Free Critical thinking for Students by Roy van den Brink-Budgen

year for the 15–19 age group represents an actual number of 0.1 to 0.2 cases a year. This means that a 6.8 per cent increase is equivalent to one or two cases every ten years!
     
    So when the CEO from the Teenage Cancer Trust said, ‘It is worrying that cervical cancer… (is) increasing in teenagers faster than in other groups. More education is desperately needed so young people can change their behaviour before it’s too late’, we would say, beware of drawing the wrong inference from percentages. (He was also talking about melanoma, an issue we considered when we were looking at sunbeds and suncreams.)
     
    There was a similar problem when Critical Thinking was described as the ‘ fastest-growing A-level in Britain’ a few years ago. This was easily explained. Because it started off from such a low figure, it was easy to be the fastest- growing A-level!
     
    So when we’re given evidence-claims in the form of a percentage, working out their significance is a task where we need to tread with care.
     
    • What is the number from which the percentage is calculated?
     
    • When comparing percentages of different groups, are the numbers themselves sufficiently comparable?
     
    In addition, when we’re looking at percentage changes over a given timescale, we need to ask these questions:
     
    • Is the timescale itself problematic? For example, a timescale could be selected because it fits with the author’s position by emphasising a particular percentage increase or decrease.
     
    • What sort of percentage change would we expect, if there was no significant difference from one period to another? We have to be careful here. It could well be that we would expect an increase or decrease anyway, for all sorts of reasons.
     
    Overall truancy rates rose to 1.1 per cent in the Spring term of 2009 compared to 1 per cent for the same term of 2008.
     
    Is this significant? The schools spokesman for the Liberal Democrat Party must have thought so, because he described the figures as ‘a disgrace. The Government’s truancy strategies are not working. Ministers have poured hundreds of millions of pounds into reducing truancy over recent years but this money seems to have been completely wasted.’ ( The Times , 27 August 2009)
     
    Our response, as Critical Thinkers, would be to say, ‘Now hold on, David Laws, we need to think more carefully about this. Is a 0.1 per cent increase significant? Does it tell us that the money spent on reducing truancy has been “completely wasted”? What sort of percentage figure are you looking for? Zero per cent? We don’t know what the truancy percentage would have been without the truancy strategies, so perhaps a 0.1 per cent increase is pretty good. Do we need to know what the figure was for years earlier than 2008? Was 2008 an unusually low figure, so that a small increase in 2009 is actually pretty good?’
     
    And so on. Quite simply, percentages can be very slippery customers, with their significance sliding through our fingers as we try to grab hold of it. We very often need to know much more before we can start drawing useful inferences.
     

REAL NUMBERS
     
    So, what about real numbers? Instead of percentages, what about the numbers from which they’re taken? Do they give us the opportunity to hold on to something much more significant?
     
    Look at the next example:
     
    Britain spends a higher amount on cosmetic surgery than any other country in Europe. In 2006 this was £497m. The second highest was Italy with £158m. In fact, if we add up the total amount spent by the countries that were second, third (France), fourth (Germany), and fifth (Spain) in the league table of spending, this total is still less than the amount spent in Britain. This shows that British people are the vainest in Europe.
     
    There’s a lot of possible evaluation we could do with this argument, especially in terms of alternative explanations giving us different significances for the evidence.