AN ANALYSIS OF VARIANCE TEST FOR NORMALITY (COMPLETE SAMPLES)
AN ANALYSIS OF VARIANCE TEST FOR NORMALITY (COMPLETE SAMPLES)
复制标题
DOI：
10.1093/biomet/52.3-4.591
复制
发表时间：
1965-01-01
期刊：
影响因子：
2.7
通讯作者：
WILK, MB
中科院分区：
文献类型：
--
作者：
SHAPIRO, SS;WILK, MB
本文的主要目的是介绍一种检验完全样本正态分布的新的统计方法。检验统计量是通过将样本顺序统计量的适当线性组合的平方除以通常的对称方差估计得到的。这一比率既是尺度不变的，也是原点不变的，因此该统计量适用于正态复合假设的检验。检验总体上的分布假设，特别是正态分布，一直是持续统计研究的一个主要领域--无论是理论上还是实践上。引起持续关注的一个可能原因是，许多统计程序都是基于特定的分布假设--特别是正态分布假设--得出的。尽管在许多情况下，这些技术比它们背后的假设更可靠，但知道潜在的假设是不正确的，可能会影响这些方法的使用和应用。此外，对具有分布检验刺激的数据体的研究可以鼓励考虑例如使变换正规化、使用诸如无分布技术之类的替代方法以及检测诸如离群值或误差之类的粗略特征。在本文中开发的测试程序的定义及其一些分析性质在§2中描述。在使用测试中有用的操作信息和表格在§3中详细说明(可独立于论文的其余部分阅读)。第四节给出了一些例子。第五节摘录了对各种替代测试的有效性进行比较的经验抽样研究的摘录。讨论和结束语“载于第6节。
The main intent of this paper is to introduce a new statistical procedure for testing a complete sample for normality. The test statistio is obtained by dividing the square of an appropriate linear combination of the sample order statistics by the usual symmetric estimate of variance. This ratio is both scale and origin invariant and hence the statistic is appropriate for a test of the composite hypothesis of normality. Testing for distributional assumptions in general and for normality in particular has been a major area of continuing statistical research—both theoretically and practically. A possible cause of suoh sustained interest is that many statistical procedures have been derived based on particular distributional assumptions—especially that of normality. Although in many cases the techniques are more robust than the assumptions underlying them, still a knowledge that the underlying assumption is incorrect may temper the use and application of the methods. Moreover, the study of a body of data with the stimulus of a distributional test may encourage consideration of, for example, normalizing transformations and the use of alternate methods such as distribution-free techniques, as well as detection of gross peculiarities such as outliers or errors. The test procedure developed in this paper is defined and some of its analytical properties described in § 2. Operational information and tables useful in employing the test are detailed in § 3 (which may be read independently of the rest of the paper). Some examples are given in § 4. Section 5 consists of an extract from an empirical sampling study of the comparison of the effectiveness of various alternative teste. Discussion and concluding remarks' are given in § 6.