Beware of big percentage changes on a trivial base

One of the oldest tricks in the statistician's book - and one of the most common big mistakes made by people in general and journalists in particular - is to overstate the importance of an apparently large percentage change which represents a small absolute change on a small starting number.

If last year four people in the USA suffered from a rare disease, and this year six people had it, that is a scary-sounding 50% increase.

But measured as a percentage of people in the USA, it's an increase of about one millionth of a percentage point.

(If I had used used the UK instead of the USA as my example, that would have been about four millionths of a percentage point.)

As Scott Adams put into the mouth of his Dilbert character, "Are you expecting a roomful of engineers to get excited about a big percentage increase in a trivial base?"

Engineers, economists and accountants have seen this kind of trap so often that we are slightly less prone to fall into it, but a lot of people do.

There is a funny but all too apposite article up on The Daily Mash" website at the moment called

"Britons impressed by big percentages."

If you understand the first three paragraphs of this post you will probably find the Daily Mash article which I have linked to above very amusing.

If you are not completely clear on why I wrote that a 50% increase could also be an increase of one millionth of a percentage point, you should probably read the Daily Mash article because the humour in the article might help you to understand something rather important about percentages.

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