Why is statistics so difficult to grasp? We go blank when the conversation turns to statistics, and we turn that cognitive dial in our heads from understanding firmly down to incomprehension. As Meaghan Nolan wrote in an article on the topic, the problem arises, “not because of a lack of ability, but because statistical reasoning is actually incredibly counterintuitive”. Here are a few of the reasons why. We are overconfident: If statistics is all about calculating (un)certainty, then overconfidence mitigates against this. An Ipsos Mori poll in 2016 that measured the gap between perception and reality for a range of issues across 40 countries found that French respondents were most likely to overestimate their country’s Muslim population. The average response in France was that 31% of the population was Muslim whereas the actual figure in 2010 was closer to 7.5%. When asked to project into the future, the average response was that by 2020, Muslims would comprise 40% of the French population. This is in contrast to the Pew Research Center that puts the projected figure at 8.3%. The French are not unique in being overconfident on this particular issue. Australians, Swedes, Canadians and Americans to name a few countries, demonstrated similarly wide gaps between perception and reality.
We jump to conclusions: With so much information coming at us throughout the course of a day, it’s natural that we develop heuristics or simple rules to help us cope. We’ll take a back road without too much thought when our normal route to work looks congested and we’ll avoid certain parts of the city after dark. While this behaviour can be very useful, it’s worth remembering that it’s much easier to form a stereotype than to question it. The head of a large bank who told us with absolute conviction that his bank’s data was too “dirty” to be useful, may have formed this view after receiving a telling off from the regulator after reporting inconsistent numbers. However, is his data really so riddled with inaccuracies that it’s impossible to target customers with greater success than he does at present? Maybe not. We think coincidences are highly unusual. They’re not: You may be familiar with the birthday paradox which works out the probability of two people in a room having the same birthday. It turns out that in a room with 23 people, there is a 50-50 chance that two of them will share the same birthday. With 75 people in the room, the probability that two of them will share the same birthday increases to a near certainty (i.e. 99.9%). Intuitively, we home in on the probability of someone else having the same birthday as ourselves and yes, that’s a pretty small number. The mistake our minds make is to impute that number to everyone else present, when in fact we should be considering that chance over all the possible pairs of combinations in the room. Our intuition can be so wrong: We’ve all smiled at the quote ascribed to British Prime Minister Benjamin Disraeli and made popular in the United States by Mark Twain about there being three kinds of lies, namely, lies, damned lies and statistics. Perhaps it’s not about statistics at all but rather how we interpret facts differently depending on how they are presented to us. As Meaghan Nolan writes in her article, research shows that “people tended to rate a cancer that was described as killing 1 286 in 10 000 people as riskier than when the same cancer was described as killing 24.14 in 100 people, even though the second rate is twice that of the first”. Who you gonna call? When these in-built biases are compounded by ego, hubris and seniority, the risk to businesses of making costly misjudgments can be significant. So when in doubt, call a statistician. Or a data scientist. They’ll tell it to you like it is.