Power Simulation for Categorical Data Using the RANTBL Function

Increases in computing power have enabled Monte Carlo simulations to become increasingly common in contemporary statistical practice. Some applications require specialized statistical software while others can be implemented with general multipurpose statistical programs. Simulations of the power of statistical tests—the probability of rejecting the null hypothesis when it is false—are among those applications that can be implemented in programs like SAS. This article will demonstrate how the SAS program, and in particular, its RANTBL function can be used to simulate the power of many statistical tests for categorical data. Furthermore, the advantages and disadvantages will be described of simulating random variables from a probability distribution defined by a table of values rather than by the parameters of a probability mass function. Code will be provided for simulating the power of the Kendall Tau-b correlation coefficient. The reason for simulating the power of the Kendall statistic is that there is no widely used power/ sample size formula for accomplishing this task. Code will also be given for simulating the power of the main predictor of a logistic regression model with a single covariate. For logistic regression models there are such formulas but they do not satisfactorily take into account the impact of covariates and this can be done in the simulation approach. Finally, guidance will be offered regarding the circumstances in which using the noncentral chi-square approach to power calculations might be easier to implement than Monte Carol simulations.