Power approximations for generalized linear models using the signal-to-noise transformation method

Abstract

ABSTRACTStatistical power is a useful measure for assessing the adequacy of an experimental design prior to data collection. In an experimental design, power is the probability of correctly concluding a factor or interaction effect in a model is significant. For a fixed model, power increases with sample size, making it a useful measure for determining the scope of a test prior to data collection. For normally distributed response variables, power calculations are widely available in experimental design software. However, many practical applications result in non-normal responses. Generalized linear models provide many useful analysis methods for non-normal responses. While statistical software routinely includes generalized linear models in analysis packages, power calculations for generalized linear models are not widely available in experimental design modules. This article proposes a signal-to-noise transformation method (SNRx) that enables generalized linear model power approximations using normal linear model power calculations, making them generally available to all practitioners. This article details the process for defining an effect size, constructing the coefficients for the test, and calculating power for the family of generalized linear models. A simulation study demonstrates that SNRx power results agree with Monte Carlo simulation.