i.e. the possibility of error = ·0746 to unity or 7·46 per cent. In other words, in a second series of cases of enteric fever under the same conditions as the above, the fatality may vary from 3·94 to 18·86 per cent., a vague result which indicates that the first series cannot be regarded as establishing more than a primá facie case in favour of any special method of treatment that may have been adopted.
Non ceteris paribus.—The necessity that data to be compared shall be collected on a uniform plan, and be of a strictly comparable nature, is very frequently ignored. The conclusion that the administration of a given antiseptic is a valuable means of treating enteric fever is not demonstrated by the fact that the fatality in the series of cases thus treated is 7 per cent., while in another series treated without antiseptics it is 14 per cent., unless it is shown that the age and other previous conditions of the patients in the two cases were not widely different, and unless the series are sufficiently long to avoid the fallacy due to paucity of data.
Errors from the Composition of Rates.—If the death-rate of A having a population of 10,000 is 10 per 1000, and of B having a population of 20,000 is 15 per 1000, the combined death-rate is not (10 + 15) ∕ 2 = 12·5. To obtain the correct combined death-rate, the number of deaths in A (=100) and in B (=300) must first be ascertained, and the death-rate on a population of 30,000 in which 400 deaths occurred will then be found to be 13·3 per 1000.
Errors from Stating Deaths in proportion to Total Deaths.—There is nothing erroneous per se in stating the proportion of deaths at one age as a ratio of the total deaths at all ages, or the deaths from one cause as a ratio of the total deaths from all causes. It is a useful and in fact the only method practicable when it is required to give the proportion of one of these to the other. But beyond this, such a ratio cannot be trusted. For instance, the proportion of fatal accidents among male infants is 12·2, and among female infants 25·1 per cent. of the total fatal accidents in the male and female sex respectively. But it would be erroneous, if it were concluded from these figures that female are more subject to fatal accidents than male infants. The only conclusion that they justify is that at higher ages females are much less subject to fatal accidents than males. In actual facts, for every 1000 infants born, only 2·9 female as against 3·1 males die under one year of age as the result of accident.
Again, suppose the case of two towns, A and B. A with a population of 10,000 has 150 annual deaths, of which 20 are caused by cancer; the general death-rate therefore being 15, and the death-rate from cancer 2·0 per 1000, while the deaths from cancer form 2 ∕ 15 of the total deaths. B, with the same population as A, has 300 deaths, its death-rate being 30 per 1000, and 40 deaths from cancer, its cancer death-rate being 4·0 per 1000; while the proportion of the deaths from cancer to the total deaths is 2 ∕ 15 as before. It is useful to know in regard to each of these individual communities that cancer causes 2 ∕ 15 of its total mortality, but no comparison between the two is practicable on this basis. The only proper comparison is between the death-rate from cancer per 1000 of population in A and B, which shows that it is twice as high in B as in A. A still more accurate method is to ascertain the number of deaths from cancer, and the number living at different age-groups, thus avoiding any errors due to variations in age and sex distribution of population.
Errors as to Averages.—The most common of these results from paucity of data (page [349]). Note that the results obtained from an average cannot be applied to a particular case. The mean duration or expectation of life, obtained from a life-table, expresses with almost mathematical certainty, the number of years of life of the members of a community taken one with another, but is often not accurate when applied to a single individual.
In Army statistics errors have arisen by failure to comprehend what is meant by the average strength of a force. The statistics must comprise the lives of a given number of persons as well as the deaths occurring among them for an entire year, or allowance must be made in this respect when required.
Hospital statistics for similar reasons are frequently fallacious. Thus death-rates have been frequently given per 100 occupied beds, which are most misleading, as the frequency of succession of patients as well as the nature of the patients’ complaints will vary greatly in different hospitals. The only proper method of stating hospital-returns is on the basis of the aggregate annual number of cases treated to a termination. The cases should be further subdivided according to age and sex and disease. Average death-rates for epidemic diseases when used to compare one community with another may give rise to erroneous conclusions. This is inseparable from the nature of such diseases. During the period under comparison, one town may happen to have, say, three epidemics, and the other four; possibly if two or three additional years had been added to the series, the place of the two towns would have been reversed as regards their average death-rate from the disease in question. The proper plan is to give the death-rates from the epidemic disease for every year recorded, to draw a curve of these death-rates for the two towns on the same scale, and to compare the height, the variations of height, and the trend of the curve in each instance.