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Power analysis for first-order interactions poses two challenges: (i) Conducting an appropriate power analysis is difficult, because the typical expected effect size of an interaction depends on its shape; (ii) Achieving sufficient power is difficult, because interactions are often modest in size. This paper consists of three parts. PART 1 addresses the first challenge. We first use a fictional study to explain the difference between power analyses for 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 slopes (median, smaller, larger), and we offer mathematically-derived sample size recommendations to detect each interaction with a power of .80/.90/.95 (for two-tailed tests in between-participant designs). 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 interactions of a typical size is .18. Then, we use simulations (≈ 900,000,000 datasets) to generate power curves for the 12 types of interactions, and test three approaches 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 (+62% gain). PART 3 introduces INT×Power, a web-application that enables users to draw their interaction and determine the sample size needed to reach the power of their choice, with the option of using/combining these approaches: www.intxpower.com.

ObjectiveScholars disagree on whether income inequality has incentive or disincentive effects. In the present research, we move beyond such debate and focus on the motivational processes that income inequality predicts. First, income inequality makes economic stratification salient, and therefore should promote perceived competitiveness. Second, competitiveness can be appraised as both a challenge and a threat, and therefore should promote both approach and avoidance motivation. MethodIn three studies (N = 2,543), U.S. residents from various ZIP codes reported the extent to which they perceived competitiveness in their town/city (Studies 1-3), as well as their economic achievement goals, achievement motives, and self-regulatory foci (Studies 2-3). ResultsLevel of local income inequality was found to be a positive predictor—via increased perceived competitiveness—of other-approach economic goals, need for achievement, and promotion focus, as well as other-avoidance economic goals, fear of failure (specifically, the shame/embarrassment component), and prevention focus. Furthermore, actual and perceived income inequality were positively correlated. ConclusionThe conceptual and empirical work herein is the first to show how the economic environment predicts individuals’ perceptions of competitiveness, influencing personal goals, motives, and orientations. It provides a more nuanced perspective on the implications of income inequality than perspectives currently available.