272 THE MISMEASURE OF MAN
tion to one dimension. Arm and leg length are tightly correlated
because they are both partial measures of an underlying biological
phenomenon, namely growth itself.
Yet, lest anyone become too hopeful that correlation represents
a magic method for the unambiguous identification of cause, con-
sider the relationship between my age and the price of gasoline
during the past ten years. The correlation is nearly perfect, but no
one would suggest any assignment of cause. The fact of correlation
implies nothing about cause. It is not even true that intense corre-
lations are more likely to represent cause than weak ones, for the
correlation of my age with the price of gasoline is nearly 1.0. I
spoke of cause for arm and leg lengths not because their correla-
tion was high, but because I know something about the biology of
the situation. The inference of cause must come from somewhere
else, not from the simple fact of correlation—though an unex-
pected correlation may lead us to search for causes so long as we
remember that we may not find them. The vast majority of corre-
lations in our world are, without doubt, noncausal. Anything that
has been increasing steadily during the past few years will be
strongly correlated with the distance between the earth and Hal-
ley's comet (which has also been increasing of late)—but even the
most dedicated astrologer would not discern causality in most of
these relationships. The invalid assumption that correlation implies
cause is probably among the two or three most serious and com-
mon errors of human reasoning.
Few people would be fooled by such a reductio ad absurdum as
the age-gas correlation. But consider an intermediate case. I am
given a table of data showing how far twenty children can hit and
throw a baseball. I graph these data and calculate a high r. Most
people, I think, would share my intuition that this is not a mean-
ingless correlation; yet in the absence of further information, the
correlation itself teaches me nothing about underlying causes. For
I can suggest at least three different and reasonable causal inter-
pretations for the correlation (and the true reason is probably some
combination of them):
- The children are simply of different ages, and older children
can hit and throw farther. - The differences represent variation in practice and training.
Some children are Little League stars and can tell you the year that