On Analysis of Factorial Experiments, Complete and Fractional

Abstract

When a large number of factors is involved in a factorial experiments, the analysis through Yates’ method becomes complicated as a very large number of combinations have to be taken and operated upon. We have given a modified method whereby suitable groups of the treatment combinations are formed and then each group is analysed separately. The separate analysis of these groups is then combined to get the final results. Further an investigation has been made to give specific direction for the suppression of factors in case of fractionally replicated designs involving factors each at two levels. It appears that the method of analysis of fractionally replicated designs through Yates’ technique is not yet perfected when factors are at more than two levels. This is because, though the aliases of geometrical components are available, such aliases are not available for linear, quadratic etc. components and their interactions. We have attempted to obtain a solution of this problem. The extended Yates’ method of analysis of factorial experiments gives directly the results of component analysis. When the design is constructed by adopting geometrical techniques in Galois fields, it becomes difficult to have its component analysis particularly in respect of those interactions which are confounded. Similar difficulties are encountered when the design is fractionally replicated. It appears that this type of difficulty can be overcome if a link between the contrasts in the two types of analysis can be established. One of the main purposes of the present investigation is to establish such a link.