GENERAL FORMULAS AND A POSITIONAL INDEXALGORITHM FOR GENERATING ORTHOGONAL CONTRASTS IN MULTIVARIABLE STATISTICAL DESIGNS
ARMY ELECTRONICS LABS FORT MONMOUTH N J
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Thi analyses deals with the evelopment of general formulas and a number-positional algorithm to generate the effect functions effects and interactions of the fact rs in orthogonal multivariable statistical design . The algorithm and general formulas pre ented are ideally suited for a computer. The application of the general formula to a 5x4x3x2 orthogonal design is elucidated by charts and tables. The algorit m developed leads to a significant simplification of the usual tec niques of analysis of variance. The positional indices serve to esta lis a biunique correspondence between the element of a datamatrix an their associated coefficient-multipliers. T e factors, their levels, the associated L-matrices of polynomial values, and the elements of the data-matrix are uniq ely represented by sets of positionally ordered numerical indices as subscripts and super cripts.