Mateu J
Departamento de Matematicas Escuela Superior de Tecnologia y Ciencias Experimentales Universitat Jaume I 12071 Castellon, Spain
Environ Manage. 1997 Sep;21(5):767-77. doi: 10.1007/s002679900066.
/ It has been recognized for a long time that data transformation methods capable of achieving normality of distributions could have a crucial role in statistical analysis, especially towards an efficient application of techniques such as analysis of variance and multiple regression analysis. Normality is a basic assumption in many of the statistical methods used in the environmental sciences and is very often neglected. In this paper several techniques to test normality of distributions are proposed and analyzed. Confidence intervals and nonparametric tests are used and discussed. Basic and Box-Cox transformations are the suggested methods to achieve normal variables. Finally, we develop an application related to environmental data with atmospheric parameters and SO2 and particle concentrations. Results show that the analyzed transformations work well and are very useful to achieve normal distributions.KEY WORDS: Normal distribution; Kurtosis; Skewness; Confidence intervals; Box-Cox transformations; Nonparametric tests
长期以来,人们已经认识到,能够使分布达到正态性的数据变换方法在统计分析中可能具有至关重要的作用,特别是对于方差分析和多元回归分析等技术的有效应用而言。正态性是环境科学中许多统计方法的基本假设,但常常被忽视。本文提出并分析了几种检验分布正态性的技术。使用并讨论了置信区间和非参数检验。基本变换和Box-Cox变换是实现正态变量的建议方法。最后,我们开发了一个与环境数据相关的应用程序,该数据包含大气参数以及二氧化硫和颗粒物浓度。结果表明,所分析的变换效果良好,对于实现正态分布非常有用。
正态分布;峰度;偏度;置信区间;Box-Cox变换;非参数检验