## Archive for the ‘Numbers & statistics’ Category

### The sky fell on me head

September 23, 2011

The ‘bits of satellite might fall on your head’ story that has been all over the news this week (see e.g. the Telegraph here) has provided a nice chance for people to get the wrong end of the statistical stick.

For instance, as I was having the last of my breakfast this morning I heard the BBC Today programme bods responding to emails and texts. Paraphrasing:

“In response to messages, we should make clear that it ISN’T a 1 in 3200 chance that you personally will be hit by a bit of falling satellite. It is a 1 in 3200 chance that someone, somewhere will be hit by some debris. The chance of it being any one particular person are millions and millions to one”

Which is, of course, the exact inverse of the lottery logic used to sell you tickets. The chance of you, personally, winning the lottery is many millions to one against. But the lottery company advertising plays strongly upon the idea that SOMEONE has to win:

“It could be you”….

…but only if you’ve bought a ticket. Or better still, several tickets – that’ll be five pounds, please.

The point is that they are deliberately playing on many people’s tendency to have trouble distinguishing logically between the odds of a rare event befalling somebody, and the odds of it befalling you in particular.

(BTW, for the satellite example, MSNBC have a discussion of where the numbers come from here).

Mind the reindeer

The mention of satellites falling to earth always reminds me of a famous story about “risk perception”, and one that I  sometimes use when teaching the medical students. The version that I know appears in Michael O’Donnell’s entertaining compendium Medicine’s Strangest Cases. I’ve told this one before on the blog, but it seems apposite here.

The story was that debris from a satellite in a decaying orbit was predicted to fall in an remote area of Lapland that was virtually unpopulated save for a few nomadic reindeer-herders. The Swedish Govt. offered to helicopter airlift the reindeer herders out of the area, at significant cost to the Swedish taxpayer.

Hermann Bondi, a famous British mathematician and Government science adviser, heard the story, crunched the numbers and confirmed that the probability of any reindeer herder who stayed put having the satellite land on them was several orders of magnitude less than the chance they would be killed in a helicopter crash on a routine helicopter flight.

So the Swedish Govt’s decision was plain daft.

Well, that depends.

Purely on the statistics, it was a wholly illogical decision. But Bondi pointed out that the Swedes had undoubtedly factored in that if they didn’t offer to evacuate people, and the satellite then landed on someone, the headlines would scream

“Heartless and negligent Govt leaves reindeer herders to die”.

While if a chopper crashed, the headline would be

“Tragic helicopter crash kills herders”

– and the Govt. would be off the hook.

The point being that it was less about the actual risk of events, and more about how people felt about both the event and the risk of it, and who was to be held responsible.

And also, looking at it from a 2011 perspective, how media reporting plays a major role in what things people worry about, and how much

Anyway, given the above, I dare say that the people hoping most fervently that the satellite debris splashes down harmlessly in an ocean somewhere are the men from NASA.

Perceptions not risk. Unfortunately.

Finally, there is another interesting point about people’s differing perception of the risks of different kinds of rare event.

Though the Today programme has obviously had some worried callers this morning, I dare say that relatively few people will be altering their actual behaviour much due to fretting about being hit by a bit of  communications satellite falling from the sky.

Similarly, the finite risk of a plane crashing does not seem to put the vast majority of people off travelling on airplanes.

But then compare the number of people – some of them among the parents at my kids’ school – who seem to believe that the exceedingly small risk of adverse events following vaccination is a good reason for not having their children vaccinated.

Risk, and perception of risk.

It’s a *****

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Update – Sat 24th: the reports are now telling us the satellite probably came down ‘somewhere over the Pacific’. Wonder if any of the bits will turn up on land?

Update – Sun 25th:  reports are still suggesting the debris probably fell into an ocean, with none reported on land. An amusing sequel is that someone apparently hoaxed some of the Canadian media with a video clip purporting to show the satellite burning up other Northern Canada.