IJE TRANSACTIONS A: Basics Vol. 31, No. 1 (January 2018) 39-45    Article in Press

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W. Alqaraghuli, A. Alkarkhi and Y. Yusup
( Received: October 24, 2017 – Accepted: November 30, 2017 )

Abstract    Three-factor interaction for two-level, three-level, and four-level factorial design was studied. A new technique and a new formula were proposed for calculating the effect of three-factor interaction based on the coefficients of orthogonal polynomial contrast. The results of the proposed procedure were in agreement with the results of the least squares method. Furthermore, the new formula is fixed and can be used for calculating the three factor-interaction easily and simply without using the complicated matrix formula with the least squares method. This formula will enhance using the coefficients of orthogonal contrast in analyzing other experimental designs.


Keywords    Two-level factorial design, Three-level factorial design, Four-level factorial design, Response surface models


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