Scatter Diagrams and Tests of Correlations
The easiest way for a researcher to check on these three assumptions [normality, 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, equal variance, and normality assumptions, then the researcher has good reason to suspect that the population is not characterized by curvilinearity, heteroscedasticity, or non-mormality. In that situation, the test on r can then be performed. If a plot of the data suggests, however, that any of the assumptions is untenable, then the regular test on r should be bypassed in favor of one designed for different kinds of data sets.
As a reader of the research literature, my preference is to be able to look at scatter diagrams so I can judge for myself whether researchers' data sets appear to meet the assumptions that underlie tests on r. Because of space limitations, however, such visual displays of the data are rarely included in research reports. 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 believe 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 violations of assumptions. I applaud the small number of researchers who take the time to perform this extra step.
(From Chapter 9 in the 6th edition, pp. 200-201)
Copyright © 2012
Schuyler W. Huck