# 20% Chance of Rain, 100% Chance of Innumeracy

It’s long been a puzzle to me why so many of my fellow commuters carry umbrellas when the weather forecast has called for, say, a 20 percent chance of rain. Me, I figure the odds are 4-to-1 in my favor. I assumed that other people are risk-averse—that is, even a small chance of getting drenched is worth the cost of carrying an umbrella. But a new study suggests something else is afoot: many people have no idea what “20 percent chance of rain” actually means.

Many people think it means that rain will fall over 20 percent of the area covered by the forecast, in which case people commuting to Manhattan from the outer boroughs, New Jersey, Connecticut or Westchester probably figure that they’ll get wet either coming or going, according to **a study led by cognitive psychologist Susan Joslyn** of the University of Washington (in Seattle, where they know something about rain). Others think “20 percent chance” means it will rain for 20 percent of the time period covered by the forecast, she and her colleagues report in the * Bulletin of the American Meteorological Society*. Only about half the population knows that “20 percent chance of rain tomorrow” means “it will rain on 20 percent of the days with exactly the same atmospheric conditions,” Joslyn said.

For their study, the scientists had 450 college students answer questions about probabilistic forecasts of precipitation. Asked how much of the time it would rain on the day being forecast and over what area, only 43 percent of the participants correctly answered, “can’t tell from this forecast.” Only when the participants were shown a forecast explicitly giving the chance of rain (20 percent) and the chance of no rain (80 percent), or a pie chart icon showing the chance of rain (as in this **“probcast” the researchers developed**), did more than half (52 percent) of the students know that the forecast had nothing to do with how much of the time or over what area it would rain.

If you misinterpret a probabilistic forecast to mean that the rain, snow or storm will definitely occur (in some percent of the area or for some percent of the time), you’re more likely to take precautions than if you understand that the event has a less-than-certain chance of occurring. If the precaution is just toting an umbrella, there’s no huge cost. But if it’s evacuating before a hurricane, closing schools before a snowstorm or the like, then the consequences of statistical illiteracy are much greater.