Thesis (M.Sc.) - Cairo University - Institute of Statistical Studies and Research - Department of Statistics and Econometrics

This work presented checking the assumption of normality which is very important in most statistical inferences especially for parametric tests (e.g. t- tests, z- test, linear regression analysis, ANOVA,.. etc.) and showed that the ordinary least squares test for normality depends on the distribution of the independent variable assuming that this variable is random. The type of the distribution of the independent variable affects the regression weights of the ordinary least squares test. The weighting function was shown when the independent variable follows the exponential and weibull distributions and a modification on Yitzhaki (1996) was presented when the variable follows the uniform distribution. In chapter 4, A power comparison of eleven of the available tests for different sample sizes, significance levels, against a number of symmetric and asymmetric distributions by conducting a monte Carlo simulation using R language version ( R x 64 3.2.2) was performed. The results showed that the kurtosis test was the most powerful test against symmetric short tailed distributions. For symmetric long-tailed, the robust jarque bera test was the most powerful test. In case of asymmetric short tailed, the shapiro wilk test was the most powerful test

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