Data Distribution: Normal or Abnormal? 2024

Farrokh Habibzadeh
Past President, World Association of Medical Editors (WAME), Editorial Consultant, The Lancet, Associate Editor, Frontiers in Epidemiology. Farrokh.Habibzadeh@gmail.com.

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.

UI MeSH Term Description Entries
D010820 Physicians Individuals licensed to practice medicine. Physician
D012108 Research Personnel Those individuals engaged in research. Clinical Investigator,Clinical Investigators,Researchers,Investigator, Clinical,Investigators,Investigators, Clinical,Survey Personnel,Investigator,Personnel, Research,Personnel, Survey,Researcher
D006801 Humans Members of the species Homo sapiens. Homo sapiens,Man (Taxonomy),Human,Man, Modern,Modern Man
D000078332 Data Analysis Process of systematically applying statistical and/or logical techniques to describe and illustrate, condense and recap, and evaluate data (https://ori.hhs.gov/education). Analyses, Data,Analysis, Data,Data Analyses
D018709 Statistics, Nonparametric A class of statistical methods applicable to a large set of probability distributions used to test for correlation, location, independence, etc. In most nonparametric statistical tests, the original scores or observations are replaced by another variable containing less information. An important class of nonparametric tests employs the ordinal properties of the data. Another class of tests uses information about whether an observation is above or below some fixed value such as the median, and a third class is based on the frequency of the occurrence of runs in the data. (From McGraw-Hill Dictionary of Scientific and Technical Terms, 4th ed, p1284; Corsini, Concise Encyclopedia of Psychology, 1987, p764-5) Kolmogorov-Smirnov Test,Kruskal-Wallis H Statistic,Mann-Whitney U Test,Rank-Sum Tests,Spearman Rank Correlation Coefficient,Wilcox Test,Wilcoxon Rank Test,Non-Parametric Statistics,Nonparametric Statistics,Statistics, Non-Parametric,Kolmogorov Smirnov Test,Mann Whitney U Test,Non Parametric Statistics,Rank Sum Tests,Rank Test, Wilcoxon,Rank-Sum Test,Statistics, Non Parametric,Test, Kolmogorov-Smirnov,Test, Mann-Whitney U,Test, Rank-Sum,Test, Wilcox,Test, Wilcoxon Rank,Tests, Rank-Sum,U Test, Mann-Whitney

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