How high can a correlation coefficient be? Effects of limited reproducibility of common cardiological measures.

In clinical studies the linear correlation coefficient is commonly used to quantify the strength of the association between two variables, such as height and weight: the value of r indicates whether the relationship is a strong one. However, actual clinical data includes an underlying physical variable plus an inevitable measurement error component that represents the reproducibility of the test used. If test reproducibility is poor, then even if the underlying physical variables are perfectly correlated, the actual observed correlation coefficient cannot be one but must be somewhat less. We present a method for calculating the reduction in correlation coefficient due to limited reproducibility, and discuss its implications with respect to experimental design and interpretation.