I’ve been doing some more reading of the annual report of the Chief Scientific Adviser, Sir Mark Walport. Or rather of the companion volume that, in its own words, “form the evidence for the Government Chief Scientific Advisor’s Annual Report 2014”.

(Question: is it ‘adviser’ with an ‘e’ or ‘advisor’ with an ‘o’? Both spellings appear.)

The document has some infographics, including these two piggies on page 85.

I’ve obscured the numbers they are representing.

What do you think the ratio of the numbers is?

Now a golden rule of infographic design is that if using a single image (in this case, a pig) to represent data then it is the areas that must be scaled not just the width or the height. For example, say we want to visualise 1 with a square which is one unit wide and one unit high, like this:

Now let’s say we want to visualise 2 with a square. It would be wrong to do this as a 2 x 2 square, like this:

The ratio we want to visualise is 2 to 1, but because we see area over any individual dimension (width or height) we see a ratio of 4 to 1.

Bearing this in mind then each dimension needs to be scaled up by the square root of 2, which is about 1.414. In other words to get the ratio of areas to be 2 to 1 we need a bigger square 1.414 units wide by 1.414 units high, like this one in black:

You can see how ‘wrong’ things looked when we scaled both dimensions by 2, rather than area by 2.

So, back to our piggies…

What estimate did you make of the ratio of the two numbers they visualise?

I’ll give you some help.

The pig on the left is 74 units wide and 55 units high. The pig on the right is 100 units wide and 75 units high.

I measured in millimetres to within 1mm either way on a printout. However, you might measure in different units or straight from the screen, which is why I’m referring to ‘units’.

It looks like the pigs are in proportion. A quick check … for the left piggie we have a ratio of 74 / 55 or about 1.35 of width to height; for the right piggie we have a ratio of 100 / 75 or about 1.33. Allowing for error in my measurements these are essentially the same ratios – so the piggies are in proportion. (Had right piggie been tall and skinny or short and fat then things would be different.)

The ratio of the areas of the pigs is (100 x 75) / (74 x 55) or about 1.84 to 1.

I’ll let you know that left piggie represents 61%.

So right piggie should represent 1.84 x 61 per cent … that’s 112%.

But here’s the graphic with the numbers from the document:

Right piggie is not 112% – it’s 83%.

So, this infographic is not a good visualisation.

Does this matter?

Well, from a purist view, you’d hope that the office of the UK Chief Scientific Adviser would get this right.

But, more seriously, I have experience in political campaigning. I know that opponents of a view may pick up on any error (trivial or not) to argue their view – “if they can’t get the simple things right can you trust them on the issues that matter?!”

Imagine if this graphic were about climate change, fracking, GM foods … .