Defining Per Capita, Rates, and Comparisons

Percent change in a value tells you only part of the story when you are comparing values for several communities or groups. Another important statistic is each group's per capita value. This figure helps you compare values among groups of different size.

Let's look at Springfield and Capital City again. This year, 800,000 people live in Springfield while 600,000 live in Capital City. Five years ago, however, just 450,000 people lived in Springfield while 550,000 lived in Capital City.

Why is this important? The fact that Springfield grew so much more than Capital City over the past five years could help explain why the number of murders in Springfield increased by so much over the same period. After all, if there are more people in a city, one might expect there to be more murders.

To find out if one city really is more dangerous than another, you need to determine a per capita murder rate. That is, the number of murders for each person in town. (That's what "per capita" means. It's Latin for "for each head.")

To find that rate, simply divide the number of murders by the total population of the city. To keep from using a tiny little decimal, statisticians usually multiply the result by 100,000 and give the result as the number of murders per 100,000 people.

In Springfield's case, 50 murders divided by 800,000 people equals a murder rate of 6.25 per 100,000 people. Capital City's 50 murders divided by 600,000 people equals a murder rate of 8.33 per 100,000 people.

Five years ago, Springfield's 29 murders divided by 450,000 people equaled a murder rate of 6.44 per 100,000 people. And Capital City's 42 murders divided by 550,000 equaled a murder rate of 7.64 per 100,000 people.

In the previous section, we found that the number of murders in Springfield increased 72 percent over five years, while the number of murders in Capital City grew by just 19 percent. But when we now compare per capita murders, Springfield's murder rate decreased by almost 3 percent, while Capital City's per capita murder rate increased by more than 9 percent.

There's the real story.

Remember when I wrote about school test scores? That's another example of how reporters can miss stories when they don't make apples-to-apples comparisons with data. It's just not fair to call schools serving poor students "failures" compared to schools with mostly of wealthy families, when family poverty is the number-one factor affecting test scores. You've got to account for family income when comparing student test scores across schools and districts. In the same spirit, figuring crime stats, economic data and other community characteristics as per capita numbers, instead of using the raw numbers of incidents, can help you make the apples-to-apples comparisons that allow you to report truthful information to your readers.

Read the rest of Robert Niles' Statistics Every Writer Should Know.

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© Robert Niles

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