ORTHOGONAL MAIN-EFFECT PLANS

Abstract : The development and presentation of orthogonal main-effect plans are presented. These plans permit uncorrelated estimates of all main effects of both symmetrical and asymmetrical factorial experiments with a minimum number of trials. An account is given of the development of orthogonal main-effect plans for symmetrical and asymmetrical factorial experiments. The plans for asymmetrical experiments are based on the proposition that if the levels of a factor occur with the levels of another factor with proportional frequencies then the two factors are orthogonal. The possibilities of blocking these plans, the efficiencies of the estimates, the randomization procedure and the method of analysis are discussed. A catalogue of orthogonal main-effect plans is included which consists of the treatment combinations of 26 basic plans, involving factors with up to 9 levels and with up to 81 trials, from which all orthogonal main-effect plans which can be constructed with 81 or fewer trials may be deduced.