Özet
Coşkun Yıldırım, M. Estimation of Transformation Parameter for Various Transformation Methods Via Shapiro-Wilk Test Statistic, Hacettepe University Graduate School of Health Sciences Master Thesis in Biostatistics, Ankara, 2023. Normal distribution assumption; It is used in many fields such as statistical analysis, models, and sampling theory. Ensuring this assumption is very important in analyzing the data correctly and interpreting the results. One of the popular methods used in cases where the assumption of normality is not provided is to apply a transformation on the variables. Within the scope of this thesis, transformation parameters that maximize the Shapiro-Wilk test statistic for Log Shift, Box-Cox, Bickel-Doksum, Yeo-Johnson, Square Root Shift, Manly, Modulus, Dual and Gpower transformation are estimated. By adding Log, Neglog, Glog, and Reciprocal transformation methods to these nine transformation methods, the performances of these transformation methods under different scenarios were examined with the Shapiro-Wilk test with Monte Carlo simulation study. In addition, Shapiro-Wilk method was compared with the maximum likelihood estimation for parameter estimation. As expected as a result of the simulation study, it was observed that Shapiro-Wilk parameter estimation method performed better than the maximum likelihood estimation method in terms of the normality transformation performance of the methods. In line with the simulation study, it is concluded that the Dual transform method performs better under most scenarios. In addition, this approach in which the parameter is estimated with the Shapiro-Wilk test statistic is available to researchers with 13 different transformation methods under Transform package in the R program, and its application is demonstrated on an open-access data set.
Künye
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