Data Distribution: Normal or Abnormal?

Abstract

Determining if the frequency distribution of a given data set follows a normal distribution or not is among the first steps of data analysis. Visual examination of the data, commonly by Q-Q plot, although is acceptable by many scientists, is considered subjective and not acceptable by other researchers. One-sample Kolmogorov-Smirnov test with Lilliefors correction (for a sample size ≥ 50) and Shapiro-Wilk test (for a sample size < 50) are common statistical tests for checking the normality of a data set quantitatively. As parametric tests, which assume that the data distribution is normal (Gaussian, bell-shaped), are more robust compared to their non-parametric counterparts, we commonly use transformations (e.g., log-transformation, Box-Cox transformation, etc.) to make the frequency distribution of non-normally distributed data close to a normal distribution. Herein, I wish to reflect on presenting how to practically work with these statistical methods through examining of real data sets.