Mean proportion and population proportion: two answers to the same question?

TLDR: The factors influencing differences between the two formulas and the implications of those differences for reporting and interpreting dietary intake data are discussed.

Abstract: Two different, but equally correct, answers can be given to a question such as "What proportion of the cholesterol that is consumed comes from eggs?" This is because the question can have two different meanings, depending on whether one is referring to the mean proportion of cholesterol from eggs or the population proportion. The mean proportion of cholesterol from eggs for a group of persons is determined by first calculating the proportion of cholesterol from eggs for each person and then taking an arithmetic mean of all the proportions. The population proportion is calculated by summing the amount of cholesterol from eggs for all persons and then dividing that by the sum of the cholesterol from all foods for all persons. These two different formulas often yield similar results. Sometimes, however, the results can be quite different because of variation in the ratio, variation in the denominator, and/or the correlation between the ratio and the denominator. Each of these formulas is designed to answer a specific question: the mean proportion addresses the question about the average per person and the population proportion addresses the question of population intakes. But because either may be used to answer the same general question, confusion may result. This article discusses the factors influencing differences between the two formulas and the implications of those differences for reporting and interpreting dietary intake data.