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 correlationcoefficient. In this article,we argue that becausePearson's correlation is composed of three distinct components (slope, error variance, and variance of X) itisbetterto lookat judgments asafunctionof these componentsratherthan as a function of Pearson's correlation. These three components of Pearson's correlation and presentation format (graphical and tabular) were manipulated factorially inthree experiments.Thefirst two experimentsused naive subjects, andthethird experimentused expertsubjects.The major conclusionswere (a) scatterplots with the same value ofPearson's correlationare judged to possessdifferent degrees of relation if the correlations are based on different combinations of the three components; (b) with Pearson's correlation held constant, the error variance is the most important component; and (c) graphical formats lead to higher judgments of reiatedness than do tabular formats, with this effect being larger for naive than for expert observers.It wasalso concluded that attempts todeterminethe psychophysical function between Pearson's correlation and judgments of relatedness are of questionable value.