| Abstract: | The fiducial approach to the two components of variance random effects model developed by Venables and James (1978) is related to the Bayesian approach of Box and Tiao (1973). The operating characteristics, under repeated sampling, of the resulting interval estimators for the “within classes” variance component are investigated, and the behaviour of the two sets of intervals is found to be very similar, the coverage frequency of 95% probability intervals being approximately 91% when the “between classes” variance component is zero but rising rapidly to 95% as the between component increases. The probability intervals are shown to be shorter on average than a comparable confidence interval based upon the within classes sum of squares, and to be robust against nonnormality in the class means. |
