First we need a bit of vocabulary -- what we call some of the kinds of rates or proportions that we commonly talk about in public health. Last time, I said that "rate" and "proportion" basically mean the same thing, and they do; but we tend to use them in slightly different contexts. We can say that:
A “rate” means the proportion of a population which either 1) has some characteristic at a given time, or 2) to which some event occurs during a given period.
In public health, a “population” normally means some defined group of humans – but in statistics, a “population” can consist of anything, and sometimes our units aren’t people – they might be hospitals, or procedures, or laboratory rats, for example.
To compute a proportion, divide the number of “cases” (people with the characteristic) by the total population of interest. If you have 18 people, and 3 of them have nose rings, the nose ring proportion is 3/18=.167=16.7%. As I said last time, all three ways of writing it mean exactly the same thing.*
There are two major kinds of rates:
Prevalence means the proportion of people who have the characteristic at a specific point in time. So, in our group of 18 people, the prevalence of nose rings is .167, or one out of six if you prefer.
The incidence is the proportion of people who acquired the characteristic within a specified period of time. Usually, it's calculated for a calendar year, but it certainly doesn't have to be! If it turns out that 2 of our 18 people already had nose rings as of January 1, 2009; and 1 of them got a nose ring for the first time during 2009, the incidence of nose rings for 2009 is 1/18=.055555555555555555555 and on to infinity which we would probably round off as .056 or 5.6%. Next time, I'll use 20 people with a prevalence of 5 nose rings and an incidence of 2 so you'll get nice simple fractions and snappy finite decimals. But the idea is the same. And now I'm going to write a dreaded formula!
# of people who
When we write formulas we like to save space by using short symbols in place of long phrases so we might write this as:
where R=number of people
*3/18 happens to be the same as 1/6, and one sixth can't actually be written as a decimal because it would be infinite, so 1.67 or 67% is only a close approximation. Not worth worrying about.