Abstract

A Note on the Correlation of Parts with Wholes JOHN J. BARTKO and KAREN D. PETTIGREW National Institute of Mental Health A brief discussion and a figure are presented on the retical interest we mention briefly k = 0 and k = co. product moment correlation p(X, Y) between two vari- We assume the first two moments finite so that u’(X) ables X and Y and its relationship with a corresponding and a’( Y) # co and also allow for at most one variable correlation p (X, Y - X) . to be a constant. Then k = 0 occurs for Y = C(constant) Part-whole correlations have been discussed on numer- i.e. uz (Y) = 0 and u’(X) finite. Consequently Cov(X,Y) = Cov (X,C) = 0, for which we define p(X,Y) = ous occasions. For example, the reader is referred to Snedecor [ 11 and the references contained therein. Part- p(X,C) to be zero and further p(X,Y-X) = p(X,C-X) - - -1. Similarly for X = C ie. u2 (X) = 0, and u’(Y) whole correlations have been dubbed “spurious” but finite then k = co. Cov (X,Y) = Cov (C,Y) = 0 and Snedecor and others maintain that