ABSTRACT. The authors describe and illustrate 6 factors that affect the size of a Pearson correlation: (a) the amount of variability in the data, (b) differences in the shapes of the 2 distributions, (c) lack of linearity, (d) the presence of 1 or more "outliers," (e) characteristics of the sample, and (f) measurement error. Also discussed are ways to determine whether these factors are likely affecting the correlation, as well as ways to estimate the size of the influence or reduce the influence of each.
Key words: correlation, errors, interpretation, Pearson product-moment correlationCORRELATION IS A COMMONLY USED STATISTIC in research and measurement studies, including studies conducted to obtain validity and reliability evidence. Understanding the meaning of a simple correlation is key to understanding more complex statistical techniques for which the simple correlation is the foundation. In basic statistics courses, students typically learn about the conceptual meaning of "relationship" between two variables (including size and direction), how to calculate and interpret a sample correlation, how to construct scattergrams or scatterplots to graphically display the relationship, and how to conduct an inferential test for the significance of the correlation and interpret the results. What is often missing in class discussions and activities, however, is a focus on factors that can affect the size of the statistic based on the characteristics of the correlation or the particular dataset used for the calculation of the correlation. Without a solid understanding of these factors, students and researchers