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Studies on Tests Using Fisher's Tanh −1 Transformation for Spearman's “Rho” and Kendall's “Tau” in Small Samples
Author(s) -
Bennett B. M.,
Choe M. K.
Publication year - 1984
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.4710260609
Subject(s) - mathematics , bivariate analysis , transformation (genetics) , spearman's rank correlation coefficient , covariance , rank correlation , rank (graph theory) , statistics , series (stratigraphy) , correlation , combinatorics , chemistry , biochemistry , gene , paleontology , geometry , biology
A series of papers by F IELLER , P EARSON et al. (1957, 1961, 1962) were concerned with the use of F ISHER'S tanh −1 transformation (= z ) for SPEARMAN'S ‘rho’ and KENDALL'S ‘tau’ rank correlation coefficients. Under the assumption of bivariate normal samples, empirical results on the means and variances for z were obtained. This paper presents results on the z transformation for small samples under a more general trivariate normal model, and reviews the accuracy of the variance and covariance approximations for z , as well as considerations on the resulting power of the tests using the z ‐transformation.