I recently wrote about the three-fold nature of math education. The goal, I wrote should be:

• To give everyone a baseline understanding of numeracy.
• To give everyone at least a few glimpses of genuine mathematical beauty and power.
• To allow those who might want to go on in mathematics-intensive fields like science, computer science, engineering, mathematics, etc. the preparation they need.

Yesterday I was listening to the radio, and happened to hear something that drove home just how important that baseline understanding of numeracy is, and why we need it for an informed electorate.

Exactly what numeracy looks like is a matter of some debate. Some folks argue that numerical literacy is basically achieved by the end of fifth grade—basic fractions, percents, operations, etc. (assuming students have learned what was being taught). Some say you need a deeper understanding of ratio and proportion, or algebra, or even geometry or polynomials, or probability and statistics. The details are important to iron out eventually, but the main point is the numeracy is analogous to literacy. We want students to know how to read, be able to easily read what’s around them, and, ideally, want to read. They may not read James Joyce or Dostoevsky, but inability to read shouldn’t prevent people from interacting with the world and having access to what they’re interested in understanding.

The same is true for math. People need to be able to read what numbers, equations, and statistics are telling them without fear or impediment. They need this for their own lives and future. But they also need it to be citizens.

Why informed citizens need numeracy: Nadine Woodward’s statistical lie

I was listening to the radio recently, and heard an interview with Spokane mayoral candidate Nadine Woodward. I’d heard that some people were skeptical of her proposals to handle homelessness punitively, by forcing homeless people to choose between addiction programs and jail time. But having not heard her speak before, I was curious to listen to her explain what was actually involved with her proposals on homelessness.

Woodward’s experience as a TV anchor was clearly serving her in the interview. She sounded like a paragon of thoughtful policy. She talked about how she came to the plan on addiction programs vs. jail time by exploring what had worked in other cities. But when the interviewer asked her about how her policy would deal with homeless people who weren’t addicted to anything, Woodward delivered a devious lie, a classic of what Charles Seife calls proofiness.

Her answer was that the vast majority of homeless people are addicts, and would hence benefit from being strong-armed into addiction programs. And then she rattled off the following statistics.

• Percentage of homeless people with alcohol addiction: 38%
• Percentage of homeless people with drug addictions: 26%
• Percentage of homeless people with mental illness: 20-25%

Total percentage with any of the above: 84 – 89%. Right? Right?

Wrong.

Can you spot the lie?

The Lie Unpacked

There’s the logical problem, which is that people with mental illness may not belong in the addiction program, but that’s more of a detail from the numeracy perspective. Let’s give her the benefit of the doubt and assume she’s got a program that’s great for addicts of any stripe, as well as people with mental illness.

The fundamental deception lies in the assumption that you can add those percentages together. What Woodward is suggesting that there are three distinct groups: mentally Ill, drug addicts, alcohol addicts.

If every homeless person belongs in at most one of these groups, then you could add the percentages together, since there would be no overlap.

But the picture could be like this.

The assumption here is that every mentally ill person is also a drug addict, and every drug addict also has a problem with alcohol. In this case, only 36% of homeless people would be candidates for Woodward’s proposal. Clearly, this is super unlikely. But it shows the nature of the lie.

Probably the real picture looks something like a classic Venn diagram, with various overlaps. Going to the extremes of no overlap vs. all overlap, we get a sense of the range of possible percentages of homeless people with one or more of these problems. That range, if the original statistics were right, goes from 38% – 89%.

More overlap means a smaller overall percentage of people in any of the categories. So if mentally ill people are more likely to be addicts (a reasonable assumption), we should expect the total of people in all three categories to be smaller in total, since the overlap is larger. Knowing nothing else, I’d estimate the percentage of homeless people in one or more of the three categories is roughly 50%.

And here is the heart of the deception: Woodward commits statistical sleight of hand by adding the percentages up, and claims that about 90% of people are in the category of her program. In actuality, it’s more like half. That’s a huge difference, large enough to call into question her entire program.

More than that, it calls her honesty and integrity into question. This kind of dishonesty is, in a way, the worst sort. It’s based on real facts, but manipulates them to produce counterfeit results. They ring true despite being false. And using statistics like this means that you look at the data, don’t like what it tells you, and use a false version of it to make your case. And just refuting it makes me focus on homeless people who are in the categories she’s talking about, which leaves you with a mental image she’s trying to plant in spite of myself.

The interviewer should have caught this and pushed Woodward on it instantly. Without journalists who can catch these lies in the moment, we rely on a numerate electorate. The only problem is, we’re not there yet. But I hope this example makes the need clear. A numerically literate electorate is vital in order for democracy to function properly.