Modified Confidence Intervals by Tukey-Williams Method and Optimal Conditions in Two-Factor Nested Variance Components Model

The confidence intervals for sigma_A^2 / sigma_C^2 in the two-factor nested variance components model with equal numbers in the cells are given in various forms by many authors. In this model, the confidence intervals by using Tukey(1951)-Williams (1962) method for sigma_A^2 / sigma_C^2 are the given by an asymptotic confidence intervals. By the simulations results of this confidence coefficients are not fit exactly for the given confidence coefficient. Thus, we would like to give one of the optimal conditions and we can find out the more improved confidence intervals by the optimal conditions for sigma_A^2 / sigma_C^2 for the given confidence intervals by using Tukey(1951)-Williams (1962) method in two-factor nested variance components model.