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Saturday, October 8, 2016

A Modest Proposal: Teach Basic Statistics in High School

Here's a modest proposal: teach basic statistics in high school. To be sure, many of us fear statistics. This, however, is ironic since most of us use them every day, whether we are discussing sports (e.g., batting averages, passer ratings), the economy (e.g., inflation, gross national product), how we or our children are performing in school (e.g., grade point averages, SAT scores), or the weather (e.g., temperature, wind chill factor). As the economist Charles Wheelan notes:
Students will complain that statistics is confusing and irrelevant. Then the same students will leave the classroom and happily talk over lunch about batting averages (during the summer) or the windchill factor (during the winter) or grade point average (always)… the same people who are perfectly comfortable discussing statistics in the context of sports or the weather or grades will seize up with anxiety when a researcher starts to explain something like the Gini index, which is a standard tool in economics for measuring income inequality.
However, we don't have to seize up with anxiety when learning statistics. Most are relatively easy to understand once they're explained, and while no measure is perfect, statistics allow us to capture a lot of information in a simplified form. More importantly, when they are applied to complex phenomena, they can help us separate the wheat from the chaff, genuine associations from spurious correlations, and actual evidence from selective anecdotes. And in a world where much of what passes for informed debate tends to rely more on the cherry picking of data than the dispassionate analysis of it, statistics can help.

So, let's teach our high school students basic statistics. It doesn't have to be a complete class. It can be a 6-week module of a mathematics course. But doing would help us avoid much of the nonsense we read in the papers, hear in the media, and so on, something that has been especially true during this election season.

Take, for instance, the reaction to polls taken after the first presidential debate. Polls by Morning Consult, YouGov, CNN, and Public Policy Polling (PPP) all found that viewers believed Hillary had won the debate. Trump supporters quickly fired back pointing at polls from TIME, the Drudge Report, and others that showed that Trump had won. The difference? The Morning Consult, YouGov, CNN, and PPP polls are scientific polls, while the TIME and Drudge Report polls are not. For example, the latter allow individuals to vote more than once and don't even try to survey a random sample of voters, a condition that is necessary in order for a survey to be reliable. It is instructive that surveys taken later in the week which showed that Hillary enjoyed a 2-3 bounce after the first debate all but confirmed the results of the scientific polls ("Election Update: Early Polls Suggest A Post-Debate Bounce For Clinton").

The idea behind random sampling is fairly straightforward (although it is hard to pull off). If done correctly, everyone has an equal chance of being surveyed. It is similar to stirring a pot of vegetable soup before tasting it. If we stir it adequately, then a spoonful should give us a pretty good idea how the rest of soup tastes. If we don't and all of the vegetables still lie at the bottom of the pot, then a spoonful won't tell us much at all.

Of course, even random samples seldom get it exactly right. However, statisticians have shown through what is known as the central limit theorem that repeated random samples tend to cluster around the correct answer (also known as the population mean), which is why averaging polls can tell us quite a bit about how people are thinking. It also should make us cautious about cherry picking the results of a single survey. Unfortunately, that's what we often do.

All of which brings us back to why we all should teach statistics in high school. Doing so won't entirely cure the human tendency highlight results that confirm our biases. But it may help us be a little more aware of them. And it may help us engage in more meaningful discussions about the world around us.

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