Asymptotic power calculations: description, examples, computer code

Abstract

This paper describes two asymptotic methods for sample size and power calculation for hypothesis testing. Both methods assume that the distribution of the likelihood ratio is approximately distributed as a central chi(2) distribution under the null hypothesis and as a non-central chi(2) under the alternative hypothesis. The approximation to the non-centrality parameter differs between the methods. It is shown how these methods can be automatically extended from constraints setting parameters to constant values to constraints positing equality of parameters. Two very simple examples are presented; one demonstrates that the information method can produce arbitrarily incorrect results. Four more comprehensive examples are then discussed. In addition to demonstrating the wide range of applicability of these methods, the examples illustrate techniques that may be used in cases in which there is insufficient initial information available to perform a realistic calculation. The availability of a computer implementation of these methods in S-plus is announced, as are routines for computing the cumulative distribution function of the non-central chi(2) and its inverse.