Human Perception and Performance
1985, Vol. I I , No. 5. 640-649
Copyright 1985 by Ihe Am
=an Psychological Association, Inc.
Judging the Relatedness of Variables: The
Psychophysics of Covariation Detection
David M. Lane, Craig A. Anderson, and Kathryn L. Kellam
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 correlation 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 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 relatedness 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 questionable value.
Although judgments of covariation between dichotomous variables have been studied extensively (see Arkes & Harkness, 1983, for a review), much less attention has been directed toward judgments of covariation between continuous variables. Central to understanding how judgments of the relation between variables are
References: Arkes, H. R., & Harkness, A. R. (1983). Estimates of contingency between two dichotomous variables. Journal of Experimental Psychology: General, 112, 117-135. Brehmer, B. (1973). Single-cue probability learning as a function of the sign and magnitude of the correlation Brehmer, B., & Lindberg, L. (1970). The relation between cue dependency and cue validity in single-cue probability learning with scaled cue and criterion variables. Organizational Behavior and Human Performance, 86. 331334. Cleveland, W. S., Diaconis, P., & McGill, R. (1982). Variables on scatterplots look more highly correlated when the scales are increased Eade, S. (1967). The effect of 'magnitude of 'criterion validity and positive cue validity upon human inference behavior. Erlick, D. E., & Mills, R. G. (1967). Perceptual quantification of conditional dependency. Journal of Experimental Psychology, 73, 9-14. Garner, W. E. (1974). The processing of information and structure Jennings, D. L., Amabile, T. M., & Ross, L. (1982). Informal covariation assessment: Data-based versus theorybased judgments. In D. Kahneman, P. Slovic, & A. Naylor, J. C, & Domine, R. K. ( 1981). Inferences based on uncertain data: Some experiments on the role of slope Uhl, C. (1966). Effects of multiple stimulus validity and criterion dispersion on learning of interval concepts. Received June 1, 1984 Revision received May 17, 1985