DISTRIBUTION DEPENDENT CORRELATIONS: A MATHEMATICAL PRINCIPLE UTILIZED IN PHYSIOLOGY, OR CORRELATION BIAS?

In many studies, we may raise the question of whether relative amounts of particular variables are positively or negatively associated, but investigations specifically focusing upon this issue seem hard to find.  Previously, we reported some general rules for associations between relative amounts of positive scale variables. The main research question of the present work was: How are correlations between percentages of the same sum brought about? One particular feature of such correlations seemed to be that distributions (ranges) of the variables were crucial for obtaining either positive or negative correlations, and for their strength, suggesting the name Distribution Dependent Correlations (DDC). Certainly, such correlations might cause bias. However, previous findings raise the question of whether DDC might have a physiological relevance as well.  In the current work, we extend and systematize theoretical considerations, and show results of computer experiments to test the hypotheses. Finally, we briefly mention a couple of examples from physiology. The results seem to support the idea that true, within-person distributions of the variables are crucial for obtaining positive or negative correlations between their relative amounts, raising the question of whether evolution might utilize DDC to regulate metabolism.