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The Correlation Heuristic: Interpretations of the Pearson Coefficient of Correlation are Optimistically Biased

This research examined the relationship between the Pearson correlation coefficient and the mean absolute differences between paired standard scores. Study 1 compared a theoretically derived relationship between the Pearson correlation values and their corresponding mean absolute differences between paired standard scores, and the corresponding empirical relationship obtained from three databases: self-administered questionnaires, students’, entrance scores and grade point averages, and students’, course grades. The theoretical and empirical relationships were similar for correlation values ranging between 0 and 0.6, reflecting approximately linear relation, with an intercept value of about 1.1 and a slope of about -0.7. Study 2 examined people’,s subjective interpretations of this relationship. Most participants, both undergraduate students and more statistically proficient participants, also estimated the relationship to be linear, though, with an intercept of 1 and a slope of -1. These subjective estimations are systematically biased compared to the theoretical and empirical values, underestimating the mean absolute differences between paired standard scores by 0.10-0.35 for correlation values ranging from 0 to 0.6. The paper discusses the negative consequences of these biased interpretations of the Pearson correlation coefficient and offers possible procedures for their correction.Keywords: Pearson Correlation, biased interpretation of correlation, heuristic thinking

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