Although I found George Hammond's treatment of R-squared
enlightening I believe that the argument has to do more with the
strength of a correlation rather than with causality in the usual
sense. (I get the impression that "physical causation" has a
connotation here unknown to me and perhaps well known in physics.)
Determination of causality is a procedural problem, not a
mathematical problem. Significant t-tests and F-test do not
guarantee causality any more than significant correlations do.
To demonstrate causality, the experimenter must show that applying a
variable generates an effect and removing the variable eliminates
the effect--like flipping a light switch. Correlations usually show
only that two variables vary dependably together. Although this is
insufficient to demonstrate causality, it may suggest investigating
procedures that will demonstrate causal efficacy. The failure to
demonstrate causality is not due to the application of correlation,
it is due to the lack of proper procedure.
The argument which George Hammond is pursuing seems to have to do
with the strength of a correlation. Is a correlation as small as 0.35
large enough to indicate a real relationship even if it is
significant? There are interesting arguments on both sides of this
issue.
Milton Steinberg, Ph.D.
Associate Professor in Psychology
Marymount College, 1365
Tarrytown NY, 10591
