Ratios can be used to depict the value of one variable divided by the value of another. A proportion, often expressed as a percentage, is a kind of ratio that can be used to represent the value of a single variable for one class divided by the value for all classes combined.
Whenever multiple ratios are involved—either across many individuals in a group or over numerous days of intake for each individual—analysts can use different ways to summarize them, and these different calculations can lead to different answers. This is because the calculations involve both summation and division, and an elementary principle of mathematics dictates that the order of these operations matters. The mathematical properties of ratios are the same, whether one is considering simple ratios, proportions, or percentages.
In survey analyses involving multiple dietary recalls per person, consideration of which kind of summary ratio to use must be made at both the group and individual levels.
At the group level, two different, but equally correct, answers can be given in response to the question “What proportion of the calcium that is consumed comes from milk?” This is because the question can have two different meanings:
Whenever ratios involve the division of one variable by another—both of them, by definition, free to vary—these two ratios can be different from one another.
Ratio of Means
The ratio of means is used to answer questions such as, “How much of all the calcium consumed by the group comes from milk?” It is calculated by summing the amount of calcium from milk for all persons and then dividing that by the sum of the calcium from all foods for all persons. The answer would be the same if both the numerator and denominator were divided by a constant, such as the sample size. Therefore, it can also be calculated by dividing the group’s mean amount of calcium from milk by the group’s mean total calcium, and for this reason it can be thought of as a ratio of means.
The ratio of means yields information about the diet of the population as a whole because both the numerator and the denominator are computed for the whole population before the ratio is derived. That is, the whole population has only one aggregate value and the distribution of the ratio among members of the population is not available. However, the ratio of means can be obtained for various subgroups in the population, if comparisons are warranted. The ratio of means has been employed to identify important sources of nutrients in the US diet as a whole and to examine diet quality using to the Healthy Eating Index-2005.
Mean Ratio
The mean ratio is used to answer questions such as, “What is the group’s daily contribution of milk to calcium intake?” It is determined by first calculating the proportion of calcium from milk for each person and then taking an arithmetic mean of all the proportions. Often, the mean ratio is similar to the ratio of means; however, sometimes they are quite different, depending on the variability in the ratio, variation in the denominator, and the correlation between the ratio and the denominator.
The mean ratio requires that a ratio be calculated for each person before averaging