## Percents and percentage points

This is another “fun with math” post meant to impart simple math knowledge that could make the world a better place.

If you aren’t a statistician/math aficionado/empirical economist, you’ve probably never thought about what a “percentage point” is or how it’s different from a “percent”. Frankly, I hadn’t either until one of my advisers in graduate school asked if I was reporting results in percent or percentage points. The realization that there was a difference was eye-opening. Basically, a “percentage point” is always out of 100, whereas a “percent” is always relative to some baseline rate. We can also think of percentage point as telling us something on an absolute scale and a percent as telling us something on a relative scale.

Let me give you an example of why it matters. What sounds scarier, if I tell you that your probability of getting into a fatal car crash is **50 percent** higher when driving over the speed limit or if I tell you that your probability of getting into a fatal car crash is **0.5 percentage points** higher when driving over the speed limit? Chances are, the first one sounds a lot worse. But the 50% number is relative to some baseline crash rate, which is probably very very low (maybe 1 in a million if we’re talking about a day’s worth of driving). So multiplying that by 1.5 still leaves you pretty safe. By contrast, raising your risk of a fatal car crash by 0.5 percentage points brings it from 0.0001% to 0.5001% - more than a 5000% increase! (By the way, “%” usually refers to “percent”. If you want to talk about percentage points, you should just write it out.)

Why should you care about this difference? Because it’s often helpful to know differences in percentage points rather than percent, especially when it comes to rare events. For example, the risks of birth defects rise dramatically in *percent/relative* terms with the mother’s age, but the *percentage points/absolute* changes are actually pretty small. According to this page, 20 year old women have about a 0.19% chance of having a baby with some chromosomal anomalies, whereas 40-year-old women have a 1.52% chance. If you calculate the percent increase in risk, it’s huge, almost 800%. But the percentage point change is clearly much smaller, just 1.33.

Moral of the story - as a rule of thumb, if you want to scare or impress someone, use percent. If someone is trying to scare or impress YOU, ask them what the percentage point/raw difference is.