Mathematical misconceptions

As an old math teacher, I was more than a little concerned by some of the comments I saw on a stats-driven story we ran in the paper today. Because the misconceptions I saw in the comments are fairly common — and because some of my former students read this blog — I thought it might be worthwhile to address a couple of the more egregious examples here, for the benefit of anyone who has slept since freshman algebra.

Misconception 1: If you don’t have data for the full year, any conclusions you draw based on that data are statistically invalid.

Reality: Full-year stats are nice to have, but as long as you’re comparing apples to apples, you can draw meaningful conclusions without them. If I compared an 11-month period in one year to full-year data for another year, my conclusions would be invalid. But if I compare an 11-month period in one year to the same 11-month period for several preceding years, I can make valid comparisons even if I don’t have that twelfth month.

Misconception 2: If numbers look bigger, they are.

Reality: Not necessarily. Remember fractions? Ratios? Decimals? Let’s look at some examples:

1/2 is bigger than 1/3, and 1/3 is bigger than 1/4.

If your odds of something happening are 1 in 14 (which can also be expressed as 1:14 or 1/14), then that thing is more likely to occur than if your odds of it happening are 1 in 18 (1:18 or 1/18).

At least one reader didn’t understand that. He was convinced that even though the number of crimes in a given jurisdiction had gone down from one year to the next, the crime rate — expressed in the article and accompanying chart as a ratio of crimes to population, reduced to lowest terms — had gone up. I assume he drew this conclusion by looking at the second number in each ratio. Since that second number got bigger, he thought that meant the crime rate was going up.

These folks aren’t alone in their confusion. A lot of people don’t understand how stats work — which makes them easy targets for unscrupulous people who do.

You shouldn’t trust stats blindly, because they can be manipulated, and people can make mathematical errors. But you don’t have to be afraid of them, either. Statistical data can be incredibly useful, but it’s hard to use a tool if you don’t know how it works.

Emily

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