# A further point about Scottish referendum polls

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Free Celtic Nationalist Jesus Surfers Sunshine Vote Yes Van (Photo credit: GerardFerry)

One (smallish) point I left out of my discussion of opinion polling a few days ago was that the “margin of error” for a 95% confidence interval varies according to the reported score.

This range of possible error is actually highest for parties or opinions that score 50% – which is more or less where the “no” vote in the Scottish referendum is polling now – for a 1000 sample poll with 95% confidence interval the range at 50% is:

$\pm 2 \times \sqrt{\frac{0.5 \times 0.5}{1000}} = \pm 3.2\%$

Good news for the yes camp? Not really, because apart from the obvious point that it is mathematically equally likely to be an over-estimate as an under-estimate, the corollary is that the error in smaller figures is less. For 30%, roughly where the yes campaign are, the error is:

$\pm 2 \times \sqrt{\frac{0.3 \times 0.7}{1000}} = \pm 2.9\%$