WS MoreOrLess: What is "rare"?
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What is the main topic discussed in this episode?
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How does More or Less introduce the question 'What is rare' and listener Les Halpin's case?
Hello and welcome to More or Less on the BBC World Service with me, Tim Harford, opening the curtains and letting the light in on the lazy use of numbers. Now, loyal listener Les Halpin recently wrote to us with a question that brought us up short. Les has motor neurone disease, a condition which is both fatal and rare. But rare is a strange word. Here is Les's email, read by an actor.
It struck me that the way we use words is clearly at odds with their precision as numbers. In particular, on TV the other day, a lightning strike on an individual was described as rare, probably 12 strikes per year, three fatal. At the same time, something like motor neurone disease is described as a rare disease with 5,000 sufferers and 1,500 deaths per year. What does rarity really mean?
There's no precise, universally accepted definition of rare. But strangely enough, there is a widely accepted definition of a rare disease. It's a disease that affects fewer than 0.05% of the population, one in 2,000 people. Both the UK authorities and the European Union use that definition. Still, that doesn't quite answer Les Halpin's question. What do we think we're saying when we use a word such as rare? And this isn't a question for a mathematician or a statistician. It's a question for a linguist or a psychologist such as Neil Stewart of the University of Warwick.
What's been done is, I guess it's a first step, it's quite crude. People say questions like, if Tim looks into the urn and sees that there are 30 prize-winning balls and he says there's a good chance of winning, how many balls do you think are in the urn? So if you said there's a good chance, maybe I'll think, well, Tim's an honest person. There are probably 25 balls in the urn. And so we'd interpret that to mean that I understand what you say when you say good chances, meaning 25% chance.
So that's how a psychologist goes about drawing up a list of words and deduces what we're trying to do when we use them. Here's a little sample from Professor Neil Stewart's list.
If we start at the bottom, we've got never, which typically people think means never. 0% chance. We've got the rarely that we're interested in here. That's coming in at an 8% chance. But it's quite variable. So some people who've said rarely actually said they thought 0%. And other people will have said numbers as high as 20%. So we've got never, rarely, seldom, improbable, uncommon, toss-up, which is coming in at 47%. Then we've got predictable, common, frequently, probable, often, likely, usually and always is up there at 94%.
Excellent. So always is twice the chance of a toss-up. Back to Neil Stewart.
The Intergovernmental Panel on Climate Change is one example where they've tried to legislate what words their researchers can use to describe certain events. So, for example, if you say very high confidence as a scientist, you have to mean at least a 9 out of 10 chance. Or if you say medium confidence, you mean a 5 out of 10 chance. And they've got a scale that maps the verbal phrases that we use to describe how confident we are onto sort of a numerical scale of probabilities.
But this is all a bit unsatisfactory, isn't it? I mean, let's say, and this is totally hypothetical, let's say the IPCC says that it's very unlikely that releases of methane from the seabed and from melting tundra will set off an uncontrolled planetary warming that ruins agriculture and condemns half the human race to starvation. In some ways, very unlikely is reassuring. And apparently, very unlikely could mean that there is a 0% chance of this outcome. but according to the IPCC risk lexicon, very unlikely, could also mean a 1 in 10 chance. So perhaps it's wiser for the boffins to stick to hard numbers, percentage probabilities, numbers affected. Then again, perhaps not. Linda Moxie is a senior lecturer in psychology at the University of Glasgow.
She explained that when we say rare, or common, or impossible, these words are doing more than merely conveying numbers imprecisely.
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Chapters
4 chapters
1
What is the main topic discussed in this episode?
0:00–0:13
2
How does More or Less introduce the question 'What is rare' and listener Les Halpin's case?
0:13–6:01
3
What numerical definitions of 'rare' exist for diseases and how are they applied?
6:01–7:49
4
How do psychologists map verbal probability words like 'rarely' to numbers?
7:49–9:26