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On the correlation of a naturally and an artificially dichotomized variable
Author(s) -
Ulrich Rolf,
Wirtz Markus
Publication year - 2004
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1348/0007110042307203
Subject(s) - fisher transformation , pearson product moment correlation coefficient , mathematics , correlation coefficient , correlation , statistics , variable (mathematics) , distance correlation , correlation ratio , random variable , table (database) , mathematical analysis , geometry , computer science , data mining
A method is suggested for estimating the correlation of a naturally ( X ) and an artificially ( Y ) dichotomized variable. It is assumed that a normal random variable ( L ) underlies the artificially dichotomized variable. The proposed correlation coefficient recovers the product moment correlation coefficient between X and L from a fourfold table of X and Y . The suggested correlation coefficient ν is contrasted with the phi correlation and the biserial η. The biserial η was proposed by Karl Pearson and is conceptually related to the new correlation coefficient. However, in addition, Pearson's biserial η invokes the assumption that the marginal distribution of L is normal, which contradicts its basic assumptions and thus does not recover the true correlation of L and X . Finally, an approximation is provided to simplify the calculation of ν and its standard error.