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. 277278)
