AH YES, statistics. The temptation to start any discussion of this subject with the aphorism popularised by Mark Twain is almost overwhelming. “Lies, damned lies, and…” You know the rest.
We can’t afford to be that dismissive. Statistics is the science of drawing informed conclusions from large amounts of data. In a sense, then, it is modern science. From trials of the latest wonder drug to the discovery of the Higgs boson, breakthroughs that advance human knowledge are these days seldom made without someone somewhere applying statistical reasoning. And as those bits of knowledge filter down to the rest of us, we are increasingly expected to make decisions – from the political to the medical – on the basis of numbers with that confidence-inspiring suffix “per cent”.
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Trouble is, few of us do that sure-footedly. Sample sizes, false positives and the difference between absolute versus relative numbers are among the factors that affect how we interpret statistics. Often, they are impossible to extract from a bare number.
It’s a systemic problem. “There are large numbers of experts – not just laypeople – who have no training in statistical thinking,” says of the Max Planck Institute for Human Development in Berlin, Germany, and author of Risk Savvy: How to make good decisions. “Children are taught the mathematics of certainty: algebra, trigonometry, geometry and the like. That’s beautiful but often useless.”
For a complex and risky world, he reckons we need a different type of preparation. “We should be taught uncertainty,” he says. And that needn’t be so difficult. For Gigerenzer, there are a few golden rules we can apply to sharpen our reasoning.
The first is to understand that there is no such thing as certainty, and that looking for it is an illusion. “There are risks everywhere and you need to quantify them,” says Gigerenzer.
The second is to look for statistics that encapsulate absolute numbers, not relative ones. Say you read that popping a certain pill will reduce the risk of having a stroke by 50 per cent. This relative number means nothing if you don’t know how likely you are to have a stroke in the first place. If that absolute number is 3 in 1000, a 50 per cent reduction will take it down to 2 in 1000 – a puny decrease.
You still might consider the pill worth taking. But wait for Gigerenzer’s third rule: always look for the other side of the story. If told about a pill’s supposed benefits, for instance, also ask about its potential risks – and make sure both are presented in the same, absolute terms. “I don’t want to know whether a drug reduces something by 50 per cent,” says Gigerenzer. “I want to know if half take it and half don’t, what happens five years later.”
In the medical arena, the same reasoning should raise a mental red flag whenever you read of a test being so-and-so per cent accurate – a meaningless figure unless you also know the test’s false-positive rate (see diagram). Similarly when “survival rates” for a certain condition are quoted or compared: this is a relative measure that can vary considerably depending on how a condition is diagnosed and tested. What you want to know is the mortality rate, an absolute figure that tells you what proportion of the population will die of the condition over a certain period.
Such rules can help anywhere you see a number with statistical trapping. They have their limits – for example when someone has wilfully cherry-picked their data or otherwise massaged the figures. But they are a good start in sorting out a damned lie from a statistic.
Expectant mothers are usually offered a test in early pregnancy to estimate the risk of their unborn child having Down’s syndrome. This takes into account an ultrasound scan, a blood test and maternal age. Those considered at high risk will be offered a further test, which involves taking a sample of the amniotic fluid or the placenta. The example shown here refers to the first trimester test only and is adapted from Risk Savvy: How to make good decisions. Always discuss the results of any medical tests with a healthcare professional.
Like this? Read: “Get smarter: 9 ideas to make your life better”
(Image: Bruno Mangyoku)
This article appeared in print under the headline “Need to know: Statistics”
