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A General Class of Correlation Coefficients for the 2 × 2 Crossover Design
Author(s) -
Chinchilli Ver M.,
Phillips Brenda R.,
Mauger David T.,
Szefler Stanley J.
Publication year - 2005
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.200410153
Subject(s) - pearson product moment correlation coefficient , mathematics , statistics , correlation coefficient , bivariate analysis , correlation , fisher transformation , sample size determination , partial correlation , geometry
The Pearson correlation coefficient and the Kendall correlation coefficient are two popular statistics for assessing the correlation between two variables in a bivariate sample. We indicate how both of these statistics are special cases of a general class of correlation statistics that is parameterized by γ ∈ [0, 1]. The Pearson correlation coefficient is characterized by γ = 1 and the Kendall correlation coefficient by γ = 0, so they yield the upper and lower extremes of the class, respectively. The correlation coefficient characterized by γ = 0.5 is of special interest because it only requires that first‐order moments exist for the underlying bivariate distribution, whereas the Pearson correlation coefficient requires that second‐order moments exist. We derive the asymptotic theory for the general class of sample correlation coefficients and then describe the use of this class of correlation statistics within the 2 × 2 crossover design. We illustrate the methodology using data from the CLIC trial of the Childhood Asthma Research and Education (CARE) Network. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)