The chapter deals with the second class of use and discusses goodness-of-fit tests designed to test formally the appropriateness or adequacy of the normal distribution as a model for the underlying phenomenon from which data were generated. The single most used distribution in statistical analysis is the normal distribution. The chapter discusses tests that assume a complete random sample is available for analysis. It purposes tests for normality grouped into five categories, chi-square test, empirical distribution function tests, moment tests, regression tests, and miscellaneous tests. A number of investigators have considered extending and modifying the Shapiro-Wilk test. Spiegelhalter used the theory of most powerful location and scale invariant tests to develop tests of normality against the uniform and the double exponential distributions. Results of power studies are not the only means for judging or comparing the normality tests.