Optimal Inverse Square Root Transformation for Response Surface Methodology: A Simulation Approach

Transformation techniques in Response Surface Methodology has received little attention in the literature when the response of design variables are not normally distributed. Various attempts to mitigate the incessant reoccurrence of the violation of normality assumption has proved abortive. This research delve into intricate of proposing inverse square root transformation, a robust transformation technique that can handle both small and large sample sizes in response surface methodology paradigm. Some transformation techniques in literature used for RSM are log, Box-Cox, square-root. These were tested and compared alongside with a newly proposed method. A Monte Carlo Simulation of different sample sizes (n = 10, 20, 50, 100, 200, 500, 1000) at different initial guess parameter for both small and large samples were used. Three tests Anderson-Darlington, Shapiro-wilk and Jarque-Berra test statistics were used to validate the consistency of the transformation methods considered and graphical representation were also used for visual inspection of the behavior of the methods. The result of the analysis revealed that inverse square root transformation method outperformed other existing method. This is achieved through comparison analysis of the methods using Bayesian Information Criterion (BIC).