An Uncertainty Principle in Demography and the Unisex Issue

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Abstract
The crude death rate of country A may be less than that of country B even if every age-specific death rate of country A is greater than each corresponding one of country B. This is an example of what statisticians (unjustly) call Simpson's paradox. What holds for death rates holds equally for all other demographic rates. Simpson's paradox can recur, reversing an inequality of rates, whenever an additional variable is introduced into a stratification. Repeated stratification of a finite population (e.g., by age, sex, education, income, region) may eventually produce comparison groups that are too small for a given difference in mortality to be detected. The trade-off between the increased homogeneity of highly stratified comparison groups and the decreased ability to detect small differences in probabilities of death is described here quantitatively by an uncertainty principle, which takes the form of an inequality. The possibility of encountering Simpson's paradox suggests that since sex is only one of many possible stratifying variables that appear to affect mortality, the use of mortality tables distinguished by sex and by no other variables is, in the absence of information about the importance of other variables, demographically arbitrary.

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