Factorial Designs, Model Selection, and (Incorrect) Inference in Randomized Experiments

Factorial designs are widely used to study multiple treatments in one experiment. While t-tests using a fully-saturated “long” model provide valid inferences, “short” model t-tests (that ignore interactions) yield higher power if interactions are zero, but incorrect inferences otherwise. Of 27 factorial experiments published in top-5 journals (2007–2017), 19 use the short model. After including interactions, over half of their results lose significance. Based on recent econometric advances, we show that power improvements over the long model are possible. We provide practical guidance for the design of new experiments and the analysis of completed experiments.