General balance, combination of information and the analysis of covariance

A resume is given of the conditions and underlying theory for general balance of an experimental design, paying particular attention to their relationships to the usual linear models for analysis of variance and the marginality relationships between the model terms. The extra conditions are defined for a design with first-order balance to have general balance, and a result is proved relating general balance to simple combinability. Algorithms and equations are described for the analysis of generally balanced designs, including combination of within-stratum information and estimation of stratum variances, and are extended to analysis of covariance.