The statistical utilization of multiple measurements
The statistical utilization of multiple measurements
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DOI：
10.1111/j.1469-1809.1938.tb02189.x
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发表时间：
1938-08-01
期刊：
影响因子：
--
通讯作者：
Fisher, RA
中科院分区：
文献类型：
--
作者：
Fisher, RA
关于多重测量利用的3个独立研究方向的结果以统一的符号表示。早在1931年，霍特林就对可能来自同一多变量总体的两个样本的比较进行了基本的显著性检验。马哈拉诺比斯和他在加尔各答的学派发展了广义距离的概念，取代了皮尔逊的S粗略的“种族相似系数”，并找到了适当估计的准确分布。与此同时，高尔顿实验室的工作人员将“判别函数”--本质上是广义方向的估计--应用于人类学、分类学和植物选择的问题。这一发展需要对共线、共面等进行适当的显著性检验，本文提供了这些检验。现在可以指定观察到的判别函数的精确度，并测试相同形式对不同物质的适用性。
The results of 3 independent lines of research on the utilization of multiple measurements are presented in a unified notation. As early as 1931 Hotelling had given the fundamental test of significance for the comparison of 2 samples drawn from possibly the same multivariate population. Mahalanobis and his school at Calcutta had developed the notion of generalized distance, to take the place of Pearson''s crude "coefficient of racial likeness" and had found the exact distribution of the appropriate estimate. Meanwhile, workers at the Galton Laboratory had applied "discriminant functions," essentially estimates of generalized direction, to problems in anthropology, taxonomy and plant selection. This development required appropriate tests of significance for collinearity, coplanarity, etc., which are supplied in this paper. It is now possible to specify the precision of an observed discriminant function, and to test how widely the same form is applicable to different bodies of material.