The Innumerati

Do the numbers add up?

Posted Aug 05, 2020

J. Krueger
Sesame's Count suffered from arithmomania, in a good way.
Source: J. Krueger

She is good with numbers.
President Donald Trump on considering his daughter Ivanka for a job at the World Bank

As humans, we have an innate ability to learn how to understand and speak a language (or more than one). Most, if properly trained, also learn how to read and write. They become literate. There is of course a lot of variability in how well people do it. The question of innateness is tricky. A positive claim usually points to studies showing that infants respond to language before they have had much occasion to practice it (Berent, 2020). Nativists do not claim that all human capabilities are innate, which makes one wonder where the threshold lies. What is the nature of learning that has no innate basis? Is the ability to become literate innate too?

As to numbers, nativists claim that we humans (and some other species) have a rudimentary ability to distinguish between ‘more’ and ‘less.’ We readily see that three peanuts is more than two peanuts, and we come to assign words to these quantities. Numeracy meets literacy. Eventually, some of us do calculus or advanced problems in probability, feats achieved by grafting effortful study onto an innate basis. Can we say that being able to do statistics is an innate capacity? Again, proof of innateness does not require that everyone masters the skill in question. Infants not exposed to human speech will not learn how to speak. Innateness is a readiness; it needs to be activated by the environment (Kimball, Smith, & Quartz, 2013).

Ellen Peters, a distinguished professor at the University of Oregon, studies numeracy (Peters, 2020), and she distinguishes between its subjective and objective variants. Many express confidence in the former. Proof of the latter requires a test. The third element of numeracy, an intuitive number sense, shall not concern us here. It is closest to the innate base and can be assessed with peanuts.

Peters defines objective numeracy as “the ability to understand and use basic probability and mathematical concepts." Peters takes her first example from Lusardi & Tufano (2009), who studied what they called debt illiteracy. I quote from Peters (2020): “You owe $3,000 on your credit card. You pay a minimum payment of $30 each month. At an Annual Percentage Rate of 12% (or 1% per month), how many years would it take to eliminate your credit card debt if you made no additional charges?” Only 35% of the research participants realized that this debt could never be paid off. These were the numerati.

Most problems related to numeracy require an understanding of numbers in the context of other numbers. In the time of COVID, we see struggles with numbers every day. Early on, the number of positive test results dominated the discussion. In time, these numbers were placed in the context of the number of tests performed, the number of lives lost, and the size of the population. These four statistics alone give rise to six second-order statistics, each with its own meaning and relevance. Tracking these first and second-order statistics over time and using various aggregation schemes (such as the 7-day running average) creates more challenges to numeracy and new opportunities for deception.

Initially, the number of deaths over the number of positive tests commanded the most attention. This ratio ignores the total number of tests performed. Early in the pandemic, we saw high mortality rates because it was mostly the sick who were tested. At the limit, everyone would be tested, with the necessary result of a lower mortality rate. The number of tests performed is a statistical nuisance variable. Responsible health professionals want this number to be high, and an exhaustive testing of the population is the ideal.

As testing became more widely available, it has become clearer that the number of deaths over the size of the population is the critical statistic. At the end of the day, the survivors will remember what percentage of the population died. Imagine a history book saying “Eighty percent of those tested died in the great plague of Monte Cassino in 1395.”

The August 3, 2020, interview President Donald Trump gave to Axios reporter Jonathan Swan highlights how treacherous ratios can be to the unprepared. Mr. Trump did not seem to grasp the concept of number of deaths relative to the size of the population — and he dismissed it as irrelevant. He has repeatedly argued that there was too much testing, and he raised this idea again in the interview. If there were fewer tests, however, the number of deaths relative to the number of tests would increase, since it is easier to test less than to die less. The President was – unwittingly, it would seem – proposing a change in testing and reporting that would make the United States look worse in international comparison. Mr. Swan missed the opportunity to point this out.

References

Berent, I. (2020). The blind storyteller: how we reason about human nature: Oxford University Press.

Kimball, M., Smith, N., & Quartz (2013, October 28). The myth of ‘I am bad at math.’ The Atlantic. https://www.theatlantic.com/education/archive/2013/10/the-myth-of-im-bad-at-math/280914/ Retrieved August 5, 2020.

Lusardi, A., & Tufano, P. (2009). Debt illiteracy, financial experiences, and overindebtedness. National Bureau of Economic Research.

Peters, E. (2020). Innumeracy in the wild: Misunderstanding and misusing numbers. Oxford University Press.