How many participants do i need to test an interaction? Conducting an appropriate power analysis and achieving sufficient power to detect an interaction

Power analysis for first-order interactions poses two challenges: (i) Conducting an appropriate power analysis is difficult, because the required sample size depends on the shape of the interaction and the size of the simple slopes; (ii) Achieving sufficient power is difficult, because interactions tend to be modest in size. This paper consists of three parts. PART 1 addresses the first challenge. We first describe a fictional study to illustrate in a simple way how power analyses differ between interactions and main effects. Then, we introduce an intuitive taxonomy of 12 types of interactions based on the shape of the interaction (reversed, fully attenuated, partially attenuated) and the size of the simple effects (small, medium, large), and we offer mathematically-derived sample size recommendations to detect each interaction with a power of .80/.90. PART 2 addresses the second challenge. We first describe a preregistered meta-study (159 studies from recent articles in influential psychology journals) showing that the median power to detect medium-sized interactions in the literature is .18. Then, we use simulations (887M simulated datasets) to generate power curves for the 12 types of interactions, and test three strategies to increase power without increasing sample size: (i) preregistering one-tailed tests (+21% gain), (ii) using a mixed design (+75% gain), and (ii) preregistering contrast analysis for a fully attenuated interaction (+63% gain). PART 3 introduces INT×Power, a web-application that enables users to draw their interaction and determine the sample size needed to reach a power of .80 with and without using these strategies: www.intxpower.com.