Corrigenda: Improved Approximation to the Non-Null Distribution of the Correlation Coefficient

1975 ◽  
Vol 70 (350) ◽  
pp. 494
Author(s):  
Helena Chmura Kraemer
Keyword(s):  
Correlation Coefficient ◽  
Null Distribution

scholarly journals Null distribution of multiple correlation coefficient under mixture normal model

2002 ◽  
Vol 30 (4) ◽  
pp. 249-255 ◽  
Author(s):  
Hydar Ali ◽  
Daya K. Nagar
Keyword(s):  
Correlation Coefficient ◽  
Mellin Transform ◽  
Statistical Tests ◽  
Null Distribution ◽  
Multiple Correlation Coefficient ◽  
Normal Model ◽  
Multiple Correlation ◽  
Multivariate Gaussian ◽  
Regression Problems

The multiple correlation coefficient is used in a large variety of statistical tests and regression problems. In this article, we derive the null distribution of the square of the sample multiple correlation coefficient,R2, when a sample is drawn from a mixture of two multivariate Gaussian populations. The moments of1−R2and inverse Mellin transform have been used to derive the density ofR2.

Comments on Huberty’s Test of the Squared Multiple Correlation Coefficient

1996 ◽  
Vol 21 (3) ◽  
pp. 288-298 ◽  
Author(s):  
Yiu-Fai Yung
Keyword(s):  
Correlation Coefficient ◽  
Null Distribution ◽  
Multiple Correlation Coefficient ◽  
Multiple Correlation ◽  
Classical Test ◽  
Chance Performance ◽  
Α Level ◽  
Better Than

It is argued that Huberty’s (1994) test for inferring a better-than-“chance” performance of the observed R2 value is inconsistent. Because there is a hidden change of the null distribution of R2, the “chance” value and the observed R2 value are not comparable in Huberty’s test. A new test is proposed for resolving these difficulties. It is shown that the new test is equivalent to an adjustment of the α-level of the classical test of the squared multiple correlation coefficient.

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