Thesis (M.Sc.) - Cairo University - Faculty of Graduate Studies for Statistical Research - Department of Mathematical Statistics

Standard statistical procedures often require data to be normally distributed and the results of these methods will be inadequate when the assumption of normality is not satisfied.Therefore, the postulation of normality is strictly required before proceeding most statistical analysis. Although a number of criteria have been available to assess the assumption of normality, these criteria do not have the same nature and power to diagnose the departures of data from normality. subsequently, the choice of appropriate test always remains an important key in the assessment of normality. Testing of normal distribution is very important since it is an underlying assumption of many statistical procedures such as t-tests, linear regression analysis, Analysis of Variance (ANOVA), etc .In this thesis and due to the importance of this subject and the wide spread development of normality tests, a comprehensive power comparison study of existing and new developed tests for normality is proposed. This study addresses the performance of 36 normality tests, for various sample sizes, considering several signi{uFB01}cance levels and for a number of symmetric and asymmetric distributions. Monte Carlo simulation was conducted to compare the performance of the test statistics in this study. The R programming software version 3.4.3 was used to carry out the study and the R package 2Power R3. General recommendations stemming from the analysis of the power of the selected tests will be considered at the end of the study

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