The distribution of the ratio of covariance estimates in two samples drawn from normal bivariate populations
成果类型：
Article
署名作者：
Hirschfeld, HO
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
DOI：
10.2307/2332407
发表日期：
1937
页码：
6579
关键词：
摘要：
This paper is a contribution to statistical tests of significance for 2-variate problems. In particular it deals with testing the difference between 2 correlation-coefficients. To this end the above random-sample distribution is developed and the case where the 2 samples have been drawn from the same normal population is more closely examined. It is shown that under these conditions the probability integral is a finite weighted sum of incomplete [beta]-functions, the weights being complete [beta]-functions and simple polynomials in [rho]2 ([rho] denoting the correlation coefficient of the underlying normal population). As [rho] approaches the value +1 or the value[long dash]1 the test is shown to approach the 2-test as a limiting form. The performance of the test is demonstrated with data from a Cambridge nutrition exp. on pigs.