Psychology of the Scientist: LXIII. Perceiving Scattergrams: Is Visual Line Fitting Related to Estimation of the Correlation Coefficient?

Abstract

Visual line fitting and direct estimation of the correlation coefficient were carried out by 50 subjects using computer-generated scattergrams as stimuli. In visual line fitting, slopes of visual lines were generally greater than the corresponding regression slopes, in agreement with the hypothesis that visual lines are placed so as to bisect the cloud of displayed points at the cloud's major axis rather than to approximate a regression line. Subjects tended to underestimate the correlation coefficient, scaling their judgments of linear structure somewhat more as if they were judging the coefficient of determination. With the actual degree of linear structure partialed out, there were no strong relationships between measures of visual line fitting and measures of estimation. While both of these tasks offer quickly-obtained correlates of linear structure in scattergrams, users should be aware of their biases. We suggest that visual lines do not approximate regression lines very well and estimates of correlation do not approximate the correlation coefficient very well, because the perceptual processes involved perform operations other than regression and correlation. In the present data, these operations appeared to be independent of each other.