On The Nonintuitive Nature Of The Correlation Coefficient: Subjective Estimation Of Three-Variable Relations

The misleading character of the correlation coefficient was investigated in two studies of intuitive statistical behaviour: subjective estimation of partial correlation and subjective estimation of the minimum possible correlation between two variables given their equal correlation with a third. Fourteen Psychology Department faculty and graduate students provided estimates of partial correlations, r[SUBxy.z'] for varying positive values of rxy and rxy = ryz. Mean estimated rxy.z values were uniformly lower than theoretical (actual) values. Twenty-four statistics students and sixteen Statistics Department faculty and graduate students furnished estimates of minimum possible correlations, min rxy' for varying positive values of rxz = ryz. For both samples mean estimated min rxy was higher than the theoretical (actual) min rxy. Thus, in both studies, subjective overestimated the degree of influence on the correlation between two variables, X and Y, of a third, constraining variable, Z. The Hazards of intuitive statistical inference in the interpretation of correlational data are are discussed.