The variable accuracy of individual observers makes us distrustful of generalities founded on imperfect reasoning or defective facts, and necessitates the use of figures. Experience tells us that a certain event is to be expected, while the numerical method can tell us how often it is to be expected. We shall discuss later on the application of the numerical method to medical problems, and the difficulties involved in it. It is sometimes said that statistics may be made to prove anything; and no doubt they may be manipulated in such a manner as to make it difficult to detect the fallacies involved in their abuse. But this ignorant or unscrupulous abuse of figures does not discredit their legitimate use, and that they have a very important and perfectly trustworthy application to medical facts will be abundantly shown in the following pages; while at the same time we hope to effectually guard against the errors which many writers have committed, and so help to rescue the subject from that disrepute into which it has undeservedly fallen.

VITAL STATISTICS.

CHAPTER I.

POPULATION.

Requirements of Correct Statistics.-Census Enumerations.-Age and Sex Grouping of Population.-Criticism of Accuracy of Census.-Methods of Estimating Population.-Registrar-General's Official Method.— Instances of Mistaken Estimates.-Estimation from Number of Inhabited Houses.-Estimation from Birth-rate.-Quinquennial Census.— Requirements of a good Census.-Effect of Migration on Population.Population Registers.-Progress of Population.-Economic Value of Population.

T

10 obtain correct vital statistics, it is essential to have (1) a correct enumeration of the population; (2) a complete and accurate registration of births and deaths and other important events in the life-history of individuals, as marriages and sickness; and (3) an accurate statement of the age, sex, and cause of death of each deceased person.

An accurate estimate of population is the first desideratum, for population forms the natural basis of all vital statistics. In comparing different communities, it is necessary to state the deaths and other statistical data in terms of the population otherwise no true comparison can be instituted.

The actual population is known only by census enumerations For the years intervening between two census enumerations estimates of the population are made.

The first census of modern times was taken in the year 1751 in Sweden. In this country the first census was in 1801, and then decennially, the ninth being taken on April 4th, 1881. The first census, in 1801, showed the number of males and females of each house and family, and the occupation, classified roughly as agricultural, trading, and others not comprised under these two heads. In 1821 information was first sought

B

as to ages, but it was left optional whether this information should be furnished or not. The first census which could be described as fairly complete was that of 1851, which was organized under Dr. Farr's supervision. It obtained information as to occupation, birthplace, relationship (husband, wife, etc.), civil condition (married, widow, bachelor, etc.), and the number of persons deaf and dumb or blind. At this census, under the powers given by the Census Act, the precise age at last birthday of each person in the country was first demanded. The accuracy of the information under this head has been impugned; but it is noteworthy that the mean age of females as returned in England exceeds the mean age of males by ten months, so that the tendency of women to understate their ages evidently only operates in comparatively small numbers.

In the census report of 1881 the age and sex distribution of the population of each urban and rural sanitary authority, as constituted that year, was given for the first time. It is now, therefore, possible in these large districts and towns to give the death-rate at each group of ages and in the two sexes separately, a result which, as we shall subsequently find, is of the highest importance (p. 101).

Dr. Farr, many years ago, found that in both the death registers and the census schedules there was a tendency for the ages to be stated in round numbers, as 30, 40, 50, etc. In classifying ages, he therefore adopted the groups 25-35, 35-45, etc., which minimises the effect of such displacement of ages. It would be well if all medical officers of health would adopt the same groups of ages in their annual reports, as comparison of results would be thus rendered possible.

The correctness of census enumerations has been doubted chiefly on three grounds: (1) the infrequency of the census; and (2) the consequent incompetence of the enumerators; and (3) misrepresentations of the enumerated, either from ignorance or wilful misrepresentation. We have already alluded to inaccuracy in respect of information as to age. Such errors are most apt to occur at the extremes of age. They are of greatest importance in the first years of life, infants being often

returned in the census a year older than their true age. The methods of checking these errors will be subsequently described. Infirmities are apt, for obvious reasons, to be understated.

The most serious error, however, occurs in regard to occupations. Master and servant are confused. Thus a watchmaker may mean either the master or a journeyman; and there are similar errors arising from the fact that of those returned under a given occupation, some are actually engaged in it, while others have retired from it.

Each succeeding census, however, is more accurate and complete, and with the advance of education among the masses of the people, the information obtained will become still more reliable.

Estimates of Population require to be made in the intervals between each census and the next succeeding one. Several methods of varying accuracy have been proposed.

1. Theoretically, if we knew the number of births and deaths, and of emigrants and immigrants since the last census, the population in any year could be accurately stated. But an uncertain number of births and a smaller number of deaths escape registration, and although the number of emigrants is roughly known, there is no information as to the number of immigrants into this country.

2. It is assumed that the increase of population in an established country like ours remains fairly constant from one decade to another. Thus, given the population of any town or district in April, 1871 and 1881, and required to find the population, say, in the middle of 1888. The difference between the two census populations divided by 10 will, on this supposition, give the annual increase of population, and this multiplied by the number of years since 1881, and added on to the population of 1881, will give the total population in April, 1888. In estimating death and other rates of a non-stationary population, the mean population of the year must be taken. For the three months between April and June, 1888, therefore, add on one-fourth of the annual increase of population.

Thus,

Popul". in 1881-Popul. in 1871 annual increase of popul".

=

If population in 1871-32,000, and the population in 1881 =36,000, what is the mean population in 1885?

400

4

36,000—32,000—400=annual increase.

10

=100=increase from Easter to Midsummer.

=

400 × 4+100+36,000=37,700 mean population of 1885.

This method of estimating the population, which assumes that the annual increase of population throughout a decade is constant in each year, is necessarily fallacious, as it makes no allowance for the increased number of parents year by year, owing to steadily increasing numbers who year by year attain marriageable years. The error is similar to the assumption that simple interest and compound interest will produce identical results. In simple interest the principal remains constant, and a constant rate of interest would produce a constant actual increase in capital. With compound interest, however, the capital (by addition of principal and interest) becomes greater each year, and consequently the interest itself increases year by year. In other words, with compound interest the rate of interest remains the same, but the principal on which the interest is calculated is increased year by year.

3. The Registrar-General's method is based on the assumption that the same rate of increase will hold good as in the previous intercensal period.

In order to show how this principle is applied, we have to consider the following problem, which, it will be seen, is practically the same as a problem in compound interest, and demands for its treatment an elementary knowledge of the