Normality tests

In statistics, normality tests are used to determine whether a random variable is normally distributed, or not.One application of normality tests is to the residuals from a linear regression model. If they are not normally distributed, the residuals should not be used in Z tests or in any other tests derived from the normal distribution, such as t tests, F tests and chi-square tests. If the residuals are not normally distributed, then the dependent variable or at least one explanatory variable may have the wrong functional form, or important variables may be missing, etc. Correcting one or more of these systematic errors may produce residuals that are normally distributed.
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A common application for distribution fitting procedures is when you want to verify the assumption of normality before using some parametric test (see Basic Statistics and Nonparametric Statistics ). A variety of statistics for testing normality are available including the Kolmogorov-Smirnov test for normality, the Shapiro-Wilks' W test , and the Lilliefors test . Additionally, you may review probability plots and normal probability plots to assess whether the data are accurately modeled by a normal distribution .