Modified Graybill-Wang’s Method Confidence Intervals for the Ratio(A) of Total Variance in Two-Factor Nested Variance Components Model

The confidence intervals for σ²A/(σ²A+σ²B+σ²C) are given in various forms by many authors in two-factor nested variance components model y_ijk=μ+A_i+B_ij+C_ijk. In this model, Graybill-Wang’s (1980) method confidence intervals for σ²A/(σ²A+σ²B+σ²C) are given by an asymptotic confidence intervals. By the simulation results of this confidence coefficients are not fit exactly for the given confidence coefficients and the ranges are too wide to use for test and estimation. Thus, we would like to give one of the modified Graybill-Wang’s (1980) method confidence intervals for σ²A/(σ²A+σ²B+σ²C) in this model. And the simulation results of this modified confidence coefficients are better than those obtained by using Graybill-Wang’s (1980) method confidence coefficients, and we can use for test and estimation.