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Checking the normality assumption in statistical procedures, particularly parametric tests, is very important as the validity of the conclusions drawn from such techniques depend to a large extent on the validity of this assumption among others. A number of methods have been proposed for assessing the validity of this assumption in statistical procedures. This book addresses the performance of eighteen of the available tests for different sample sizes, significance levels, and for a number of symmetric and asymmetric distributions through the conduct of Monte-Carlo simulation.