Wednesday, 26 May 2010

Extrapolation to Absurdity

Here is a typical newspaper article using statistics wrongly, this particular article is from The Independent about the number of people who can recognise Winston Churchill. The article describes a study carried out on behalf of the Royal Mint to celebrate 70 years since Churchill became Prime Minister for the first time. People were asked to identify famous 20th Century Prime Ministers and only 19% could not name Churchill but this increased to 32% of 25-34 year olds and 44% of those aged 16-24.

So assuming a linear model and extrapolating beyond the range of the dataset the report predicts that in about 80 years time Churchill will no longer be recognised. This is wrong for two reasons:
  1. The model is unlikely to be linear - the recognition factor is likely to tail off more slowly in the future as there will always be a core of Churchill recognisers that will be above zero (historians and politicians for example).
  2. You cannot extrapolate outside of the experimental range with confidence. So what they could say that in 8 years time the number of 24-34 year olds who cannot recognise Churchill will rise to 44% (those sampled who are now 16-24 and did not recognise him, still cannot do so in the future sample).

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