THE CORRELATION BETWEEN VARIATE-VALUES AND RANKS IN SAMPLES FROM A CONTINUOUS DISTRIBUTION
THE CORRELATION BETWEEN VARIATE-VALUES AND RANKS IN SAMPLES FROM A CONTINUOUS DISTRIBUTION
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连续分布样本中变量值与等级之间的相关性
DOI：
10.1111/j.2044-8317.1954.tb00138.x
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发表时间：
1954
期刊：
影响因子：
--
通讯作者：
A. Stuart
中科院分区：
文献类型：
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作者：
A. Stuart
涉及排名的方法已经被心理学家使用了半个世纪;尽管在早期的发展中，它们受到了严厉的批评，但近年来，它们的康复和扩展已经进入了新的方向。目前对排序方法的兴趣已经在本杂志上发表的几篇论文中以及最近Burt和Morris（1953）的通信中得到了展示。本文从理论上研究了观测值之间相关性的大小和它们有时被取代的秩值。研究发现，在两种最常见的统计分布类型（正态分布和均匀分布）的样本中，这种相关性非常高。对于小到25的样本，正态分布为0.94，均匀分布为0.96;这些值随着样本大小的增加而增加，分别接近0.98和1的极限。在这种情况下，有理由用它们的秩来代替原始观测值，因为由此节省的计算量几乎不会带来效率的损失。调查的结果也对其他理论上感兴趣的问题产生了影响。
Methods involving rankings have been used by psychologists for half a century; and, although in their early development they were subjected to severe criticism, recent years have brought their rehabilitation and extension in new directions. Current interest in ranking methods has been displayed in several papers published in this Journal and very recently in the correspondence by Burt and Morris (1953). The present paper investigates theoretically the magnitude of the correlation between observations and the rank values by which they are sometimes replaced. It is found that in samples from the two most commonly considered types of statistical distribution, the normal and the uniform, this correlation is very high. With a sample as small as 25, it is .94 for the normal distribution and .96 for the uniform distribution; and these values increase, with sample size, towards limits of .98 and 1 respectively. In these circumstances there is justification for replacing the original observations by their ranks, since the consequent saving in computation entails very little loss of efficiency. The results of the investigation also turn out to have bearing on other matters of theoretical interest.