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Barack Obama (BO)	Mike Huckabee (MH)
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Sep. 5, 2007 - News

A More Accurate Estimate the Margin of Error of a Random Poll

The margin of error (MoE) estimate reported in random polls is only strictly true for statistics of 50%; otherwise it is an overestimate. Consider the latest Fox News/Opinion Dynamics Poll, in which the reported MoE is 5.5%. This estimate was obtained using the formula

MoE = 100%/sqrt(N) (1)

where N=314 is the number of people polled. But if the measured statistic is f, which may be greater or less than 50%, a more accurate formula is

MoE = 200%*sqrt(f*(1-f)/N). (2)

Consider the reported percentage of 29% of Republican voters surveyed who said they would vote for Rudy Giuliani. Thus we have f=0.29. Plugging into formula (2), we find

MoE = 200%*sqrt(0.29*0.71/314) = 5.1%,

which is slightly less than the reported figure of 5.5%. Thus it is more precise to say that we are 95% confident that the percentage of registered Republicans in the United States who say they will vote for Rudy Giuliani in the primaries is between 23.9% and 34.1%.

Note that (2) reduces to (1) when f=0.5. Also note that if f is very small or very close to 1, the MoE becomes small.