Power Analysis for Regression Coefficients: The Role of Multiple Predictors and Power to Detect all Coefficients Simultaneously

Abstract

Many tools exist for power analyses focused on R 2 Model (the variance explained by all the predictors together) but tools for estimating power for coefficients often require complicated inputs that are neither intuitive nor simple to estimate. Further compounding this issue is the recognition that power to detect effects for all predictors in a model tends to be substantially lower than power to detect individual effects. In short, most available power analysis approaches ignore the probability of detecting all effects and focus on probability of detecting individual effects. The consequences of this are designs that are underpowered to detect effects. The present work presents tools for addressing these issues via simulation approaches provided by the pwr2ppl package (Aberson, 2019) and an associated Shiny app.