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Activity Number:
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406
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Type:
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Contributed
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Date/Time:
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Thursday, August 15, 2002 : 10:30 AM to 12:20 PM
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Sponsor:
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General Methodology
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| Abstract - #301389 |
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Title:
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Moments of the Fisher Transform: Applications Using Small Samples
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Author(s):
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Salma Marani*+ and Rachel Fouladi+ and James Steiger
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Affiliation(s):
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U. T. M. D. Anderson Cancer Center and U. T. M. D. Anderson Cancer Center and University of British Columbia
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Address:
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1515 Holcombe Blvd., Box 243, Houston, Texas, 77030, 1515 Holcombe Blvd, Box 243, Houston, Texas, 77030, U.S.A.
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Keywords:
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Correlation ; Fisher transform ; Moments
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Abstract:
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This paper presents a theoretical development that extends the known theory on the distribution of the sample correlation coefficient and the Fisher Transform (Fisher, 1921). Several well-known correlational procedures use the Fisher Transform or its square as the basis of hypothesis testing. These procedures assume that the variance of the Fisher Transform can be approximated adequately as 1/(n-3). We present results that demonstrate that, for small sample size, this is not necessarily true. Exact moments of the Fisher Transform and its square are computed for both null and non-null correlations. An extension of the classic series expansion formulae of Hotelling (1953) for the moments of the correlation coefficient and the Fisher Transform are derived for both the null and non-null case and compared with the exact moments of the Fisher Transform. Monte Carlo experiments are used to demonstrate how these formulae may produce significant improvements in the small sample performance of tests for pattern hypothesis on correlation matrices.
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- The address information is for the authors that have a + after their name.
- Authors who are presenting talks have a * after their name.
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