On the choice of transformations of the correlation coefficient with or without an outlier |
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Authors: | M.S. Srivastava G.C. Lee |
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Affiliation: | University of Toronto , Toronto, Ontario, M5S 1Al |
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Abstract: | Five transformations of the correlation coefficient, namely, Fisher's z, Nair's u, Sankaran's v, Ruben's y and Samiuddin's t are compared numerically using confidence intervals. Samiuddin's ts transformation is close to the exact nominal confidence level for a small sample size ≤ 25 from a bivariate normal density. For a sample size > 25 both Samiuddin's ts and Fisher's z can be used. In the presence of an outlier (on a minor axis), both Fisher's z and Samiuddin's ts are not affected as long as |p| ≤ 0.3 but are seriously affected when |p&| > 0.3. |
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Keywords: | Correlation coefficient transformations: Fisher Nair Sankaran Ruben Samiuddin confidence interval outlier robustness |
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