A Green Party activist writes as follows before setting off for a month’s continental holiday:

*The Indy has an article today that bigs up the Green Party: it says the latest poll (actually a poll of polls so should be, very marginally, more accurate than just one?) shows an increase in the Green vote from – wait for it – 5 per cent to 6 per cent. I’m not getting excited yet because I imagine the confidence interval on the two figures would dwarf any supposed increase, but do you have any idea what the confidence intervals on these figures are likely to be? A friend here, who knows I’m likely to be standing for the Greens in Putney in the elections for the Westminster Laughing House in May 2015, sent me the link in some excitement, but I fear it’s utter bollocks. Any thoughts? My feeling is that any supposed “increase” is completely illusory, but it would be good to have a more informed view. **The article can be found here.*

Of course the article fails to say anything about the polls or how many of them there are or how they are combined.

Opinion polls tend to have a sample size of about 1000. We want to know whether an apparent increase in Green support from 5% to 6% is significant. So we ask what the probability of getting at least 60 people in a sample of 1000 declaring Green support is if the underlying propensity to vote Green is really 0.05. From the properties of the binomial distribution (see here for instance) this comes out at 0.087, or about 9%. So there **might** be a real effect, **if** you accept a 10% significance level and **if** the sampling in the poll is unbiased–I imagine it’s less reliable for Green supporters than for the larger parties.

You could argue that it’s a poll of polls, so presumably the effective sample size is bigger, and the significance somewhat better than 9%. For instance, if the effect was equal to a new poll with a sample size five times the original survey, then you would repeat the calculation above for *at least 300 people in a sample 5000 declaring Green support*.

But the article gives no useful information at all! Poor show all round…

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Tags: Green Party, politics, statistics

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