THE SPURIOUS CORRELATION OF RATIOS THAT HAVE COMMON VARIABLES - A MONTE-CARLO EXAMINATION OF PEARSONS FORMULA

Pearson (1897) investigated correlations of ratios of bone measurement s and found that although the correlations among the original measures were low, the correlations among ratios with common measures were abo ut .5. To understand this result, he developed an approximate equation for the correlations of ratios. In the present study, Monte Carlo met hods were used to show that Pearson's equation is fairly accurate and that correlations among ratios with common elements (e.g., X/C, Y/C) a re indeed at least partly spurious, as Pearson concluded. This finding should serve as a two-fold warning to those who might correlate ratio s that have common elements: (a) Interpretation of the observed relati onship between such ratios may at best be tenuous, and (b) the relatio nships among the elements themselves may call into question the useful ness of addressing a hypothesis that can be tested only with a correla tion between ratios that share elements.