Poll Dance

Spot the connexion between these two news headlines:

The people don’t want a referendum on Europe, insists No 10

and

NOW 80% DEMAND VOTE TO QUIT EU

Yes, that's right, they're both reporting on the same opinion poll.

The trick is in the question.  Respondents were asked "Which of the following statements comes closest to your view?", with the options:

• No need for a referendum in the foreseeable future
• There should be a referendum, but now is not the time
• There should be a referendum now

Of 2006 respondents, 379 (18.9%) chose "no need", 626 (31.2%) chose "yes but not now", and 1001 (49.9%) chose "yes, now".

So a Downing Street spokeswoman could say without lying "The British people do not want a referendum on the European Union at the moment", because most respondents (by a majority of 0.2%) don't want a referendum now.  The Telegraph headline drops the qualification "at the moment" because headline writers like to keep things snappy.  And the Express could say honestly enough by their standards "A new poll showed more than 80 per cent of voters are crying out for a referendum", because indeed the poll shows that 81.1% of respondents think there should be a referendum.  "Demand" and "Crying out" are wild exaggerations, but it's the Express; readers expect nothing less.  Note that the "Now" in the headline refers to the time of the opinion poll, not when the vote is wanted.

Opinion pollster Antony Wells remarks "Referendums are popular per se, whatever the subject asked about, people will support having a referendum on it."  To which I would add: they're much less enthusiastic about voting in the referendum itself: the turnout at the referendum on AV was 42%, compared with 65% at the last general election.

Also, there's a gap between "no need for a referendum" and "there should be a referendum".  Another option could have been included along the lines of "I might want a referendum in the future as the EU evolves, but there's no need for one as things stand".  I think that would have increased the total "no need" vote.

A fair representation of this poll would be "Half the population wants a referendum now on the EU, and only 19% is willing to rule out a referendum for the foreseeable future".  Is there any demand for fair representations?

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Incidentally, this was an online opinion poll.  I don't think the method is worse than telephone or face-to-face polling.  It shouldn't be confused with online polls which are open for anyone to vote in: they're worthless.

The capitalist yolk

The BBC has a story about the probability of getting six double-yolked eggs in a box of six.  It points out that young hens are more likely to lay double-yolked eggs, and those eggs are larger than normal, so if you buy a box of large eggs which happen to have been selected from eggs laid by young hens, the odds of their all being double-yolked are much shorter than the one in a million trillion they first thought of.

Well yes, but the odds must still be pretty long.  And there have been other similar stories, not least this one about a woman who opened 29 double-yolked eggs in a row from a box of 30.

When something wildly improbable seems to have happened, it's as well to consider alternative explanations.  Here's a clue from David Spiegelhalter, Professor of the Public Understanding of Risk, who was intrigued to find he could buy a box of double-yolked eggs from Waitrose: he mentions it in this article.

It turns out that double-yolked eggs can be identified easily enough by shining a light through them - "egg candling".  (It's safe to try this at home.)  Egg producers operate egg-grading machines: I suppose the machines include automated candlers as part of the grading process.  So it's not unlikely that some machines automatically separate double-yolked eggs. Some of those eggs will be sold as such for a premium, if demand exists.  And if the demand is less than the number of double-yolked eggs produced, they'll just get put into regular boxes for the appropriate size of egg.  I reckon the odds of this happening sometimes would be very close to one.