Thomas J R, Nelson J K, Thomas K T
Department of Health and Human Performance at Iowa State University, USA.
Res Q Exerc Sport. 1999 Mar;70(1):11-23. doi: 10.1080/02701367.1999.10607726.
Frequent violations of the assumption that data are normally distributed occur in exercise science and other life and behavioral sciences. When this assumption is violated, parametric statistical analyses may be inappropriate for data analysis. We provide a rationale for using a generalized form of nonparametric analyses based on the Puri and Sen (1985) L treated as a chi 2 approximation. If data do not meet the assumption of normality, this nonparametric approach has substantial power and is easy to use. An advantage of this generalized technique is that ranked data may be used in standard parametric statistical programs widely available on desktop and mainframe computers, for example, regression, analysis of variance (ANOVA), multivariate analysis of variance (MANOVA) within BioMed, SAS, SPSS. Once the data are ranked and analyzed with these programs, the only adjustment required is to use a standard formula to calculate the nonparametric test statistic, L, instead of the parametric test statistic (e.g., F). Thus, rank-order nonparametric models become parallel with their parametric counterparts allowing the researcher to select between them based on characteristics of the data distribution. Examples of this approach are provided using data from exercise science for regression, ANOVA (including repeated measures) and MANOVA techniques from SPSSPC. Using these procedures, researchers can easily examine data distributions and make an appropriate decision about parametric or nonparametric analyses while continuing to use their regular statistical packages.
在运动科学以及其他生命科学和行为科学中，经常会出现违背数据呈正态分布这一假设的情况。当这一假设被违背时，参数统计分析可能不适用于数据分析。我们基于被视为卡方近似的普里和森（1985年）的L提出了一种使用广义非参数分析形式的基本原理。如果数据不符合正态性假设，这种非参数方法具有强大的功效且易于使用。这种广义技术的一个优点是，排序后的数据可用于在台式计算机和大型计算机上广泛使用的标准参数统计程序中，例如，生物医学、SAS、SPSS中的回归分析、方差分析（ANOVA）、多变量方差分析（MANOVA）。一旦数据经过排序并用这些程序进行分析，唯一需要的调整就是使用标准公式来计算非参数检验统计量L，而不是参数检验统计量（例如F）。因此，排序非参数模型与其参数对应模型并行，使研究人员能够根据数据分布的特征在它们之间进行选择。使用来自运动科学的数据，针对SPSSPC中的回归分析、方差分析（包括重复测量）和多变量方差分析技术给出了这种方法的示例。使用这些程序，研究人员可以轻松检查数据分布，并在继续使用常规统计软件包的同时，对参数分析或非参数分析做出合适的决策。
