18.9 per 1,000; to find the average death-rate for the other twenty-seven towns:

5,115,352

=

20.5.

Fallacies arising from Stating Deaths in Proportion to Total Deaths. These have already received consideration (pages 100, 111, 168). They present themselves under two heads. The deaths at one age are stated in proportion to the total deaths at all ages; or the deaths from one cause are stated in proportion to the total deaths from all causes. In both cases the same fallacy is involved. A relationship is attempted to be established between two factors, both of which are variable in value. An alteration in the total deaths on one hand, or in the deaths at one group of ages or from one cause on the other hand, might equally affect the proportion between the two, though the conclusions to be drawn in the two cases would by no means be necessarily identical.

We may add a further illustration of this fallacy, furnished by Mr. (now Sir Edwin) Chadwick's address to the Association of Sanitary Inspectors (August, 1888). He stated that among the gentry and professional persons the deaths of children under five years of age in Brighton formed 8.93 per cent. of the total deaths, while among the wage-earning classes they formed 45.44 per cent. From these facts he would infer that the conditions of life for persons of the upper classes are about five times

(45.44)

8.93

as favourable among the well-to-do as among the poor.

Such a conclusion is by no means warranted by the facts. The numbers dying at different ages among two populations, cæteris paribus, vary with the number living at the same ages; so that with the greater population under five among the poor we should expect a higher percentage of deaths under five than among the well-to-do. Unless we know the relative population under five in each case, we are not justified in drawing any conclusion from the preceding figures. This instance may serve to emphasize what has been previously said as to the importance of stating the deaths at any group of ages in terms of the number living at the same group of ages, and not as a percentage of the total deaths.

The same authority, in the address alluded to, gives another comparison which is equally fallacious. For the wage classes in Brighton the mean age at death, he states, is 28-8 years, for the well-to-do 63 years. The facts that the poor have a much larger number of children than the rich, and that the rich are largely formed of persons who began life poor, but have gradually worked their way into comfortable circumstances, are entirely ignored in this erroneous method of comparison between the two classes.

These examples illustrate the importance of the method first formulated by Mr. Milne, that the total deaths must be stated in proportion to the total number living, and that this method must be applied at each group of ages. They also illustrate the importance of a complete and accurate knowledge of the age (and sex) constitution of the population, a subject which has been repeatedly dwelt on in this book, and which forms the keynote to the rational interpretation of Vital Statistics.

124,580

124,530

APPENDIX II.

Mortality and Sickness Experience of the Ancient Order of Foresters Friendly Society for the Five Years, 1871-75 -Males (Neison).