Estimating Correlations from Single-Sample Distributions of Measurements

Abstract

Abstract The correlation coefficient between two variables (e.g., blood constituents) in normal individuals (or in patients) is usually estimated from measurements of both variables in single samples from the individuals studied. This coefficient is supposed to represent a correlation between the two variables within the average individual. However, unless all the subjects have identical mean values, the "single-sample" coefficient also reflects the correlation of mean values across individuals, generally different from the average intra-individual correlation. Even when both intra-and interindividual correlations are equal, the "single-sample" coefficient underestimates the true intra-individual correlation unless corrected for measurement errors. Using data from normal individuals, two examples are presented: in one case (calcium-total protein), the corrected single-sample coefficient appears to be an unbiased estimate of the desired correlation, whereas in the other example (albumin-globulins), it is quite misleading. These examples support the need for multiple, independent samples from each individual to assure a valid estimate of the average intra-individual correlation between two variables