A Comparison of Estimation Methods on the Coverage Probability of Satterthwaite Confidence Intervals for Assay Precision with Unbalanced Data

Construction of closed-form confidence intervals on linear combinations of variance components were developed generically for balanced data and studied mainly for one-way and two-way random effects analysis of variance models. The Satterthwaite approach is easily generalized to unbalanced data and modified to increase its coverage probability. They are applied on measures of assay precision in combination with (restricted) maximum likelihood and Henderson III Type 1 and 3 estimation. Simulations of interlaboratory studies with unbalanced data and with small sample sizes do not show superiority of any of the possible combinations of estimation methods and Satterthwaite approaches on three measures of assay precision. However, the modified Satterthwaite approach with Henderson III Type 3 estimation is often preferred above the other combinations.