Row-column Designs for Factorial Experiments in Two Rows

Abstract

In a row-column design set up, because of practical considerations it may not be possible to accommodate more than two experimental units in a column. One application of row-column designs with two rows is in factorial experiments where the treatment structure is factorial in nature. Due to cost and time considerations, it may not be possible to run a design for estimation of all the factorial effects. The experimenter may, however, be interested in orthogonal estimation of all the main effects and two factor interactions. Thus it is required to obtain a general method of construction of row-column designs with two rows, which permit orthogonal estimation of all main effects and two factor interactions in factorial experiments and at the same time minimize the number of runs (or design points). To deal with such situations, a general method of construction of row-column designs with two rows for orthogonal estimation of main effects and two factor interactions in factorial experiments in minimum number of runs has been given for orthogonal parameterization. A catalogue of efficient row-column designs for 2-level factorial experiments (number of factors ranging between 2 and 9) in minimum number of replications has been prepared. Here in all the designs main effects and two factor interaction are estimated orthogonally. A SAS program for checking the orthogonal estimation of main effects and two factor interactions has been prepared. A web application of generation of these designs has also been developed. The above discussion relates to the factorial experiments run in block design or row-column design, where the interest of the experimenter is in orthogonal paramertization of the factorial effects. However, in some experimental situations, like designs for 2-colour micro-array experiments, where null state or baseline may exist, the experimenter would be interested in baseline parameterization rather than orthogonal parameterization. Since the designs obtained are in incomplete columns, it is important to study the efficiency of designs obtained. In other words, there is a need to obtain a general procedure of generating w-efficient row-column designs in two rows for n-factors mixed level factorial experiments based on baseline parameterization. To deal with such situations, a general procedure of obtaining w-efficient row-column designs in two rows for n-factors mixed level factorial experiments based on baseline parameterization has also been developed. A catalogue of w-efficient row-column designs in two rows for n-factors mixed level factorial experiments based on baseline parameterization has been prepared. To make these designs available through online a web application has also been developed.