Percentagewise, it’s a common error
If a price doubles, is it 200 per cent higher? No, it’s 100 per cent higher.
That’s a rule worth remembering, as it’s frequently ignored. I was reminded of it by an interesting paper in the latest issue of Pharmacotherapy comparing the cost of statin prescribing in the US and the UK.
The authors conclude that the US healthcare system paid four times as much for these widely-prescribed drugs as the NHS, a difference only partially accounted for by the difference in prescribing rates between the two countries. Total costs for matched groups of 280,000 people aged 55-64 in each country in 2005 were $64.9 million in the US and $15.7 m in the UK.
That’s a factor of four but is it, as the authors say, “approximately 400 per cent higher”? No. In cash terms it’s $49.2m higher, and that is 319 per cent of $15.7m. So it’s approximately 300 per cent higher.
This is a common error – see, for example, this handy guide - and a good reason for not using for percentages for increases of more than 100 per cent. A host of websites picked this story up and without exception repeated the error, usually in the headline.
If the authors had said US costs were 400 per cent of UK costs, they would have been right. But 400 per cent higher? I’m afraid not.
Anonymous (not verified) wrote,
Fri, 13/01/2012 - 20:41
Another common error I see is when something goes from 10% of a whole to 15% and they say it increased by 5% when it actually increased 50%.
robert (not verified) wrote,
Sat, 14/01/2012 - 18:20
A similar error being made, but in reverse, is the media confusion over inflation indices.
If in UK inflation is 5% this year and 3% next year, they keep saying things such as the cost pressure on consumers will ease in 2012. Pensioners with a 5% State Pension rise from next April are winners because inflation this year is only 3%. Nonsense.
In April 2013 prices will have risen over the whole period 5+3% = 8%+
If folks have had no pay rise or reduced hours over this period they are even worse off next year (8+ against 5%).
Pensioners have had no rise in reality, they have suffered a a fall. Over a year their costs (food ,fuel, transport) have gone up around 12% in reality but even at say 5% inflation they have had to wait and pay out for a full year plus this year before the original 5% is restored then they face another year at +3% inflation.
Anonymouse (not verified) wrote,
Wed, 18/01/2012 - 11:55
Robert has a good point. What is even more interesting is that normally the rate reported is the year on year change. It tells you nothing about what is happening in the most recent times. Who really cares if inflation has changed from January last year. Is it not better to focus on is it easing or rising in the most recent months as that is more relevant?
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