Friday, May 25, 2012

Fast food, dodgy infographics, implausible claims

The Daily Mail reported on Wednesday that US restaurant portion sizes had quadrupled(!) since the 1950s, a claim faithfully reproduced from the Center for Disease Control's (CDC) website.  The article comes complete with this infographic.

Now, it should be immediately obvious (if you remember your GCSE maths) that something is not quite right with this picture: the fountain soda looks truly enormous.  Taking the numbers in the diagram on faith for the moment (but see below), the volume of a cup has increased from 7 oz (200 ml) to 42 oz (1.25 l), a worrying factor of six increase.  In accordance with this, the 'NOW' cup on the diagram is 6 times taller than the 1950s cup.

Regrettably, the cup is also 6 times wider, so the area taken up by the modern container is 36 times its vintage counterpart, and so appears to contain nearly 2 US gallons (about the same as a household bucket).  No wonder people are getting fat.  The cup ought to be  √6 = 2.45 times taller and larger, which would look a little less dramatic.  This is sort of misleading graphical presentation not a new phenomenon, and Edward Tufte's excellent books (great for the coffee table) give many other examples. Similar comments apply to the burger and fries, of course.

A further thought occurs.  Since this is a pictorial representation of a three-dimensional object, presumably the eye is deceived into believing that the depth of the cup has increase by a factor of 6 as well?  In that case the cup size has increased from 7oz to a worrying 12 US gallons, or 45 litres.  Assuming that people have a density close to that of water (we almost float), this is about the same as the volume of your skinny friend who weighs 45 kg (100 lbs).  You'd probably couldn't drink a friend-sized container of coke.  Hence the modern receptacle should only be 1.8 times larger than its predecessor (1.8 is the cube root of 6).

Based on a similar analysis, the new burger appears to weigh 6.5 lbs (3 kg) and the fries 4 lbs (1.8 kg).  Makes me feel hungry just thinking about it.

All this aside we might ask whether the numbers used in the diagram are actually plausible at all.  Any British visitor to the US will have found time to comment on the sizeable portions provided in restaurants, but is it really true that the average portion has increase by a factor of four?  It's striking that from the two photos given in the Daily Mail article, the 1950s burger and chips and modern McDonald's meal don't look all that different.

No source is given by the CDC, so I'm unable to check their information (though I will do if I get the chance).  It is rather reminiscent of claims about cannabis being '25 times stronger' than in the 1960s, which were based on comparing the weakest weed from then with the strongest skunk from now.  42oz is a very large soda!  It's more than two and a half US pints, or two imperial pints.  Even in the US, most fast food restaurants would offer that as one of their largest sizes.  Similarly 7oz is pretty small; it's hard to imagine serving anything smaller than 200ml (same as a fun size can).

Obesity is clearly a very big problem (pun impossible to avoid), and it's very likely that restaurant portions have increased.  But overstating the impact of any one particular cause is not helpful, and bad infographics just make me angry.

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