Closed-form confidence intervals for functions of the normal mean and standard deviation

Abstract

Confidence interval methods for a normal mean and standard deviation are well known and simple to apply. However, the same cannot be said for important functions of these parameters. These functions include the normal distribution percentiles, the Bland–Altman limits of agreement, the coefficient of variation and Cohen's effect size. We present a simple approach to this problem by using variance estimates recovered from confidence limits computed for the mean and standard deviation separately. All resulting confidence intervals have closed forms. Simulation results demonstrate that this approach performs very well for limits of agreement, coefficients of variation and their differences.