Judging the relatedness of variables: The psychophysics of covariation detection.

Abstract

Previous research on how people judge the relation between continuous variables has indicated that judgments of scatterplots are curvilinearly related to Pearson's correlation coefficient. In this article, we argue that because Pearson's correlation is composed of three distinct components (slope, error variance, and variance of A") it is better to look at judgments as a function of these components rather than as a function of Pearson's correlation. These three components of Pearson's cor-relation and presentation format (graphical and tabular) were manipulated factorially in three experiments. The first two experiments used naive subjects, and the third experiment used expert subjects. The major conclusions were (a) scatterplots with the same value of Pearson's correlation are judged to possess different degrees of relation if the correlations are based on different combinations of the three com-ponents; (b) with Pearson's correlation held constant, the error variance is the most important component; and (c) graphical formats lead to higher judgments of relat-edness than do tabular formats, with this effect being larger for naive than for expert observers. It was also concluded that attempts to determine the psychophysical function between Pearson's correlation and judgments of relatedness are of ques-tionable value. Although judgments of covariation between dichotomous variables have been studied ex-tensively (see Arkes & Harkness, 1983, for a review), much less attention has been directed toward judgments of covariation between con-tinuous variables. Central to understanding how judgments of the relation between vari-ables are made is the determination of the psy-chophysical function between measurable characteristics of the relation and human judgments of it. Two studies have addressed this question by seeking to determine the psy-chophysical function between Pearson's cor-relations and subjects ' judgments of covaria-