On The Graduation of the Rates of Sickness and Mortality Presented by the Experience of the Manchester Unity of Oddfellows during the period 1893–97

Abstract

In considering the various methods of graduation open to us, we were impressed, having regard to the large number of series to be dealt with, by the great facility and rapidity with which formulæ of summation can be applied with the certainty that the results obtained will conform closely to the unadjusted facts. For the Sickness Tables the summation method is especially suitable, since the average number of weeks (or rate) of sickness at any age is necessarily separable for practical purposes into “periods of attack”, e.g., in the case of the Manchester Unity Experience, 1893–97, “First 3 Months”, “Second 3 Months”, “Second 6 Months”, “Second 12 Months,” and “After 2 years”, the successive values of each of which must form a regular series, whilst the sum of any two sections forming a “period of attack” in general use (e.g., First 6 Months = First 3 Months + Second 3 Months) must be equally regular in progression. It is obvious that if a summation method be adopted, and the same formula be used throughout, a combination of any two or more of the graduated series will be itself a graduated series, and will, indeed, be identical with the result of an independent graduation of the combined unadjusted rates.