There's an advertisement running on TV at the moment for a loan company. In it someone wants to borrow £70 for five days and is told it will only cost him £9.20. So he can get the £70 today and five days later he can pay back £79.20. It's pretty clear and it's up to the student whether he borrows it or not. Less clear, though stated in the print at the bottom of the screen, is that this equates to an annual percentage rate of 2689%. So if he doesn't pay back his £70 for a year it will have become £1882. After two years it would be more than £50,000. Of course it's very unlikely that the loan company wouldn't intervene rather more quickly than that.
This is an example of how language can be used to hide mathematical facts. It's actually rather unusual in that an absolute figure is being used to hide a percentage. Much more common is the other way round, especially in the press and even more especially in reporting of science.
We routinely see instances in the press of quoted figures along the lines of "eating x causes a 25% higher risk of cancer"* and this, as it is stated, is entirely meaningless. The figures are usually abstracted from scientific papers which have details of exactly what the quoted figure means and how it was derived but the newspapers very rarely bother with that because good science doesn't make for good sound bites.
What they do when quoting statistics like this is use the "relative risk increase" which is a very misleading figure. What they need to do is quote the "absolute risk" or the "absolute risk increase".
In the example above 25% sounds quite dramatic but if the sample size was 1000 and in the population not eating X four developed cancer while in the sample eating X five did then the absolute risk has has gone from 0.4% to 0.5% an "absolute risk increase" of 0.1%, or one in a thousand, which isn't even statistically significant compared to the background level.
This 0.1% is EXACTLY the same information as the previous 25% but described using a much less dramatic, and much more easily understood, figure. Words and mathematics sometimes make very uneasy bedfellows, especially when mediated by the people with a vested interest - be it the vested interest of a loan company wanting to make money or a journalist wanting to sell papers.
(*Incidentally I chose this example because one of the books I read , Ben Goldacre's excellent Bad Science, suggested facetiously that the newspapers are engaged in a process of dividing every substance on Earth into two groups - ones that cause cancer and ones that cure it, in the case of at least one of our National papers in the UK we get an X causes/cures cancer story, pretty well every week.)
This is an example of how language can be used to hide mathematical facts. It's actually rather unusual in that an absolute figure is being used to hide a percentage. Much more common is the other way round, especially in the press and even more especially in reporting of science.
We routinely see instances in the press of quoted figures along the lines of "eating x causes a 25% higher risk of cancer"* and this, as it is stated, is entirely meaningless. The figures are usually abstracted from scientific papers which have details of exactly what the quoted figure means and how it was derived but the newspapers very rarely bother with that because good science doesn't make for good sound bites.
What they do when quoting statistics like this is use the "relative risk increase" which is a very misleading figure. What they need to do is quote the "absolute risk" or the "absolute risk increase".
In the example above 25% sounds quite dramatic but if the sample size was 1000 and in the population not eating X four developed cancer while in the sample eating X five did then the absolute risk has has gone from 0.4% to 0.5% an "absolute risk increase" of 0.1%, or one in a thousand, which isn't even statistically significant compared to the background level.
This 0.1% is EXACTLY the same information as the previous 25% but described using a much less dramatic, and much more easily understood, figure. Words and mathematics sometimes make very uneasy bedfellows, especially when mediated by the people with a vested interest - be it the vested interest of a loan company wanting to make money or a journalist wanting to sell papers.
(*Incidentally I chose this example because one of the books I read , Ben Goldacre's excellent Bad Science, suggested facetiously that the newspapers are engaged in a process of dividing every substance on Earth into two groups - ones that cause cancer and ones that cure it, in the case of at least one of our National papers in the UK we get an X causes/cures cancer story, pretty well every week.)
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