Goodness-of-fit procedure developed based on machine learning algorithm for normal distribution

It is very important to check the normality assumption for the accuracy and reliability of statistical analyses. Whether a data set used in statistical analysis has a normal distribution is basically determined by two different methods. These are graphical methods and goodness-of-fit tests for normal distribution. However, when these methods are used alone, they may provide conflicting results in determining normality for all cases. In this study, as an alternative to the existing methods in the literature, a procedure based on a machine learning algorithm is developed to determine whether a data set conforms to the normal distribution. The Type I error rate and power of this procedure, which is based on a machine learning algorithm, is compared with the well-accepted and widely used goodness-of-fit tests for the normal distribution under symmetric and asymmetric distributions in a comprehensive simulation study. The performance of the developed procedure was also analyzed in terms of accuracy, precision, sensitivity and F1 score. As a result of extensive comparisons, it is observed that the goodness-of-fit procedure based on the machine learning algorithm for the normal distribution, which is presented for the first time in the literature, outperforms the normality tests considered in this study for almost all cases.