Modified Confidence Intervals Using Broemeling’s Results for the Ratio(A) of Total Variance in Two-Factor Nested Variance Components Model

The confidence intervals for σ²/(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, Broemeling found out the confidence intervals for σ²A/σ²C, the confidence intervals for σ²A/σ²B and the confidence intervals for σ²/(σ²A+σ²B+σ²C). But the simulation results of those confidence intervals for σ²/(σ²A+σ²B+σ²C) don’t fit exactly and the ranges are too wide to use for test and estimation. Thus by using those two results of confidence intervals for σ²A/σ²C and σ²A/σ²B, we found out a new modified confidence intervals for σ²/(σ²A+σ²B+σ²C). By the simulation results, we showed that our modified confidence intervals are better than those obtained by using Broemeling’s results of confidence intervals for σ²/(σ²A+σ²B+σ²C) and we can use for test and estimation.