Can Nonrandomized Experiments Yield Accurate Answers? A Randomized Experiment Comparing Random and Nonrandom Assignments

Abstract A key justification for using nonrandomized experiments is that, with proper adjustment, their results can well approximate results from randomized experiments. This hypothesis has not been consistently supported by empirical studies; however, previous methods used to study this hypothesis have confounded assignment method with other study features. To avoid these confounding factors, this study randomly assigned participants to be in a randomized experiment or a nonrandomized experiment. In the randomized experiment, participants were randomly assigned to mathematics or vocabulary training; in the nonrandomized experiment, participants chose their training. The study held all other features of the experiment constant; it carefully measured pretest variables that might predict the condition that participants chose, and all participants were measured on vocabulary and mathematics outcomes. Ordinary linear regression reduced bias in the nonrandomized experiment by 84–94% using covariate-adjusted randomized results as the benchmark. Propensity score stratification, weighting, and covariance adjustment reduced bias by about 58–96%, depending on the outcome measure and adjustment method. Propensity score adjustment performed poorly when the scores were constructed from predictors of convenience (sex, age, marital status, and ethnicity) rather than from a broader set of predictors that might include these. Please see the online supplements for a Letter to the Editor. Keywords: : Nonrandomized experimentPropensity scoreRandomized experimentSelection bias