The Probability Range of Confidence Intervals for σ²_A/σ²_C in Two-Factor Nested Variance Component Model

In the two-factor nested variance component model with equal numbers in the cells is given by y_ijk = μ+ A_i + B_ij +C_ijk , the confidence intervals of the variance component of σ ²_A/σ²_C were obtained in various forms by many authors. This article shows the probability ranges of these confidence intervals for σ²_A/σ²_C proved by the mathematical computation.