The White House is touting that, “The average American family would get a $4,000 raise under the president’s tax cut plan.” This sounds pretty good, right? Who wouldn’t want a tax plan that would put an extra $4,000 into their pocket?
The thing is, of course, that an average tells you nearly nothing about what any particular person will get, or even what most people will get. Suppose that out of 100 people, you give one $400,000 and everyone else nothing. Then everyone has received, on average, $4,000. But it would be folly to think that this would help everyone.
What’s the problem here? What the White House press secretary tweeted could be exactly and precisely true, and yet terribly misleading. This is because statistical thinking is difficult and often quite counter-intuitive. However, being able to understand statistical concepts and, most importantly, common pitfalls in statistical understanding, is necessary to be an informed citizen of the twenty-first century.
A less-misleading measure for understanding the overall benefits of the tax plan is the median, which is the amount of money such that half of everyone receives more and half receive less. Knowing that the average is $4,000 tells us nothing about the median; it could be $4,000, it could be $0 (as in my example above), it could even be negative, if enough people pay more taxes and a few people get enormous tax breaks. But unless you’ve learned about the difference between the regular average (which statisticians call the mean) and the median, it is easy to be fooled into thinking you’ll get an extra $4,000 or so.
Statistical thinking is necessary to understand public affairs and even nutritional advice, and it can be quite tricky to understand properly without training. For example, in 2015 it was widely reported that regularly eating red meat (and particularly processed meats) increases the risk of colorectal cancer by as much as 17 percent each day it is eaten. This seems like quite a high risk, until one considers what this means by comparison with the base rate of the disease, its general prevalence.
The National Cancer Institute estimates that 4.3 percent of people will be diagnosed with colorectal cancer sometime in their lifetime. This means that someone who eats red meat every single day will increase their risk from 4.3 percent to 5 percent over their lifetime. Out of 1,000 people who eat no red meat at all, we would expect around 43 of them to contract the disease, while out of 1,000 who eat red meat every day we would expect 50. Not an enormous difference, and not one likely to impel most people to action.
We ought to institute statistical thinking as a core element of the high school curriculum, with key precursors to be taught in elementary school. A free and democratic society requires a citizenry that cannot be easily swayed by statistical flimflammery.
Shlomo Argamon is a professor of computer science and the director of the Master of Data Science Program at the Illinois Institute of Technology.
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