Sequential confidence intervals for variance components in one-way random models

A sequential procedure is introduced to construct controlled width confidence intervals for the among groups variance component, as well as for certain ratios of variance components, in one-way random models. Width is controlled in the sense that it does not exceed a predetermined precision d. Several asymptotic results concerning the proposed procedure are given along with simulation results to assess its performance in moderate sample size situations. The proposed interval is also compared with the confidence interval based on the modified large sample method. In addition, some alternatives are suggested to accelerate the proposed procedure. An expression for the asymptotic expected sample size, which was obtained as a by-product of the sequential procedure, is used to discuss planning considerations in one-way random designs.