Approximate confidence intervals for the three-factor mixed model

The analysis of variance table does not always yield the appropriate error term for tests of hypotheses or confidence interval estimation. When the design is balanced, an approximation due to Satterthwaite (1946) is often employed. While this works well in many cases it does not always produce the expected results. The three-factor mixed model is a case in point. Naik (1974) proposed an interval estimation procedure for this model which is conservative. In this paper we propose two simple approximate confidence interval procedures as alternatives to both Satterthwaite's and Naik's procedures. Simulation results comparing the new procedures to the standard procedures are also reported.