Comparative examination of normality tests in zootechnical data

The normal distribution is of great importance in statistics. In order to apply parametric tests to the data, it is a prerequisite that the data are taken from a normally distributed population. There are many normality tests in the literature. In this thesis, Lilliefors, Jargue-Bera, Anderson-Darling, Shapiro-Wilk, curvature and kurtosis tests were analyzed, it was aimed to compare the probability (p) values of the tests and to examine them in terms of Type I error and power. Probability (p) values as a result of the analysis made in the R 4.2.1 version (R Core Team, 2021) package program, the Jargue-Bera, Anderson-Darling and Shapiro-Wilk tests were calculated as the probability (p) values were calculated at the 0.05 significance level. While the Lilliefors test rejected the H_0 hypothesis stating that the data were taken from a normally distributed data set, in the analysis made in the package program, the probability (p) value was accepted at the 0.05 significance level, and the hypothesis was accepted. The Jargue-Bera test had the smallest Type I error in various simulation trials and different sample volumes for the normal distribution. Type I errors of the Shapiro-Wilk test and Anderson-Darling tests were very close to 5% at the initial Type I error rate. Shapiro-Wilk test had the highest power value in various simulation trials and different sample volumes for Gamma distributions that are not normal in terms of power, followed by Jargue-Bera and Anderson-Darling tests. Lilliefors test had an average power value. Keywords: Normality test, normal distribution, jargue-bera, liliefors, shapiro-wilk, anderson-darling, kurtosis, type 1 error, power