Abstract: One of the important assumptions of data is the normality on which most of the statistical model and procedures rely on regarding the validity of given data hypothesis. Assuming the normality assumption blindly may affect the accuracy of inferences and estimation procedures. As observed, the collected data from real field are not always follow the normality assumption. So, data must be verified with adequate statistical test before used. There are various kinds of goodness of fit tests in literature. Some of them are special purpose tests, so that they are suitable and perform well for some special situations. Others are omnibus tests that are applicable to general cases. Most commonly used tests are Pearsonís chi-squared test and EDF (empirical distribution function) tests, such as Kolmogorov-Smirnov, Cramer-Von-Mises and Anderson-Darling test. The chi-squared test is easy to use but they are generally less powerful than EDF tests. In this paper we want to study the performance of twelve different tests for normality including the above mentioned tests. Considering various sample sizes and different alternative hypotheses results are obtained and displayed in different tables. Finally, discussions are made on the basis of the results.

Keywords: normality test; power comparison; simulation method, alternative of the form symmetrical and asymmetrical distribution