Thomas A. Welton

“ 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. ”

“ 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. ”

“ The actual mortality seems in general to be lower than that shewn in the Life Table, sometimes to the extent of five or six or even nine per cent. If, therefore, we were to compute the numbers of deaths on the basis of the Life Table, the result would be found to exceed the recorded deaths by many thousands. ”

“ On applying to the census figures of 1861 and 1871 for each of the eleven divisions, the proportional corrections shewn in Statements A and B, certain results were obtained, of which the following is an example:—
The final result of the above calculation is a column of differences which, if the rate of mortality in Lancashire and Cheshire exactly equalled that of the nation, would represent the gain or loss at each age on a balance of migrations. ”

“ When the irregular results of Table III for females are compared with the much more probable results shewn in Table IV, and the assumptions by which the latter were arrived at, and through the adoption of which the registered births and deaths, the returns at successive censuses of the numbers of the female population at several ages, and the computed losses by migration have been brought into p. 12close agreement, are considered, I think it will be seen that it is very much safer to adopt my corrections than to rely on the actual returns. ”

“ We should therefore be justified in looking for a certain correspondence between the proportions p. 5of females who might be expected to survive, according to the Life Table, and those proportional figures which represent a comparison of the census figures of 1861 with those of 1851. In point of fact, we discover that, at ages 10–20, the proportions who should survive the next ten years, according to the Life Table, are far exceeded by those who apparently do survive ”

“ Estimates of the loss or gain of population through migrations at each age.
Table III exhibits the results obtained by computing the first and second of these elements, and showing the remaining difference between the two sets of census figures, as the combined result of migrations and errors.
On examining this table, I thought it extremely probable that the numbers of deaths at high ages were exaggerated, because I know of no reason for supposing that the census numbers at such ages are less than the truth; and if they are equal to or more than the real numbers of the living, we are p. ”

“ These ratios, like those obtained from the corrected female population, shew a great deal of regularity, and resemble those derived from the English Life Table very closely, whilst they deviate widely from those based upon the uncorrected census figures. ”

“ 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. ”