Normality assessment, few paradigms and use cases

Background: The importance of applying the normality tests is underlined by the way of continuing the statistical protocol for numerical data within inferential statistics, respectively by the parametric or non-parametric tests that we will apply further on.

Methods: To check the calculation mode, we used sets of random values and we performed the normality assessment using statistical calculation programs. We took non-Gaussian data (n = 30, n = 50, n = 100, n = 500) and Gaussian data (n = 30, n = 50, n = 100, n = 500) for which we checked the normality of the data. Data chosen for this study were most representative for each batch (n).

Results: The application of normality tests to the data under study confirms that the data are non-Gaussian for the first data set. For the Gaussian data sample, the verification of normality is confirmed by the results.

Conclusion: For data up to 50 subjects, it is recommended to apply the Shapiro-Wilk test, but also to apply graphical methods to confirm the accuracy of the result. If the data samples have more than 50 values, the D’Agostino & Pearson omnibus normality test should be applied and if the statistical program does not contain this test, the Shapiro-Wilk test can be applied (in the case of SPSS). Graphical methods, although they require some experience, are useful for identifying the normality of distributions with a small number of data.