ON
THE INACCURACIES
WHICH PROBABLY EXIST IN THE
CENSUS RETURNS OF AGES.

By Thomas A. Welton, F.S.S., &c.

Some years ago, before the publication of the third volume of the Census of England and Wales, 1871, I was anxious to calculate the approximate death rates in particular parts of England, amongst females at certain ages, during each of the years 1851–1870.  I therefore applied myself to the preliminary process of estimating the population in each year at the ages in question.

I found that it was not safe to assume that, if population in a given county or district had increased generally, at a certain rate, there had been an increase at each particular age at something like the same rate.  On the contrary, there was a surprising irregularity in the respective rates of increase or decrease observed amongst persons of the several ages in the same population.

Such being the state of the facts, I abandoned all thought of deducing from the total numbers enumerated in 1871 any reliable estimates of the numbers at particular ages, unless indeed some other mode of treatment of the figures could be found leading to more regular results.

On comparing with the population enumerated in 1851 the numbers, ten years older, found to be living in 1861, I obtained other sets of ratios, which are shown in Table II.

The following is a comparison between the proportions for England and Wales, shewn in Table II, and the numbers out of 100 living in 1851 who would have survived in 1861 according to the English Life Table No. 3.

Again, we have reason to believe that some of the children under five years old are returned as being fully of that age, whilst next to none who have attained five years of age would be returned as being younger.  This would account for the dissimilarity of the ratios of survivors at the earliest period of life.

By assuming, as experimental suppositions, that the proportionate errors in the censuses of 1851 and 1861 at each age were equal, and that female emigration and immigration neutralised each other, I obtained a set of corrections of the census enumerations of females which indicated that there was a tendency in the case of young persons under twenty to exaggerate their ages, but that women aged 25–30, and at each successive quinquennial period of life, at least up to 55–60, had a tendency to understate their ages.  There was likewise a certain disposition to return ages in round numbers of years, though this was far less remarkable than in the Irish census of 1851, from which the following figures are taken.

It will be obvious how great the utility of censuses taken at intervals of five years would be, in enabling us to measure more accurately the results of these tendencies to mis-state ages, and particularly the effect of ages being returned in round numbers.

The corrections applicable to the returns of males could not be even approximately determined without taking into account the effects of emigration upon the numbers of that sex.  And as the rates of mortality are subject to considerable variation, year by year, I came to the conclusion that more reliable results must be sought by the aid of—

By the aid of the “English Life Table No. 3” it was ascertained that in a population resulting from births increasing at 1 per cent. per annum, the following numbers would represent the proportions of persons living and dying at high ages:—

From the above table it may be deduced that, supposing persons aged 71–75 call themselves (or are described as being) on an average six months older than their true age, and if after 75 the exaggeration averages an entire year, a very great impression must be thereby made upon the returns.

Having arrived thus far, I thought it would be convenient in the first instance to try whether these suggestions, which I imagine will be deemed moderate and probable, would suffice to explain the apparent influx of aged persons, shown in Table III; and whether other suppositions, not less reasonable, would serve to overcome the remaining difficulties which appear on the face of that table.

Finding it quite impossible to believe in the successive migrations which must have taken place, if this extract from Table III represented the truth, I pursued the enquiry as to what is the alternative of such a belief.

Proceeding to calculate what corrections must be made in the census returns of the numbers of females, if the amended estimates of losses by death and the calculated results of migrations be adopted, I first assumed that each of the three censuses of 1851, 1861, and 1871 might be rendered erroneous by misstatements as to ages in fixed proportions at the several periods of life.

These results require us to believe that, whilst our calculation of the effect of migrations in 1851–60 was near the truth, the similar estimate for 1861–70 was rather beside the mark.  The numbers now required to be substituted, however, appear to me to be acceptable, especially when we have regard to our inability to form any opinion as to the ages of those persons of English birth who returned in large numbers from the United States about the time of the war of secession.

The next thing to do was to ascertain what transpositions of the census figures are involved, in case we accept the numbers shewn in Table IV as being approximately correct.

Table V exhibits these transpositions, and it will be seen that they lead to the conclusions shewn in the following statement:—

As the operation by which the age-returns are to be corrected is essentially one of transposition, I suppress the ratios upon the footing of which I constructed Table IV, and would employ the proportions shewn in Statement A, in applying similar corrections to the population returns in detail.  In the absence of any means of judging what variations there may be in different parts of the country in the extent of the misrepresentations as to ages, I should be inclined to make use of these proportions in every case, though not without apprehending that inaccuracies of some consequence may thus be fallen into.

One more test may be applied before we finally adopt the figures exhibited in Table IV as representing (very nearly) the true female population.  The ratios borne by the population there shewn to exist in 1861 and 1871 respectively, plus emigrants, to the numbers ten years earlier, may be computed and compared with those already shewn, which were derived from the English Life Table No. 3, thus:—

Having thus arrived at a sufficiently near approximation to the truth in the case of females, it remains for us to endeavour to do the same in that of males.  The effect of emigration must be first computed, which may be done thus:—

The above figures are based on an augmented estimate of unregistered male births, to correspond with the increased estimate of unregistered female births used in compiling Table IV.

The total loss or gain of male inhabitants at each age, resulting from the above migrations, might possibly have been as under, assuming the course of events to have been quite unvarying year by year:—

As, however, those who departed in the earlier years of the decennium 1861–70 for the United States, may, to a great extent, have returned home, as well as many of those who had previously left the country, it seems natural to suppose that the emigrants of 1861–70 were, on the whole, much younger than the above Table would shew.

The result of a careful study of the various figures has been to convince me that the ages of male children, as well as those of female children, are overstated.  At the age 15 and under 20 males do not appear to exaggerate their ages so often as females do.  From 25 to 70 there seems to be a general but slight tendency to understate age, to the extent, on an average, of a quarter or at most nearly half a year.  After 70, the same tendency to exaggerate age, which was noticed in the case of females, seems to prevail.

In Tables VI and VII are contained the same approximate facts respecting males, as are furnished by Tables IV and V for our female population.  The figures of all these statements have been arrived at empirically, but so as to involve the most moderate and regular corrections which will meet the difficulties of the case.

The resulting proportions of supposed accurate and inaccurate returns at each age may be thus shewn:—

Shewing the proportions (per cent.) of male population returned at each age, who were really older or younger than represented.