Robust Confidence Interval for a Ratio of Standard Deviations

Abstract

Comparing variability of test scores across alternate forms, test conditions, or subpopulations is a fundamental problem in psychometrics. A confidence interval for a ratio of standard deviations is proposed that performs as well as the classic method with normal distributions and performs dramatically better with nonnormal distributions. A simple and accurate sample size planning formula is proposed for estimating a ratio of standard deviations with desired confidence and precision.