Tables of the Ordinates and Probability Integral of the Distribution of the Correlation Coefficient in Small Samples.

1938 ◽  
Vol 33 (204) ◽  
pp. 751
Author(s):  
Francis McIntyre ◽  
F. N. David
Keyword(s):  
Correlation Coefficient ◽  
Small Samples ◽  
Probability Integral

A Monte Carlo Investigation of the Fisher Z Transformation for Normal and Nonnormal Distributions

2000 ◽  
Vol 87 (3_suppl) ◽  
pp. 1101-1114 ◽  
Author(s):  
Kenneth J. Berry ◽  
Paul W. Mielke
Keyword(s):  
Monte Carlo ◽  
Correlation Coefficient ◽  
Bivariate Normal Distribution ◽  
Small Samples ◽  
Bivariate Distributions ◽  
Nonnormal Distributions ◽  
Monte Carlo Investigation ◽  
Sample Correlation ◽  
Heavy Tailed ◽  
Z Transformation

The Fisher transformation of the sample correlation coefficient r (1915, 1921) and two related techniques by Gayen (1951) and Jeyaratnam (1992) are examined for robustness to nonnormality. Monte Carlo analyses compare combinations of sample sizes and population parameters for seven bivariate distributions. The Fisher, Gayen, and Jeyaratnam approaches are shown to provide useful results for a bivariate normal distribution with any population correlation coefficient ρ and for nonnormal bivariate distributions when ρ = 0. In contrast, the techniques are virtually useless for nonnormal bivariate distributions when ρ#0.0. Surprisingly, small samples are found to provide better estimates than large samples for skewed and symmetric heavy-tailed bivariate distributions.

Correlation Coefficient Matrix Based PD Feature Dimensional Reduction

2014 ◽  
Vol 945-949 ◽  
pp. 2499-2504
Author(s):  
Yu Wang ◽  
Jin Sha Yuan ◽  
Hai Kun Shang ◽  
Song Jin
Keyword(s):  
Correlation Coefficient ◽  
Power Transformer ◽  
Partial Discharge ◽  
Back Propagation ◽  
Coefficient Matrix ◽  
Back Propagation Neural Network ◽  
Small Samples ◽  
Diagnostic Feature ◽  
Dimension Characteristic ◽  
Correlation Coefficient Matrix

The abstraction of diagnostic feature from field condition monitoring data is a significant research challenge. A new dimension reduction method based on correlation coefficient matrix is proposed aimed at the high-dimension characteristic parameters in the process of pattern recognition for partial discharge in power transformer. The CCM is constructed by parameters extracted from partial discharge signature in power transformer. The parameters that have similar classification characters are reduced directed by the correlation analysis result. The reduced PD features are inputted to the pattern classifiers of probabilistic neural networks (PNN). The results show that the parameter dimension is reduced and the classifier construction is simplified, and the recognition effect is better than that of the traditional back propagation neural network (BPNN) in the condition of small samples.

Fisher’s Tanh−1 Transformation of the Correlation Coefficient and a Test for Complete Independence in a Multivariate Normal Population

1987 ◽  
Vol 12 (3) ◽  
pp. 294-300
Author(s):  
John R. Reddon
Keyword(s):  
Correlation Coefficient ◽  
Type I Error ◽  
Normal Population ◽  
Error Rates ◽  
Small Samples ◽  
Type I ◽  
Multivariate Normal ◽  
Type I Error Rates ◽  
Complete Independence ◽  
Multivariate Normal Population

Computer sampling from a multivariate normal spherical population was used to evaluate Type I error rates for a test of P = I based on Fisher’s tanh−1 variance stabilizing transformation of the correlation coefficient. The range of variates considered was 5 to 25 and Type I error rates were estimated for several sample sizes with 2,500 independent replications. Except for small samples the test was well behaved. After the test converges to an acceptable Type I error rate it is preferable to Box’s test of P = I.

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