Odds are we should teach probability and statistics


Among the many educational reforms that I think we ought to enact in the United States, and probably throughout the world, one of the most useful would be to begin teaching all students about probability and statistics.  These should be taught at a far younger age than that at which most people begin to learn them—those that ever do.  Most of us don’t get any exposure to the concepts until we go to university, if we do even there.  My own first real, deep exposure to probability and statistics took place when I was in medical school…and I had a significant scientific background even before then.

Why should we encourage young people to learn about such seemingly esoteric matters?  Precisely because they seem so esoteric to us.  Statistics are quoted with tremendous frequency in the popular press, in advertising, and in social media of all sorts, but the general public’s understanding of them is poor.  This appears to be an innate human weakness, not merely a failure of education.  We learn basic arithmetic with relative ease, and even the fundamentals of Newtonian physics don’t seem too unnatural when compared with most people’s intuitions about the matter.  Yet in the events of everyday life, statistics predominate.  Even so seemingly straightforward a relation as the ideal gas law (PV=nRT, relating the volume, temperature, and pressure of a gas) is the product of the statistical effects of innumerable molecules interacting with each other.  In this case, the shorthand works well enough, because the numbers involved are so vast, but in more ordinary interactions of humans with each other and with the world, we do not have numbers large enough to produce reliable, simplified formulae.  We must deal with statistics and probability.  If we do not, then we will fail to deal with reality as accurately as we could, which cannot fail to have consequences, usually bad ones.  As I often say (paraphrasing John Mellencamp) “When you fight reality, reality always wins.”

If people—by which I mean most people, preferably all people—understood basic probability, and the statistics that go along with it, many tragedies could be minimized and possibly avoided.  Perhaps the most glaring example is the problem of air travel versus driving.  We hear about airline disasters, and they terrify us.  Yet the reason we hear about them—the reason they become newsworthy—is because they are vanishingly rare.  They fall into that old cliché of journalism: “‘Dog bites man’ isn’t news, but ‘man bites dog’ is.”  The statistical rarities make headlines precisely because they are rarities.  According to the World Bank’s data, as quoted in The Telegraph, in 2016 the risk of death per passenger trip in air travel worldwide was less than 1 in 11,000,000.  There were only 325 reported deaths worldwide that year, which was admittedly a relative low, but typical years still produce only about four to five hundred deaths worldwide.  Four to five hundred may sound like a lot, but when we compare it to the thirty to forty thousand traffic-related deaths annually in the United States alone, we see that the statistics are very much in favor of air travel.  Most people worry far more about flying than about a run to the grocery store in the family car—and this is a serious mistake.  Unfortunately, car crashes fall into the “dog bites man” pattern and are so common that we rarely hear about them.  Also, the deaths are spread out over a large number of people and a huge area.  Yet, those numbers mean that an average of about eighty people die in car crashes in the US every day.  Why are no political movements afoot promoting speed regulators on all new cars, or the automatic disabling of phones when one is driving, or stricter punishments for DUI’s, or even fitting breathalyzers into the ignition for all cars?

I’m not necessarily endorsing all those changes (though it’s hard to see how one could be ethically against them at first glance), but it’s interesting to view a contrasting case that demonstrates our failure to understand statistics and probability.

Roughly a month ago, a mass shooting occurred in a school a few miles from where I live, and seventeen people were killed.  This was an atrocity, and every one of those deaths is a tragedy, but the event, and its coverage, wildly skews public understanding and focus regarding gun violence.  Though mass shootings are terrible, and we should certainly strive to prevent them, they catch our attention partly because they are a case of “man bites dog.”  All the mass shooting deaths combined in any year add up to a fraction of a percent of total gun-related deaths (which are roughly comparable to the traffic-related deaths, at thirty to forty thousand a year, and two-thirds of which are suicides).  It’s certainly worthwhile to reduce the chances of mass shootings, all other things being equal, and it’s reasonable to debate whether “assault rifles” should be more restricted than they are, but even if we were to eliminate that problem completely, we would not have made a noticeable mark on gun-related deaths.  In this case, conservatives calls for the improvement of national mental healthcare might actually do more good (though they were not focused on suicide, nor, as far as I can tell, were they motivated honestly to improve the overall problem of gun violence).

It’s interesting to see how statistics, even when used to convey legitimate points, are used inconsistently, and are overwhelmed by emotional and ideological reactions.  As a case in point, I have seen quite a few memes put out by various left-leaning sites, arguing—accurately—that the risk of terrorist violence to a given American is vanishingly small, and is hardly a priority when compared with other, much greater risks to which we are regularly exposed.  Yet these same sources—sometimes within the same discussion—will argue against “assault weapons” as being the scourge of America and cite mass-shootings as the national emergency (despite the facts I noted above).  I don’t think these people are disingenuous.  I think they really care, and have strong, well-intentioned feelings about these subjects, but those feelings swamp their statistical understanding, partly because that understanding is woefully limited.

When I was in medical practice, I used to tell my patients who played the lottery that they should never make a special trip just to buy a lottery ticket, because their odds of winning were almost certainly lower than their odds of dying in a car crash on their way to or from the store.  It’s hard for people to recognize this because humans don’t naturally think in a statistical fashion; it requires training to do so, but that training can equip us to have a much better grasp of reality.  If the public were better trained in statistics and probability, they would, for example, be much less frightened by the listed side-effects at the end of every pharmaceutical ad, or at least would be able to avail themselves of the deeper data and to more reasonably decide whether using a given drug would be likely to have for them greater benefit than cost.

Similarly, though much of the anti-vaccine movement is couched in flagrant pseudoscientific nonsense and silly ideology, its purveyors would find themselves faced with a far more difficult persuasive task if the general public had the savvy to recognize that the rate of even mild side-effects of a typical vaccine are far lower than the rate of suffering and complications from the diseases against which they help to protect us.  An average of about 36,000 Americans die yearly from influenza.  In comparison, only roughly 2000 cases of vaccine-related complications (the total from all vaccines, not just flu vaccines) are reported every year, fewer than a tenth of which (100 to 200) are fatal.  None of these deaths can definitively be said to have been caused by the vaccine, because the source of the reporting is not controlled.  Likewise, there has literally been no correlation (let alone causation) found between vaccination and autism, this despite exhaustive research, prompted partly by public reaction to (now known to be) spurious data and to such mental giants as Jenny McCarthy.

Understanding of probability and statistic could lead to the significant diminution, if not the disappearance, of much magical thinking that plagues us.  It could discourage at least some people from wasting their hard-earned money on gambling.  It could lead to improved voter insight into numerous public-policy issues, and thus to better electoral and legislative outcomes.  Perhaps more importantly, it could simply lead more people to have a better, more accurate, understanding of the wonderful world in which we find ourselves.

I think we should begin to teach probability and statistics as soon as students have mastered the basic tools required to deal with the subjects—before teaching trigonometry or calculus, possibly before teaching geometry, and certainly before students have left their required mathematics courses.  It needn’t be dry subject matter.  The basics can be taught, and directly experienced, using in-class examples of coin flips and dice rolls, in which students participate, doing multiple trials and comparing their individual outcomes with the expected numbers, pooling results to show how a greater number of samples gives a general increase in accuracy.  This could be a real case of hands-on learning leading to real, practical understanding of how the world works, in the best tradition of science classroom demonstrations.  A relatively simple grasp of statistics would help the average student at least to have a general understanding of why, if they flip a fair coin ten times, they will only have about a 25% chance of getting five heads and five tails.  They may not be able to do the pertinent calculations at the drop of a hat, but at least they will understand the reason for this seemingly counterintuitive fact.

Of course, this teaching would require that the teachers understand the subject matter, and would probably entail recruiting more mathematically literate teachers into the educational community, which would probably involve offering better salaries to teachers, and would thus require more money put into education.  These are subjects for another post; I strongly endorse all of them, and they would be well worth their cost.

Greater statistical literacy might be the beginning of greater insight into the data with which we are all regularly met, and give us the ability to see through fear-mongering headlines such as the one stating that 90% of people have a gene that increases their risk of high blood pressure (printed in response to a discovery that, in a studied population, roughly 10% of people had a gene that protected them from hypertension).  We might also be less frightened by statistics* that say a daily fry-up for breakfast increased the risk of pancreatic cancer by 20%…because we would better understand the data that shows the baseline risk is quite small, and that 20% of that is even smaller.

Many such insights are possible.  It’s difficult to predict in what ways and to what degree the increased knowledge of statistics and probability would improve our lot, but improvement in knowledge, all other things being equal, tends to lead to improvement in decision-making.  Even if it didn’t, a better understanding of the nature of reality is, almost always, a wonderful thing.

*Described in an excellent episode of the BBC Radio 4 program The Infinite Monkey Cage, starring Brian Cox and Robin Ince.

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