正态性的初步检验：一个常见概念的一些统计学方面
Preliminary testing for normality: some statistical aspects of a common concept.
作者信息
Schoder V, Himmelmann A, Wilhelm K P
机构信息
proDERM, Institute for Applied Dermatological Research, Schenefeld, Hamburg, Germany.
出版信息
Clin Exp Dermatol. 2006 Nov;31(6):757-61. doi: 10.1111/j.1365-2230.2006.02206.x.
BACKGROUND
Statistical methodology has become an increasingly important topic in dermatological research. Adequacy of the statistical procedure depends among others on distributional assumptions. In dermatological articles, the choice between parametric and nonparametric methods is often based on preliminary goodness-of-fit tests.
AIM
For the special case of the assumption of normally distributed data, the Kolmogorov-Smirnov test is the most popular choice. We investigated the performance of this test on four types of non-normal data, representing the majority of real data in dermatological research.
METHODS
Simulations were run to assess the performance of the Kolmogorov-Smirnov test, depending on sample size and severity of violations of normality.
RESULTS
The Kolmogorov-Smirnov test performs badly on data with single outliers, 10% outliers and skewed data at sample sizes < 100, whereas normality is rejected to an acceptable degree for Likert-type data.
CONCLUSION
Preliminary testing for normality is not recommended for small-to-moderate sample sizes.
背景
统计方法在皮肤病学研究中已成为一个日益重要的主题。统计程序的适当性尤其取决于分布假设。在皮肤病学文章中，参数方法和非参数方法之间的选择通常基于初步的拟合优度检验。
目的
对于数据呈正态分布这一假设的特殊情况，柯尔莫哥洛夫-斯米尔诺夫检验是最常用的选择。我们研究了该检验在四种非正态数据类型上的表现，这四种类型代表了皮肤病学研究中大多数的实际数据。
方法
进行模拟以评估柯尔莫哥洛夫-斯米尔诺夫检验的表现，具体取决于样本大小和正态性违背的严重程度。
结果
在样本量小于100时，柯尔莫哥洛夫-斯米尔诺夫检验在存在单个异常值、10%异常值和数据偏态的数据上表现不佳，而对于李克特量表型数据，正态性被拒绝到可接受的程度。
结论
对于中小样本量，不建议进行正态性的初步检验。
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