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The unworthy attraction of spurious accuracy

(Photo: Sky UK Limited)
 I was interested to see a press release announcing that Sky News was to begin broadcasting a daily Climate Show, highlighting the latest information on climate change. It is obviously extremely good that a broadcaster is taking climate change seriously, but it looks as if Sky has fallen for one of the oldest problems in the book when it comes to reporting data: spurious accuracy.

I can only guess, but my suspicion is that the show has a bit of a problem with daily reporting on a topic that is changing relatively slowly. There's only so much drama you can put into a slow moving topic, but by making the show daily, Sky would need some impressive graphics, including their huge on-screen display. When I saw this, something leapt out at me. Apparently the average global temperature has gone up by 1.123456789 °C  since 1880. Clearly this was just a test number for the display (though it's a shame it appeared in their publicity photo), but equally it seems likely that they intend to display the increase in average temperature to nine decimal places - presumably so it can dramatically tick upwards during the show. But there's a big problem with this.

The good news is, we know where Sky is getting their data - and it is genuinely impressive that they have an attribution for it on their graphic, pointing to the University of Oxford's Global Warming Index. Even so, nine decimal places seems impossibly accurate for a number that is notoriously difficult to calculate. The Earth is a big place and temperatures around the world at the same time can vary hugely, making the deduction of a realistic value really tricky. The Oxford gang do a great job - there's a good paper here describing how it's done. But the interesting thing is to look at the uncertainty in these figures.

In the 2017 paper, Haustein et al tell us that 'the human-induced warming in May 2017, calculated relative to the period 1850–79*, reached +1.01 °C with an uncertainty range of +0.87 to +1.22 °C (5–95% confidence interval).' This tells us that with a reasonable degree of confidence, the rise was somewhere between 0.87 and 1.22 degrees (though it would not be extremely unlikely for it to be outside that range). The value, then is accurate(ish) to about 0.18 degrees either way. This means that the only safe figure is a 1 °C rise. You could probably push this to 1.0 °C. But any further accuracy is pure fantasy.

A value that shows nine decimal places may look pretty on the screen, but it is hugely misleading to the viewer. You wouldn't be impressed if a courier told you that a parcel would arrive at 10.50am, and when it didn't arrive they said 'Oh, that just means it will come sometime this year.' Yet that's far closer than is nine decimal places to one decimal place. Spurious accuracy can result in all kinds of misunderstandings when it is misinterpreted. It can also backfire on the scientists when they have to revise a value. For example, if the temperature rise were calculated more accurately, it might turn out to be, say, 0.9 or 1.2 - this would make it seem like they were stabbing in the dark when they had apparently previously claimed to know it to such accuracy.

So, please Sky News, consider dropping this feature - or if you must make use of this spurious accuracy, please display the confidence intervals on the display too (and explain them). Otherwise the result will not do climate science any service whatsoever.

* So strictly speaking this is not since 1880, but we'll let Sky off on that one.

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