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Activity Number:
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341
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Type:
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Contributed
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Date/Time:
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Wednesday, August 11, 2004 : 10:30 AM to 12:20 PM
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Sponsor:
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Section on Nonparametric Statistics
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| Abstract - #300745 |
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Title:
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Interval Estimation for Rank Correlation Coefficients Based on the Probit Transformation with Extension to Measurement Error Correction of Correlated Ranked Data
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Author(s):
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Bernard A. Rosner*+ and Robert J. Glynn
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Companies:
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Harvard Medical School and Brigham & Women's Hospital
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Address:
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Channing Laboratory, Boston, MA, 02115,
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Keywords:
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ANOVA ; nonparametric statistics ; nutritional epidemiology ; regression dilution bias
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Abstract:
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The Spearman rank correlation coefficient \rho_S is routinely used as a measure of association between two non-normally distributed variables. However, confidence limits for \rho_s are only available for \rho_s\neq 0 under the assumption of bivariate normality. We introduce an indirect approach based on the use of the probit transformation for obtaining confidence limits for rho_s for an arbitrary bivariate distribution for (X,Y). This will also allow us to test the hypothesis H_0: \rho_s = \rho_0 vs. H_1: \rho_s \neq \rho_0 for arbitrary \rho_0. In some nutritional applications, the rank correlation between nutrient intake as assessed by a gold standard instrument and a surrogate instrument is used as a measure of validity of the surrogate instrument. However, if only a single replicate (or a few replicates) are available for the gold standard instrument, then the estimated rank correlation will be downwardly biased due to measurement error. We use the probit transformation as a tool for specifying a ANOVA-type model for replicate ranked data.
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