Computer aided construction of efficient designs for making treatment-treatment and treatment-control comparisons

Abstract

This paper describes an algorithm for computer-aided search of weighted A-optimal / weighted A-efficient block designs for making test vs test and tests vs control comparisons, the weights depending upon the importance of the comparisons. The computer aided search of designs is implemented by modifying the interchange and exchange algorithms of Jones and Eccleston (1980). The algorithm also computes the lower bounds to weighted A- efficiency in addition to finding an optimal/ nearly optimal block design. The algorithm has been translated into a computer program using Microsoft Visual C++. Using this programme, a search for weighted A-efficient designs for making test vs test and tests vs control comparisons has been made for v ≤ 20, b ≤ 50, k ≤ 20 and n ≤ 300 such that average replication number of treatments is not more than 20 and v > k. A total of 15, 259 designs with lower bound to A-efficiency ≥ 0.9500 were obtained. The comparison of the designs generated was made with the already existing efficient designs in the literature. This comparison revealed that in almost all the cases, the designs searched through the algorithm were either equally efficient or better than the existing designs with the same parameters.