About chalk and cheese

Frequency measures.

Frequency measures

The concepts of proportion, ratio and rate are reviewed, as well as the differences between the three frequency measures.

Many times we find things that people insist on mixing and confusing though they are clearly different. This is when we often resort to the saying that they “are like chalk and cheese”, which actually means they are clearly distinct.

Well, in epidemiology we have a clear example of chalk and cheese in the case of the type of most used frequency measures. I’m talking about the mess we form with the terms ratio, proportion and rate.

Frequency measures

Although all of the three are different things, there’s much tendency to confuse with each other, and not only among rookies: there are examples in books of epidemiology of rates that are not so, of ratios that are proportions and anything we want to imagine.

Let’s see them one by one and we’ll see how they are actually like chalk and cheese.


Moving on, we will say that a ratio is the relative magnitude of two quantities of any two variables. It’s calculated by dividing one of the magnitudes (numerator) by the other (denominator), comparing the two in such a way. The key point of the ratio is that numerator and denominator don’t need to be related. Not even they have to be of the same quality of things. We can compare eggs with eggs or chestnuts with people who have an apartment in Albacete (forgive me if I cannot think of an example in which this comparison can be useful).

Ratios can be used for descriptive or analytical purposes. For descriptive purposes they compare men/women participating in a trial, or the ratio of cases and controls, etc. For analytical purposes they can be used to study disease between case and controls, mortality between two groups, etc. Typical examples of ratios are relative risk and odds ratio.


On the other hand, a proportion is a comparison of a part of something in relation to the whole, and can be expressed as a fraction, a decimal number or a percentage. By definition, the numerator must be included in the denominator. For example, the number of obese people who swear they eat little divide by the total number of obese give us the proportion of obese people swearing eating little (usually strikingly higher than expected). If we multiply it by a hundred, we get the percentage.

Proportions also represent the probability of an event to occur, so their values range from zero to one or from zero to one hundred if we use percentages. An example of proportion is the incidence, which represents the risk of getting the disease in a population at a given period of time.

A proportion can be converted into a ratio. You just have to subtract the numerator from the denominator a divide them again. For example, in a study in which 35 men and 25 women participate, the proportion of male participant would be 35/60 = 0.58. But if you want to know the ratio of males to females, it would be 35/(60-35) = 1.4.


The third concept in discord is rate. A rate is a measure of the frequency with which an event occurs in a specific population during a given period of time. Being based the measure of frequency on the size of the population, rates are very useful to compare event frequencies at different times, locations, etc., as well as among populations of different sizes.

Here I want to call your attention to the often misnamed prevalence rate. Prevalence measures the number of individuals in a population who have the disease at any given time. But if you think about it, the sick (numerator) are included in the denominator, so prevalence is actually a proportion and not a rate.

Examples of actual rates would be infant mortality, specific mortality, crude birth rate, etc.

We’re leaving…

And we’re done for today. I will not increase the confusion over that matter with other epidemiological measures with similar names. Because there are more, as the incidence proportion, incidence rate, etc. But that’s another story…

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