Open AccessTESTING DIFFERENCES BETWEEN MULTIPLE CORRELATIONS
Author(s) -
Sympson James B.
Publication year - 1979
Publication title -
ets research report series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.235
H-Index - 5
ISSN - 2330-8516
DOI - 10.1002/j.2333-8504.1979.tb01188.x
Subject(s) - statistics , mathematics , sample (material) , correlation , population , sample size determination , set (abstract data type) , statistical hypothesis testing , confidence interval , computer science , demography , chemistry , geometry , chromatography , sociology , programming language
The procedure for testing differences between multiple correlations that is suggested in textbooks on applied statistics is limited to the case where a single group of individuals has been observed and the two multiple correlations to be contrasted are based on two sets of predictor variables, S 1 and S 2 , such that S 2 is a proper subset of S 1 . In this paper, four new statistical procedures are proposed that can be applied in other commonly occurring situations. A significance test is described that can be utilized when the multiple correlations to be contrasted are calculated in two independent samples. In this case, the predictor sets S 1 and S 2 can have any relationship to each other: S 1 can be a proper subset of S 2 , or vice versa; S 1 and S 2 can be mutually exclusive; or the two sets can intersect, with each set having one or more predictors unique to itself. This test is suitable for both small sample and large sample applications. A large sample significance test is proposed for the case where the multiple correlations to be contrasted are calculated either in one sample or in two samples in which individuals are matched on a one‐to‐one basis. As in the independent groups case, the predictor sets S 1 and S 2 can have any relationship to each other. Following a brief discussion of unbiased estimation of squared multiple correlations, two procedures for constructing approximate confidence limits for the population difference between two squared multiple correlations are presented. These procedures are closely related to the significance tests described earlier.