A unifying computational method for the analysis of complete factorial experiments

A computational method which may be used for the calculation of sums of squares in the analysis of variance of complete factorial experiments and in the computation of main effect or interaction means is described. The method is elucidated as unifying since one method can be used for a variety of purposes each previously requiring different methods. The programming advantages of such a method are obvious. The following variants are discussed: (1) the standard analysis of variance; (2) analyses omitting certain levels of one or more factors; (3) separate analyses for some levels of a factor or for combinations of levels of more than one factor. These are performed simultaneously; (4) the calculation of main effect or interaction means. The method expects the data in standard order and it leaves the data in that order so that many analyses of the same data can be performed without rearrangement. The total sum of squares, excluding a replication sum of squares, is partitioned into all polynomial partitions and their interactions each with one degree of freedom. This is so even if factors have unequally spaced factor levels.

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