Humans are intuitively not good at proportions and other statistical concepts, but those concepts can be taught. They are not, and politicians and partisan news sources use public misunderstanding of these concepts to their advantage.
Washington Post, James Surowiecki, 12 Nov 21: Covid misinformation spreads because so many Americans are awful at math, subtitled, “Two-step calculations are hard enough for some, but assessing vaccine effectiveness requires multiple steps.”
These observations aren’t new — they’ve been around for decades; they came to my attention in college, and then again in James Allen Paulos’ Innumeracy in 1988 — but they’re always apt, perhaps now more so than ever.
What’s often called motivated reasoning is at least partly to blame — people believed something that was mathematically nonsensical because they wanted to believe it. But too many people couldn’t recognize it as mathematically nonsensical. Americans are generally bad at math. A 2012 global study of the math skills of 16-to-65-year-olds found that American adults were less numerate than adults in most other developed countries. On a scale ranking skills from Level 1 to Level 5, with Level 5 the highest, 60 percent of Americans were at Level 2 or below, and almost 30 percent were at Level 1, which meant they struggled with even two-step calculations. That’s a serious problem when it comes to evaluating vaccine effectiveness, since doing so requires multiple steps: looking at what percentage of total covid hospitalizations or deaths are among the vaccinated, looking at what percentage of the population is vaccinated, and then adjusting for that and for age to calculate how much more likely an unvaccinated person is to be hospitalized or die.
And of course, right wing media are quick to pounce on such misunderstandings, and amplify them, because like lawyers they are out to win, not to be right.
Another example of a frequent statistical misunderstanding, or deliberate manipulation, is this confusion between raw numbers and rates.
Some of these tricks are straightforward. When Vermont, which has the highest vaccination rate of any state, saw coronavirus cases rise from a very low base in late summer to a few hundred a day, and saw hospitalizations climb into the double digits, vaccine skeptics didn’t say that Vermont still had some of the nation’s lowest case and hospitalization rates, or that its absolute numbers were still very small. Instead, they said Vermont’s cases were up “10,000%.”
Always beware any story about an alarming percentage increase. Check the raw numbers. They are likely very low. A change from 1 to 2 is a 100% increase.
And so on. A lot of these examples fall under the general description of comparing apples and oranges, implying – often quite deliberately – that two statistics are comparable when they’re actually measuring something quite different. This whole article is a catalog of such examples.
There is no quick fix for innumeracy. But public health officials can help mitigate the problem by being rigorous in their messaging and careful to present data in a clear, comparative way. (Connecticut’s weekly covid reports, for instance, show not just the absolute numbers but also the relative risk of infection and hospitalization for unvaccinated people in an easy-to-understand format.) If they don’t, their mistakes will be weaponized by anti-vaxxers to spread fear, uncertainty and doubt.
What would the US, or the world, be like if the population were actually intelligent and well-versed in concepts like economics and proportions were well understood? What would happen if the entire world’s population were as intelligent and educated as the best of us? (I suspect that, at a minimum, all of our problems would quickly be solved.)
Can we find an example, a subculture, where these things are true…? I’ll explore.