Modified Tukey-Willams’ Confidence Intervals for Variance of A in One-Factor Components of Variance Model

The confidence intervals for σ²A are given in various forms by many authors in one-factor components-of-variance model yij=μ+Ai+eij. In this model, the simulation results of Tukey (1951) - Willams’ (1962) method confidence intervals for σ²A are not fit exactly for 100(1-a)% confidence intervals. By the simulation results, those confidence intervals are close to 100(1-a)% when J is large but this J is too large to use in the simulation as well as the ranges of width are too wide to use for estimation and test. We gave a new modified Tukey (1951) - Willams’ (1962) method confidence intervals for σ²A in one-factor components of variance model. And we showed by the simulation that our modified confidence intervals for σ²A are better than those obtained by using Tukey (1951) - Willams’ (1962) methods.