What does correlation measure? There is no quick
answer. Typically it is taken to measure "strength
of linearity." That is: given data in a scatterplot,
how close is it to a line. However, there are many
caveats:
The value of the correlation coefficient depends
on the nature of the variability of the variables of
interest. Not just the residual variability (error),
but the marginal variability as well.
Comparing correlations--particularly values that
are close--from unrelated studies is unwarranted. (A
deeper analysis is required.)
A typical "interpretation" of
correlation involves its square, r2, the
coefficient of determination. Fair enough, in the
sense that this value actually measures something.
However, what it measures is not consistent with the
units formulated in the data.
When data in two variables is averaged, the
resulting correlation is larger than it is for the
original data.
