ON SELECTING POWER TRANSFORMATION PARAMETERS WITH THE PRESENCE OF AN OUTLIER
This study assesses the new approach of the Box-Cox Transformation to estimate power parameters using five criteria: the traditional Maximum Likelihood Estimation; coefficient of determination; p-value of Shapiro-Wilk test statistics for the residual’s normality of the estimated linear regression of the transformed response vector; p-value related to residual’s normality; and the Mean Square Errors of the estimated nonlinear regression of the original response vector. The efficiency of these criteria is studied to determine the optimal transformation parameter in the presence of an outlier within a response variable in simple linear regression. The computational algorithm has been developed and applied to medical data. The authors concluded that it is difficult to obtain a feasible solution for all criteria from which an optimal power parameter can be selected. Therefore, the researcher's experience can be considered a decisive factor in choosing according to the priorities of the comparison between the criteria.
Simple linear Regression, Box-Cox Transformation, Maximum Likelihood Estimation, and Outliers