A little follow up to my testosterone comment (written in German):
When three variables are correlated to each other, and two of the three correlations are known, the range for the third correlation is restricted according to this formula (Olkin, 1981):



Now comes the new part: here's the graphical representation of that range restriction:




As one can see, one, or both of the two given correlations have to be fairly high to imply a positive third correlation.


Olkin, I. (1981). Range restrictions for product-moment correlation matrices. Psychometrika, 46, 469-472. doi:10.1007/BF02293804

Tags: statistics

This is the evolution of a bivariate correlation between two questionnaire scales, "hope of power" and "fear of losing control". Both scales were administered in an open online study. The video shows how the correlation evolves from r = .69*** (n=20) to r = .26*** (n=271). It does not stabilize until n = 150.

Data has not been rearranged - it is the random order how participants dropped into the study. This had been a rather extreme case of an unstable correlation - other scales in this study were stable right from the beginning. Maybe this video could help as an anecdotal caveat for a careful interpretation of correlations with small n's (and with 'small' I mean n < 100) …

The evolution of correlations from Felix Schönbrodt on Vimeo.

Tags: statistics