Confidence Interval Approximation For Treatment Variance In Random Effects Models

Abstract

In a random effects model with a single factor, variation is partitioned into two as residual error variance and treatment variance. While a confidence interval can be imposed on the residual error variance, it is not possible to construct an exact confidence interval for the treatment variance. This is because the treatment variance is distributed as a linear combination of two chi-square variables, an expression which does not have a closed form. Approximate procedures have been provided in the literature. This paper proposes a new approximate procedure for the construction of a confidence interval for the treatment variance of a random effects model having a single factor. The new procedure uses the chi-square relationship between the residual error variance and its sample estimate.