The core message of a number of books I’ve recently had the great pleasure to read has been fairly simple. Have a look. Check it out. Put your numbers in perspective. In a world awash with statistics and cognitive biases imploring us to cheer mindlessly for our own team, having the skill and wherewithal to step back and carefully ask: “can this really be so?” is golden.
One of recently passed celebrity professor and YouTube phenomenon Hans Rosling’s most profound advice for countering misinformation about the state of the world is precisely this: put all numbers in perspective. Never accept unaccompanied numbers – never believe the numerator without checking the denominator. What matters, as Bryan Caplan never ceases to emphasize as the GMU Economics creed, “are statistics, not emotions – and arguments, not stories.”
But, a statistic may never be left alone, Rosling maintains, but always compared to other relevant numbers. What share of its total category does this statistic represent? What was it last year, 5 or 10 or 20 years ago? Is there some self-evident change in associated behavior that is relevant or ought to explain it? A century ago street cars used to kill and injure hundreds of people every year, but since very few American cities make use of street cars today, the casualty is fortunately much lower. If we keep in mind that miles travelled by cars far outnumber miles travelled by street cars, reporting the number of street car deaths – while probably correct – entirely miss the point when discussing traffic safety. In How Not To Be Wrong, Mathematics professor Jordan Ellenberg quipped
Dividing one number by another is mere computation ; knowing what to divide by what is mathematics.
Here’s another example. If I told you about 23 000 individual deaths and spent a brief 10 second on each of them, going through the list would take me almost three days. On a personal level like that, 23 000 deaths is an absurd, insane, catastrophe-style event that few people are emotionally equipped to handle – essentially the size of my hometown, wiped out in a single year. If I told you those 23 000 deaths were due to antibiotic resistant diseases in the U.S. last year, the pandemic scenarios working through your mind quickly escalate. That many! Let’s find the nearest bunker!
If I then told you that cancer and heart diseases (each!) claim the lives of about 20x that, the fear of lethal apocalyptic germs consuming the world ought to quickly recede. Oh.
Here’s another example. It is entirely correct to point out that the number of people killed in worldwide airplane accidents in 2018 (556 people) was much higher than the year before (44 people) and the year before that (325 people). Would one be excused for believing that air travel is getting more risky and dangerous? Forbes, for instance, ran a roughly accurate story claiming that airline fatalities increased by 900%.
Not in the slightest. The number of fatalities from air travel has been falling for decades, all while the number of flights and miles travelled have increased exponentially, meaning that the per-flight, per-mile or per-passenger risk of death has kept dropping. Not to mention that alternative modes of travelling like driving is magnitudes more dangerous.
While Rosling teaches us to figure out what the base rate is, i.e. putting our statistic into appropriate perspective, one of Philip Tetlock’s tricks for becoming a ‘Superforecaster’ is to use Bayesian updating of one’s beliefs. This picks up precisely where Rosling’s idea left off. Once we know where to start, we have to amass more information, numbers and observations from other points of view – Bayesian updating is a popular method to incorporate and synthesize new information with the old.
In short “Calculation, like logic, is your friend” (Landsburg 2018: 44). Statistics matter and numbers can deceive. In order to better understand our realities and see through mistakes that others make – either intentionally to deceive or persuade, or unintentionally through ignorance – we must embrace the core message of people like Ellenberg, Tetlock, Duffy, Rosling or Pinker.
Always Be Comparing Thy Numbers. Never accept an unaccompanied statistic. Never trust numerators without denominators.