Simultaneous Confidence Intervals for the Linear Functions of Expected Mean Squares Used in Generalizability Theory

Abstract

This paper demonstrates a method, derived byKhuri (1981), of constructing simultaneous confidence intervals for functions of expected values of mean squares obtained when analyzing a balanced design by a random effects linear model. The method may be applied to obtain confidence intervals for the variance components and other linear functions of the expected mean squares used in generalizability theory, with probability of simultaneous coverage guaranteed to be greater than or equal to the specified confidence coefficient. The Khuri intervals are compared with the approximate intervals obtained by usingSatterthwaite’s (1941, 1946) method in conjunction with Bonferroni’s inequality.