On study of optimality and orthogonality in a class of fractional factorials

Abstract

Kishen (1945) and Kiefer (1959) defined A-optimal criterion for efficiency of the design which will give minimal average variance for all the estimated effects. Mood (1946) and Kiefer (1959) defined D-optimal criterion which will give minimum generalized variance for all the estimated effects. Ehrenheld (1955) and Kiefer (1959) defined E-optimal criterion for the efficiency of the design. As none of the design will satisfy all these criteria simultaneously so a compromise has to be made for providing the set of points which perform uniformly better with respect to all the three criteria of optimality. This led us to define a new concept of C-optimality. On the other hand if the experimenter aims at minimizing the extent of non-orthogonality of different order effects in preference to optimality he can adopt the concepts of R1m and C-orthogonality which have been introduced in Chapter-III. The designs for cultivator’s field trials have been used to demonstrate the above concepts of optimality and orthogonality. When the criterion C-optimal was considered then amongst the 1st ten ranks set No. 3 comes out to be best design which not only satisfied the requirements of a good design for cultivator’s field but it is also near optimum for providing the best estimates of parameters beta. This design is superior to the one currently being adopted by I.C.A.R. for cultivator’s field trials and also involves lower cost of experimentation.