Systematic Methods for Analyzing 2n3mFactorial Experiments with Applications

Two systematic procedures to facilitate the analysis of a complete 2 n 3 m factorial experiment are discussed. The methods are applicable when all the quantitative three-level factors are equally spaced and when the contrasts involving qualitative three-level factors appear as if the three-level factors were in fact quantitative and equally spaced. Algorithm I systematizes the calculation of the factor effects for the 2 n 3 m series of designs. Algorithm II yields the set of fitted values, and hence the residuals, based on those factor effects which have been judged to be non-negligible. The two algorithms have additional and possibly more important uses in studying fractionated 2 n 3 m factorial experiments. Algorithm I can be used to facilitate the writing down of the cross-product matrix for any desired set of factor effects for a specified set of treatment combinations. For the special case of the standard fractionated 2 n–p series of designs the two algorithms can be used to find the set of defining contrasts corresponding to a given set of treatment combinations or to find the set of treatment combinations corresponding to a given set of defining contrasts.