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.

Serum lipopolysaccharide associated with new-onset atrial fibrillation in patients with non-small-cell lung cancer a retrospective observational study

“…Statistical analysis was performed using SPSS 26.0 and R software. Kolmogorov–Smirnov method was used for normality test ( 16 ). Measures obeying normal distribution were expressed as mean ± standard deviation (SD), and statistical analysis was performed by unpaired t -test; measures not normally distributed were expressed as median (Q75, Q75), and statistical analysis was performed by Mann–Whiney U -test.…”

Nurse perceptions of practice environment, quality of care and patient safety across four hospital levels within the public health sector of South Africa

“…Normality of the data was tested using the Kolmogorov–Smirnov test, but due to the unlikelihood of non-significant p -values in such a large sample size, more significance was ascribed to results from Q-Q plots. The points in the Q-Q plot lies close enough to the straight line to retain the assumption that the data distribution is normal for all variables [ 35 ].…”

Entamoeba histolytica: In Silico and In Vitro Oligomerization of EhHSTF5 Enhances Its Binding to the HSE of the EhPgp5 Gene Promoter

“…The ImageJ software, version 1.54, (Bethesda, MD, USA) was used to quantify the relative protein expression through pixel analysis. For the statistical analysis, we assessed the normality of the data distribution using the Shapiro-Wilk test, chosen for its high sensitivity with small to moderate sample sizes [70]. This evaluation was conducted using GraphPad Prism software, version 8.0.1.…”