Chapter XXI: Section 5: Coefficients of Correlation

As birth controllers rely very much upon statistics, and as figures may very easily mislead the unwary, it is necessary to point out that the Malthusian contention that a high birth-rate is the cause of a high 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
correlation is made with the mortality at each age class:

TABLE II

Under 1 year 0.3647 ± 0.0986
1-19 years 0.4884 ± 0.0816
20-39 years 0.6228 ± 0.0656
40-59 years 0.5028 ± 0.0801
60 years and over 0.2577 ± 0.1001

"A peculiar configuration is observed in these coefficients in that a
quite pronounced positive correlation exists at the central age
group, but disappears with some regularity towards both extremities
of life. If the mortality has any influence upon the natality this
cannot be in the form of replacement of lost infants and deceased old
people, therefore, as has frequently been suggested. That a high
death-rate at the child-bearing age should be conducive to increased
fertility is absurd, neither does it seem likely that a large number
of children should make the parents more liable to diseases which are
prevalent at this period of life. The reasons must, then, be looked
for in a common factor.

"Now the only disease of importance representing the same age-curve as
do the correlation coefficients is tuberculosis. This disease causes in
France 2 per cent. of the deaths under one year, 24 per cent. of the
deaths from 1 to 19 years of age, not less than 45 per cent. from 20 to
39, 18 per cent. at ages 40 to 59, and less than 2 per cent. at the
ages over 60. Will a high tuberculosis mortality, then, be conducive to
great fertility, or do we have to fear that a decrease of the natality
will be the result of energetic measures against tuberculosis? Hardly.
The death-rate may be reduced, then, without detrimental effects upon
the birth-rate.

"What can the factor be which influences both the tuberculosis
incidence and the birth-rate? We know that the prevalence of
tuberculosis is conditioned principally by poverty and ignorance of
hygiene. The Parisian statistics, as compiled by Dr. Bertillon and
recently by Professor L. Hersch, show a much higher birth-rate in the
poor wards than in the richer districts, and the high birth-rates may
be furnished largely by the poorer elements of the population. A
comfortable degree of wealth does not imply a low birth-rate, as is
abundantly shown elsewhere, and one of the important questions which
suggest themselves to the French statistician and sociologist is
evidently the following: How can the intellectual and economic standard
of the masses be raised without detriment to the natality?

"We believe that the time is opportune for solving this question. The
past half-century has been lived under the shadow of defeat and with a
sense of limitations, and of impotence against fate. This nightmare is
now thrown off, and, the doors to the world being open and development
free, the French people will learn that new initiative has its full
recompense and that a living and a useful activity can be found for all
the sons and daughters they may get. The habit of home-staying is
broken by the war, and new and great undertakings are developing in the
ruined north-east as well as in the sunny south." [34]

[Footnote 25: _The Lancet_, 1879, vol. ii, p. 703.]

[Footnote 26: Poverty is a term of wide import admitting many degrees according as the victim is deprived more or less completely of the ordinary necessities in the matters of food, clothing, housing, education, and recreation. As used by Malthusians and spoken of here it means persistent lack of one or more of these necessary requisites for decent living. Vide Parkinson, _Primer of Social Science_ (1918), pp. 225 sqq.]

[Footnote 27: The infant mortality rate is the number of deaths of infants under one year old per 1,000 births in the same year.]

[Footnote 28: See Saleeby, _The Factors of Infant Mortality_, edited by Cory Bigger. _Report on the Physical Welfare of Mothers and Children_, vol. iv, Ireland (Carnegie U.K. Trust), 1918.]

[Footnote 29: _Fifty-fifth Annual Report of the Registrar-General for Ireland, containing a General Abstract of the Numbers of Marriages, Births, and Deaths_, 1918, pp. x, xxix, and 24.]

[Footnote 30: _Eighty-first Annual Report of the Registrar-General of Births, Deaths, and Marriages in England and Wales_, 1918, pp. xxiv, xxxii, and xxxv.]

[Footnote 31: This is also the emphatic testimony of Sir Arthur Newsholme, in his _Report of Child Mortality_, issued in connection with the _Forty-fifth Annual Report of the Local Government Board_ (dated 191?), PP. 77-8.]

[Footnote 32: Knud Stouman, "The Repopulation of France," _International Journal of Public Health_, vol. ii, no. 4, p. 421.]

[Footnote 33: Dr. Major Greenwood. Vide _The Declining Birth-rate_, 1916, p. 130.]

[Footnote 34: _International Journal of Public Health_, vol. ii, no. 4, p. 423.]