death-rate is not only contrary to reason and to facts, but is also
contrary to the very figures which they quote. A high birth-rate is often
associated with a high death-rate, but a general or uniform correspondence
between birth-rates and death-rates has never been established by modern
statistical methods. To these methods brief reference may be made. A
coefficient of correlation is a number intended to indicate the degree of
similarity between two things, or the extent to which one moves with the
other. If this coefficient is unity, or 1, it indicates that the two things
are similar in all respects, while if it be zero, or 0, it indicates that
there is no resemblance between them. The study of correlation is a first
step to the study of causation, because, until we know to what extent two
things move together, it is useless to consider whether one causes the
movement of the other; but in itself a coefficient of correlation does not
necessarily indicate cause or result. Now in this country, between 1838 and
1912 the birth-rate and the death-rate show a correlation of .84; but if
that period be split into two, the correlation from 1838 to 1876, when the
birth-rate was fluctuating, is _minus_ .12, and in the period after 1876
the correlation is _plus_ .92. This means that the whole of the positive
correlation is due to the falling of the death-rate, and that birthrates
and death-rates do not of necessity move together. [33]

After a careful examination of the vital statistics for France, Knud
Stouman concludes as follows:

"In France no clear correlation exists between the birth-rate and the
death-rate in the various Departments. The coefficient of correlation
between the birth-rate and the general death-rate by Departments
(1909-1913) was 0.0692+-0.1067, and including Alsace and
Lorraine--0.0212+-0.1054, indicating no correlation whatsoever. A
somewhat different and more interesting table is obtained when the