CHAPTER X.
CORRELATION: ILLUSTRATIONS AND PRACTICAL
METHODS.
L. Necessity for careful choice of variables before proceeding to calculate r—
2-8. Illustration i: Causation of pauperism—9-10. Illustration
ii.: Inheritance of fertility—11-13. Illustration iii.: The weather
and the crops—14. Correlation between the movements of two
variables :—(a) Non-periodic movements: Illustration iv.: Changes
in infantile and general mortality—15-17. (3) Quasi-periodic move-
ments : Illustration v.: The marriage-rate and foreign trade—
18. Elementary methods of dealing with cases of non-linear regression
—19. Certain rough methods of approximating to the correlation
coefficient—20-22. The correlation ratio,
1. Tae student—especially the student of economic statistics, to
whom this chapter is principally addressed—should be careful to
note that the coefficient of correlation, like an average or a
measure of dispersion, only exhibits in a summary and compre-
hensible form one particular aspect of the facts on which it is
based, and the real difficulties arise in the interpretation of the
coefficient when obtained. The value of the coefficient may be
consistent with some given hypothesis, but it may be equally
consistent with others; and not only are care and judgment
essential for the discussion of such possible hypotheses, but also
a thorough knowledge of the facts in all other possible aspects.
Further, care should be exercised from the commencement in the
selection of the variables between which the correlation shall be
determined. The variables should be defined in such a way as
to render the correlations as readily interpretable as possible,
and, if several are to be dealt with, they should afford the answers
to specific and definite questions. Unfortunately, the field of
choice is frequently very much limited, by deficiencies in the
available data and so forth, and consequently practical possibilities
as well as ideal requirements have to be taken into account. No
general rules can be laid down, but the following are given as
illustrations of the sort of points that have to be considered.
1901
