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 a reader of the research literature, my preference is to be able to look at scatter diagrams so I 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 my feeling that researchers should communicate in words what they saw when they looked at their scatter diagrams.
I feel that too many researchers move too quickly from collecting their data to testing their rs 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. I applaud the small number of researchers who take the time to perform this extra step.
(From Chapter 9, p. 221)
Copyright © 2012
Schuyler W. Huck