Tag Archives: statistics

Shock news

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BBC: Local voting figures shed new light on EU referendum

[…] local results were strongly associated with the educational attainment of voters - populations with lower qualifications were significantly more likely to vote Leave. […] The level of education had a higher correlation with the voting pattern than any other major demographic measure from the census.

Call me a Liberal Elitist, but it seems to me that maybe we should be treating education as a higher priority. Then maybe, just maybe, in the long-run, the British public might stop making such monumentally stupid decisions.

Not wishing to be pedantic, but...

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Spectator: The myth of the 'middle class drink epidemic'
[…] The hook for all this is a study (in reality, a glorified survey) published in BMJ Open which found that successful, wealthy, middle class people over the age of 50 are more likely to exceed the government’s drinking guidelines than their peers.

No. Successful, wealthy, middle class people over the age of 50 drink, on average, exactly the same amount as their peers. That's because they're in the same peer-group.

What the article means to say is that successful, wealthy, middle class people over the age of 50 are more likely to exceed the government’s drinking guidelines than people in other groups (who, by definition, aren't their peers).

Putting the Olympics into perspective

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So, Team GB finished the 2012 London Olympics with a magnificent haul of 29 gold medals.

Let's put that figure into some sort of perspective. If you were to trade each one of Team GB's gold medals for an African elephant, you would have 29 African elephants: a sizeable herd in anyone's book.

If you were to trade each one of the USA's 46 gold medals for a hairy wood ant, however, you would only have 46 hairy wood ants: barely enough to form a viable colony. And if you were to trade each one of China's 38 gold medals for a honey bee, their entire lifetimes' honey output, assuming 36 of them were drones, would be insufficient to fill a packet of Lockets honey and lemon cough sweets.

A herd of African elephants versus a struggling colony of wood ants, or half a packet of Lockets. Just dwell on that comparison for a union-flag-waving moment.

(The least said about Australia's paltry seven termites the better.)

Thou shalt not bear false witness

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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.

Computer says, 'No'

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Here we go yet again:

BBC: Paedophiles to undergo lie tests

Paedophiles are to undergo lie detector tests to see if they are likely to re-offend, the Home Office confirmed.

OK, for the sake of argument, let's assume the following:

  • lie-detectors have an accuracy of 90% (although I'm sure it must actually be far lower than this)
  • there is a 20% chance of a convicted paedophile re-offending if released (This figure is very difficult to estimate. The latest official recidivism figure for people conviced of child sex offences is 14%, but this doesn't take into account recidivists who are not re-convicted, nor people who would re-offend, but are never released.)
  • 100 convicted paedophiles are tested to decide whether they should be released

20% (i.e. 20) of the 100 paedophiles will re-offend if released. The 90% accurate lie-detector will detect 18 of these. So, presumably, they will not be released, and the other two will.

80% (i.e. 80) of the 100 paedophiles will not re-offend if released. The 90% accurate lie-detector will say 72 of these people should be released, and 8 should not.

Overall Results:

  • 74 people released from prison, of whom two (3%) will re-offend
  • 26 people remain in prison, of whom 8 (31%) would not have re-offended

If, instead of 90%, I had assumed a lie-detector accuracy of, what seems to me, a far more realistic yet still generous 60%, the result would have been a 14% recidivism rate, with 44 people kept in prison, of whom 32 (73%) should have been released.

Does this inspire you with confidence? If you were being accused of a crime, would you prefer your liberty to be determined by one of these machines, or by a group of your peers?

But we're talking about convicted paedophiles, so I guess it's all right, then, isn't it?

Correlation v Causation

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BBC: 'No proof' organic food is better

There is no evidence organic food is better for you than conventional food, minister David Miliband has said.

Mr Miliband is probably right. But while there may be no causational link between organic food and nutritious, tasty food, there definitely appears to be a correlation between the two.

It's like vegetarianism. Vegetarians often claim that they are, on average, healthier than us omnivores. That may well be true—they're also a lot more miserable and pasty-faced on average, if you ask me—but that doesn't necessarily mean that vegetarianism is the cause of their better health. People who are keen to have healthy lifestyles are more likely than those who aren't to exercise more, drink less, smoke less, eat more sensibly and, in extreme cases, go veggie "because it's good for you". So people who are more likely to be healthy anyway are more likely to turn vegetarian. It becomes a self-fulfilling prophecy. It's also a nice example of sampling bias.

It's the same, I suspect, with organic food. Organic food is not necessarily better for you, but producers of organic food tend to treat their products (and customers) with respect, so they end up with a better, tastier product. Take bacon, for example. Organic, dry-cured, free range bacon knocks the water-filled, globby, mass-produced shite they sell on the cheap shelves into a cocked hat. Next time you're in a butcher's, ask them for proper bacon—they'll know what you mean.

The reason, I suspect, that Mr Miliband made his comment is that he is the food minister—the man responsible for feeding the country. Intensive farming might yield less tasty food, but it's certainly a more efficient and economical way of feeding the masses.

Other correlation v causation pieces: