arms (five factors with two or three levels each), a classical experiment requires nearly twice the sample size as a Bayesian experiment to obtain a given MDE.

Conclusions

Bayesian methods are a valuable tool for researchers interested in studying complex interventions. They make factorial experiments with many treatment arms vastly more feasible.

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