<P> An example from the 2004 U.S. presidential campaign will be used to illustrate concepts throughout this article . According to an October 2, 2004 survey by Newsweek, 47% of registered voters would vote for John Kerry / John Edwards if the election were held on that day, 45% would vote for George W. Bush / Dick Cheney, and 2% would vote for Ralph Nader / Peter Camejo . The size of the sample was 1,013 . Unless otherwise stated, the remainder of this article uses a 95% level of confidence . </P> <P> Polls basically involve taking a sample from a certain population . In the case of the Newsweek poll, the population of interest is the population of people who will vote . Because it is impractical to poll everyone who will vote, pollsters take smaller samples that are intended to be representative, that is, a random sample of the population . It is possible that pollsters sample 1,013 voters who happen to vote for Bush when in fact the population is evenly split between Bush and Kerry, but this is extremely unlikely (p = 2 ≈ 1.1 × 10) given that the sample is random . </P> <P> Sampling theory provides methods for calculating the probability that the poll results differ from reality by more than a certain amount, simply due to chance; for instance, that the poll reports 47% for Kerry but his support is actually as high as 50%, or is really as low as 44% . This theory and some Bayesian assumptions suggest that the "true" percentage will probably be fairly close to 47% . The more people that are sampled, the more confident pollsters can be that the "true" percentage is close to the observed percentage . The margin of error is a measure of how close the results are likely to be . </P> <P> However, the margin of error only accounts for random sampling error, so it is blind to systematic errors that may be introduced by non-response or by interactions between the survey and subjects' memory, motivation, communication and knowledge . </P>

How to get margin of error in statistics