The Range of Confidence Intervals for σ²_A/(σ²_A + σ²_B + σ²_C) in Two-Factor Nested Variance Component Model

The two-factor nested variance component model with equal numbers in the cells given by y_ijk = μ+ A_i + B_ij +C_ijk and the confidence intervals for the ratio of total variances components, σ²_A/(σ²_A + σ²_B + σ²_C) are obtained in various forms by many authors. This article shows the probability ranges of these confidence intervals for σ²_A/(σ²_A + σ²_B + σ²_C) proved by the mathematical computation.