The effects of sample size and variability on the correlation coefficient

The purpose of the study was to investigate the effects of variability as a function of sample size on the Pearson product-moment correlation coefficient (PCC) under the assumption of a perfect relationship between two variables. The effects of sample size (subjects/trials) and variability on the PCC were demonstrated using a computer model. The model was also used to evaluate selected examples taken from the literature. The results indicated that variability in excess of 10% of the range for each variable resulted in a mean reduction of the shared variance by 50% or greater. Although sample size did not affect the mean PCC, it did have a dramatic effect on extreme percentile values producing unreliable results. These results indicate that a small PCC value can be an artifact of variability. It is suggested, therefore, that one should be cautious when stating conclusions regarding the relationship between two variables without having knowledge of the associated variabilities.