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Different types of statistical tests have been used for evaluation of the normality of selected data files. The files have been simulated to be on the border of normality. The results of the tests have been compared. It has been found that some files have been, using some type of a test, marked as normal, but using another type of a test, marked as non-normal. It is possible to find similar results by normality testing of data files obtained from production. Therefore, complementary tools for assessment of normality of the files under test have to be used. This paper compares results of normality testing of some simulated files by three basic tests of normality: test of elective skewness and kurtosis, Anderson-Darling test, and Kolmogorov-Smirnov test. It gives also directions indicating which other tools of exploratory analysis have to be used for verification of results obtained by different tests of normality.