Journal Article
The difference between alternative averages
Vaupel, J. W., Zhang, Z.
Demographic Research, 27:15, 419–428 (2012)
Abstract
BACKGROUND
Demographers have long been interested in how compositional change, e.g., change in age structure, affects population averages.
OBJECTIVE
We want to deepen understanding of how compositional change affects population averages.
RESULTS
The difference between two averages of a variable, calculated using alternative weighting functions, equals the covariance between the variable and the ratio of the weighting functions, divided by the average of the ratio. We compare weighted and unweighted averages and also provide examples of use of the relationship in analyses of fertility and mortality.
COMMENTS
Other uses of covariances in formal demography are worth exploring.