A novel approach for Box-Cox transformation via meta analysis and its web application

The assumption of normality is one of the common assumptions in health studies. In cases where the normality assumption is not met, one of the frequently used solution methods is to transform on a non-normally distributed data set. One of the frequently used transformation methods is the Box-Cox transformation method. Box-Cox transformation method is a power transformation method with unknown transformation parameter. In this thesis, we proposed a new approach for the estimation of the unknown transformation parameter of the Box-Cox transformation method. Our proposed approach is based on combining different parameter estimation methods with meta-analysis. We compared our propesed approach and other methods under different scenarios with the Monte Carlo simulation study. As a result of the simulation study, it has been seen that our proposed approach has a more successful performance in parameter estimation than other methods. Moreover, we applied the proposed approach on two different real data. In addition, we made our proposed approach accessible to researchers as a function named "boxcoxmeta" under the AID library in the R program. Finally, we have developed an internet-based tool involving our proposed approach in this thesis. Keywords: Box-Cox transformation, Meta analysis, Normality tests, Statistical software