Thou shalt not bear false witness

Misleading diagram
A misleading chart.

Here's a totally misleading chart from the BBC website, supposedly showing the relative numbers of Anglicans and Catholics in the UK and Ireland compared to the population as a whole.

Wow! Look at that! The Anglicans are over half-way up the chart when compared with the whole population, and the Catholics over a third of the way up. Not bad!

Until you realise that it is the areas of the semi-circles we should be looking at, not the diameters. The clue's in the figures given in the labels on the chart (which totally misleadingly point to the semi-circles' diameters): 65.6M population, 9.3M Catholics—that's one in seven a Catholic, not one in three. 65.6M population, 26.5M Anglicans—that's 40% Anglicans, not over 50%. But who's going to check the figures when there's a simple, reassuring chart? Apart from me, I mean.

Same data, different chart
How I would have drawn the chart.

And, to make matters worse, they've overlaid the semicircles. Or have they? How are we supposed to know if it's just the yellow area which represents the proportion of Anglicans, or if it's the total of the yellow and red areas? (I have calculated the areas, so I believe it's the latter.)

Actually, it's even more misleading than that. Think of the chart as being like a Venn diagram: Anglicans are indeed a subset of the entire population of the UK and Ireland, as are Catholics, but Catholics are most definitely not a subset of Anglicans. In fact, you could argue that the exact opposite is true: historically, the original Anglicans were a subset—or, rather, subsect—of the Catholic Church. And some of them might soon be again, according to the BBC article.

Setting aside the question of what counts as a Catholic or Anglican (I am a devout Atheist, but I was christened against my will by the Anglican church, so does that make me an Anglican?), and setting aside the fact that the church membership figures quoted were provided by the Catholic Church and the Church of England (who might be a little bit biased), this chart seems designed to give a misleadingly high impression of the churches' memberships. It would be interesting to know whether the BBC just obtained the figures from the churches, or whether they obtained the chart as well.

I have banged on previously about how 3-D pie charts can be misleading, but I find these overlaid semi-circular charts far more obnoxious. What on earth is wrong with showing a simple, 2-D pie chart?

Rant over.

Richard Carter

A fat, bearded chap with a Charles Darwin fixation.


  1. Many years ago I was attending 'Nightschool' at the Salford School of Management. The first lesson on Stats and Data was 'First decide what you want your readers to believe' then choose the data presentation systems that will put over your point of view.........

    I think the modern term is 'Spin Doctor'


  2. Obviously you're getting in a Huff again.I totally agree - that is misleading. Although the CoE being what it is, Catholics could become a subset if they wanted to.

    There's a movement against using pie charts, because most people don't compare areas very well. A stacked bar chart is what is suggested instead, although that's a bit boring.

  3. Huff should be required reading for all 11 year olds. I use it with engineering undergrads now to make a tiny contribution to the spring tide of statistical ignorance.

  4. "There's a movement against using pie charts, because most people don't compare areas very well."

    Surely this is madness, at least where pies are concerned.

    Take your average man to a pie-shop and tell him he can have any slice he chooses for a set price. I will wager he will choose the largest nearly infallibly even if they are only a few % different.

    If I were in charge this would be tested in a large Government-funded study using pies and cheesecakes. I'm sure I would be proved right. And I would probably be re-elected very cheaply because people like pie.

    Areas of circles, of differing diameter, however, are notoriously difficult to judge. Offer a whole 4" pie or half a 6" pie and I would back the whole pie being chosen more than 50% of the time.

    I agree - this chart must have been calculated to mislead.

    PS your comment box does not like two spaces after a fullstop.

Leave a comment

Your email address will not be published. Required fields are marked *