Past President, World Association of Medical Editors (WAME), Editorial Consultant, The Lancet, Associate Editor, Frontiers in Epidemiology.
J Korean Med Sci. 2024 Jan 22;39(3):e35. doi: 10.3346/jkms.2024.39.e35.
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.
确定给定数据集的频率分布是否服从正态分布是数据分析的第一步。虽然通过 Q-Q 图对数据进行直观检查被许多科学家所接受，但它被认为是主观的，不受其他研究人员的认可。对于样本量≥50 的数据，使用带有 Lilliefors 修正的单样本 Kolmogorov-Smirnov 检验，对于样本量<50 的数据，使用 Shapiro-Wilk 检验是定量检查数据集正态性的常用统计检验方法。由于参数检验假设数据分布是正态的（高斯分布，钟形分布），与非参数检验相比更稳健，因此我们通常使用变换（例如对数变换、Box-Cox 变换等）使非正态分布数据的频率分布更接近正态分布。在此，我希望通过检查实际数据集来反思如何实际使用这些统计方法。
