A GROUP OF SPLIT-PLOT DESIGNS WITH A HETEROSCEDASTIC MODEL

For a group of split-plot designs it is assumed that the error variance is constant for a particular experiment but it varies from experiment to experiment. Assuming error variances to be known, estimators of the treatment parameters are obtained by weighted (generalised) least squares method and the corresponding analysis is given. For unknown error variances, an adjustment of the statistics using estimated weights is proposed for removing much of the resulting bias. The adjustment stems from a theorem due to Meier (1953).