Factorial Designs, Model Selection, and (Incorrect) Inference in Randomized Experiments
CESifo, Munich, 2020
CESifo Working Paper No. 8137
Factorial designs are widely used for studying multiple treatments in one experiment. While “long” model t-tests provide valid inferences, “short” model t-tests (ignoring 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 all interactions, over half their results lose significance. Modest local power improvements over the long model are possible, but with lower power for most values of the interaction. If interactions are not of interest, leaving the interaction cells empty yields valid inferences and global power improvements.
Empirical and Theoretical Methods