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A mathematical theory is presented which when applied to a comparison of the registrars lists of births and deaths with a list obtained in a house-to-house canvass gives an estimate of the total number of events over an area in a specified period. It also gives the extent of registration. Allowance is made for the fact that the chance of an event being missed on 1 list may not be independent of its chance of being missed on the other list. The theory is applied to an enquiry that was conducted in 1947 over an area known as the Singur Health Center near Calcutta covering the years 1945 and 1946 separately. It is found that the estimated total number of events for the area is usually greater when the estimate is built up by summing the totals for individual groups than when it is computed at once for the aggregated population. This observation according to the theory confirms positive dependence and indicates that the greater figure is closer to the truth. The annual number of births and deaths in the Singur Health Center (total population 64000) is estimated subject to a standard error of from 1-3%. The registration is estimated to vary from about 40-70% with a standard error of about 3%. Higher estimates of the number of deaths were obtained under 3 different approaches to subdividing the population into homogeneous groups. Separate calculations were prepared for each of the 4 political subdivisions comprising the Center for each sex separately and for sex and age groups. In each case the separate estimates obtained for the subpopulations were combined to obtain 3 estimates of the number of deaths for the population of the Center as a whole. The largest estimated number of deaths was obtained using the 3rd approach. This suggests that the subdivision into sex and age groups minimized the correlation of events missed in the 2 data collection systems. (summaries in FRE SPA)
Sekar et al. (Sun,) studied this question.