Scatter Diagrams and Tests of Correlations

The easiest way for a researcher to check on these two assumptions [linearity and equal variances] is to look at a scatter diagram of the sample data. If the data in the sample appear to conform to the linearity and equal variance assumptions, then the researcher can make an informed guess that linearity and homoscedasticity are also characteristics of the population. In that situation, the test on r can then be performed. If a plot of the data suggests, however, that either of the assumptions is untenable, then the regular test on r should be bypassed in favor of one designed for curvilinear or unequal variance conditions. As readers of the research literature, our preference is to be able to look at scatter diagrams so we can judge for ourselves whether researchers' data sets appear to meet the assumptions that underlie tests on r. Because of space limitations, however, technical journals rarely permit such visual displays of the data to be included. If scatter diagrams cannot be shown, then it is our feeling that researchers should communicate in words what they saw when they looked at their scatter diagrams.

Consider Excerpts 10.32 and 10.33 [not shown here]. In the first of these excerpts, the researcher reports how she looked at a scatter diagram and found that the data conformed to the linearity and equal variance assumptions. In Excerpt 10.33, a pair of researchers makes reference to the linear characteristic of the scatterplot that was included in the research report. The researchers who conducted these two studies deserve credit for examining their scatter diagrams to check for linearity before computing their correlations.

We feel that too many researchers move too quickly from collecting their data to testing their correlations to drawing conclusions based upon the results of their tests. Few take the time to look at a scatter diagram as a safety maneuver to avoid misinterpretations caused by curvilinearity and/or heteroscedasticity. We applaud the small number of researchers who take the time to perform this extra step.

(From Chapter 10, p. 277-278)