On testing the correlation coefficient of a bivariate normal distribution

Metrika ◽  
1980 ◽  
Vol 27 (1) ◽  
pp. 189-194
Author(s):  
M. N. Goria
Keyword(s):  
Normal Distribution ◽  
Correlation Coefficient ◽  
Bivariate Normal Distribution ◽  
Bivariate Normal

Effects of Scaling on the Correlation Coefficient: Additional Considerations

1978 ◽  
Vol 15 (2) ◽  
pp. 304-308 ◽  
Author(s):  
Warren S. Martin
Keyword(s):  
Normal Distribution ◽  
Correlation Coefficient ◽  
Correlation Coefficients ◽  
Bivariate Normal Distribution ◽  
Information Loss ◽  
Simulation Data ◽  
Pearson Product Moment Correlation ◽  
Bivariate Normal ◽  
Amount Of Information ◽  
Restricted Number

Distortion in the Pearson product moment correlation due to a restricted number of scale points is evaluated in two ways. First, a simulation of the bivariate normal distribution is used to estimate the effects of varying the number of scale points on the product moment correlation. This procedure demonstrates a substantial amount of information loss. Second, other correlation coefficients and some methods to correct for this loss are discussed and related to the simulation data.

scholarly journals A Modification of Linfoot's Informational Correlation Coefficient

2017 ◽  
Vol 46 (3-4) ◽  
pp. 99-105
Author(s):  
Georgy Shevlyakov ◽  
Nikita Vasilevskiy
Keyword(s):  
Normal Distribution ◽  
Correlation Coefficient ◽  
Strong Correlation ◽  
Bivariate Normal Distribution ◽  
Correlation Measure ◽  
Bivariate Normal ◽  
Large Samples ◽  
Wide Range ◽  
Symmetric Version

Performance of the Linfoot's informational correlation coefficient is experimentally studied at the bivariate normal distribution. It is satisfactory in the case of a strong correlation and on large samples. To reduce the bias of estimation, a symmetric version of this correlation measure is proposed. On small and large samples, this modified informational correlation coefficient outperforms Linfoot's correlation measure at the bivariate normal distribution in the wide range of the correlation coefficient.

A Postscript to “A Note on a Geometric Interpretation of the Correlation Coefficient”

1983 ◽  
Vol 8 (4) ◽  
pp. 311-314
Author(s):  
Philip H. Sorensen
Keyword(s):  
Normal Distribution ◽  
Correlation Coefficient ◽  
Regression Coefficient ◽  
Bivariate Normal Distribution ◽  
Geometric Interpretation ◽  
Focal Points ◽  
Bivariate Normal

Essential dimensions for drawing an ellipse that bounds a constant probability area of a bivariate normal distribution may be computed from only knowledge of the correlation coefficient ( ρ) or the standardized regression coefficient ( ßzx). The length of the latus rectum of the ellipse is [Formula: see text] (1 – ρ) and the distance between focal points is [Formula: see text] (1 + ρ). Other values may be expressed in terms of ρ or derived from the foregoing. The geometry is illustrated and a set of curves for reading values directly from knowledge of ρ> 0 is provided.

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