# How to Describes the Descriptive Statistics in Reseach Paper

**Topics:**Pearson product-moment correlation coefficient, Correlation and dependence, Spearman's rank correlation coefficient

**Pages:**31 (6347 words)

**Published:**December 16, 2012

Human Perception and Performance

1985, Vol. I I , No. 5. 640-649

Copyright 1985 by Ihe Am

=an Psychological Association, Inc.

0096-1523/85/$00.75

Judging the Relatedness of Variables: The

Psychophysics of Covariation Detection

David M. Lane, Craig A. Anderson, and Kathryn L. Kellam

Rice University

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 made is the determination of the psychophysical function between measurable characteristics of the relation and human

judgments of it. Two studies have addressed

this question by seeking to determine the psychophysical function between Pearson's correlations and subjects' judgments of covariation (Cleveland, Diaconis, & McGill, 1982; Jennings, Amabile, & Ross, 1982), and both

found judgments to be a positively accelerated

function of Pearson's correlation. Jennings et

al.'s data were fit well by the function 1 - (1 —

r2)*, and, although this function did not fit the

data obtained by Cleveland et al. quite as well,

We t hank Alma Anorga for her help in conducting Experiment 1. Requests for reprints should be sent to David M. Lane

at the Department of Psychology, P.O. Box 1892, Rice

University, Houston, Texas 7 7251.

the fit was still reasonably good. Thus, although

the precise mathematical f orm of the psychophysical function may be in doubt, the general shape of the function appears to be clear.

Despite this initial success in finding a function of Pearson's correlation that fits h uman judgments reasonably well, it is probable that

some aspects of the j udgment process are

missed when the relation between the variables

is summarized by Pearson's correlation. Specifically, because Pearson's correlation is itself based on the three components of a linear relation between variables (slope, the variance of X and error variance as explained below),

some information about the individual effects

of these components may not be contained in

the function relating values of Pearson's correlation to h uman judgments. The problem of analyzing judgments of covariation in terms

of these three components is similar to the

problem of analyzing judgments of coldness

in terms of the two components of heat loss

(air temperature and wind velocity) in that in

both cases there are underlying components

and a commonly accepted method for combining...

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