Accuracy of Correlation Coefficient with Limited Number of Points

Abstract

This study was designed to determine the minimum number of points required for continuous scaled variables before the Pearson product moment correlation coefficient (PPMCC) ceases to be an accurate estimate of their original correlation coefficient. The study was performed on samples from normal, exponential, and uniform distributions by using Monte Carlo techniques. After the PPMCC was determined for each sample, multiple grouping procedures were applied and the PPMCCs were recalculated to determine the effect of scaling on the correlation coefficient. The results showed that the PPMCC obtained by using transformed discrete ordinal-level variables tended to underestimate the true parameter. The minimum number required for precise PPMCC is five and the use of PPMCC with five or more points is recommended.