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

Factorial designs are widely used to study multiple treatments in one experiment. Although 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-five journals (2007–2017), nineteen use the short model. After including interactions, more than 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.