Chapter 8 COMPUTATION OF RATES AND OTHER MEASURES Random variation in numbers of deaths, death rates, and mortality rates and ratios Deaths and population-based rates--Except for 1972, the numbers of deaths reported for a community represent complete counts of such events. As such, they are not subject to sampling error, although they are subject to errors in the registration process. However, when the figures are used for analytical purposes, such as the comparison of rates over a time period or for different areas, the number of events that actually occurred may be considered as one of a large series of possible results that could have arisen under the same circumstances (22). The probable range of values may be estimated from the actual figures according to certain statistical assumptions. In general, distributions of vital events may be assumed to follow the binomial distribution. Estimates of standard error and tests of significance under this assumption are described in most standard statistics texts. When the number of events is large, the standard error, expressed as a percent of the number or rate, is usually small. When the number of events is small (perhaps less than 100) and the probability of such an event is small, considerable caution must be observed in interpreting the conditions described by the figures. This is particularly true for infant mortality rates, cause-specific death rates, and death rates for counties. Events of a rare nature may be assumed to follow a Poisson probability distribution. For this distribution, a simple approximation may be used to estimate a confidence interval, as follows. If N is the number of registered deaths in the population and R is the corresponding rate, the chances are 19 in 20 that 1. N - 2ûN and N + 2ûN covers the "true" number of events. 2. R - 2 R/ûN and R + 2 R/ûN covers the "true" rate. If the rate R corresponding to N events is compared with the rate S corresponding to M events, the difference between the two rates may be regarded as statistically significant if it exceeds 2 x [û of (R1 squared/N1 + R2 squared/N2)] For example, if the observed death rate for Community A were 10.0 per 1,000 population and if this rate were based on 20 recorded deaths, then the chances are 19 in 20 that the "true" death rate for that community lies between 5.5 and 14.5 per 1,000 population. If the death rate for Community A of 10.0 per 1,000 population were being compared with a rate of 20.0 per 1,000 population for Community B, which is based on 10 recorded deaths, then the difference between the rates for the two communities is 10.0. This difference is less than twice the standard error of the difference 2 x [û of (10.0 squared)/20 + (20.0 squared)/10] cmpmor85.doc - Page 1 of the two rates, which is computed to be 13.4. From this, it is concluded that the difference between the rates for the two communities is not statistically significant. cmpmor85.doc - Page 2