Row–Column Designs for 2^n factorial 2-Colour Microarray Experiments for Estimation of Main Effects and Two-Factor Interactions with Orthogonal Parameterization

Abstract

A method of construction of row–column designs for estimation of main effects and two factor interaction effects in 2^n factorial microarray experiments based on orthogonal parameterization has been developed in minimum number of replications. A catalogue of designs for 2 ≤ n ≤ 9 has been prepared. The catalogue also gives the main effects and two-factor interactions confounded in different replications and the factorial effects that are not confounded in a replication. The efficiency factor of estimable main effects and two-factor interactions has been given. For each 2^n factorial, two designs have been given, one in which main effects are estimated with more efficiency and another in which two-factor interactions are estimated with more efficiency. A procedure of construction of row–column designs for estimation of all factorial effects with odd number of factors has been given. Row–column designs with unequal replication of different treatment combinations have also been obtained for estimation of all main effects and two-factor interactions