In reporting on the American Presidential election campaign the BBC publishes a 'poll of polls' calculated by taking the median of the results of the most recent five polls.
When I checked today's figures I thought there was a mistake.
The Poll of Polls showed Clinton ahead by 5 percentage points, while the individual polls showed leads of 0, 2, 3, 7 7 with median 3.
However taking medians of the figures showing total support for each candidate gives 49 for Clinton and 44 for Trump, with a lead of 5 for Clinton.
So the difference of the medians is not equal to the median of the differences. That may be a reason for treating the median with caution.
In the case of opinion polls based on samples of different sizes, I'd be inclined to use a weighted mean, weighted by the sample sizes. That calculation gave means of 47.47 for Clinton and 44.18 for Trump, a lead of about 3 points for Clinton.
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