Construction of Latin Square Design from Confounded 33 Factorial Experimental Designs

Abstract

For practical experimental work, it becomes impossible to perform all experiments of a multi-factor experiment in a complete factor structure due to the complexity of the problem and the fact that the number of possible factor combinations in a multi-factor experiment is a product of the levels of the single factors. This result in waste of time, uses large amount of test materials, uses large number of experimental animals, and involves many people, which tend to increase experimental uncertainty. This work introduces a fundamental method to reduce the experimental work very considerably in relation to the complete factorial experiment, group such experiments into small blocks. A , factorial experimental design was considered which effects were confounded into 9 (nine blocks) of 27 (twenty-seven) effects at three levels (0, 1, 2) each. 10 (Ten) generalized interaction terms were obtained and three of the terms were selected and used to construct a Latin square design of order 3. Also show how ANOVA can be constructed for each Latin square formed.