A Program for Large‐Scale Non‐Orthogonal Analysis of Variance and Covariance

Current programs for the analysis of variance in non‐orthogonal data do not in general provide for the estimation of variance components, the analysis of covariance between parallel variates or the accommodation of models containing more than 100‐200 parameters. This paper describes a Univac 1107 program which does provide these features. By using a combination of direct and indirect methods of calculating sums of squares and cross‐products, the program can deal with very large models containing up to 2,640 parameters in up to five main cross‐classifications. The first four classifications may contain up to 140 parameters, and the remainder must belong to the final classification. Up to five parallel variates can be analysed simultaneously to give all possible analyses of variance and covariance. Components of variance and covariance are given for all classifications. The program was written with the needs of cattle artificial insemination field progeny test data in view, but it should be useful for the analysis of a variety of survey‐type studies in which one classification (such as schools, shops, farms) is overwhelmingly large, as well as for unbalanced data in general.