Generalized Power Calculations for Generalized Linear Models and more

Abstract

The powercal command can compute any one of the five quantities involved in power calculations from the other four. These quantities are power, significance level, detectable difference, sample number, and the standard deviation (SD) of the influence function, which is equal to the standard error multiplied by the square root of the sample number. powercal can take arbitrary expressions (involving constants, scalars, or variables) as input and calculate the output as a new variable. The user can therefore plot input variables against output variables, and this often communicates the tradeoffs involved better than a point calculation as output by the sampsi command. General formulas are given for calculating the SD of the influence function when the detectable difference is a linear combination of link functions of subpopulation means for an outcome variable distributed according to a generalized linear model (GLM). This general case includes a very broad range of special cases, where the parameters to be estimated are differences between subpopulation proportions, arithmetic means and algebraic means, or ratios between subpopulation proportions, arithmetic means, geometric means, and odds. However, powercal is not limited to GLMs and can even be used with rank methods.