The true standard error of the statistic is the square root of the true sampling variance of the statistic.
These two may not be directly related, although in general, for large distributions that look like normal curves, there is a direct relationship. The standard error. The standard error can be used to create a confidence interval within which the "true" percentage should be to a certain level of confidence.
The estimated percentage plus or minus its margin of error is a confidence interval for the percentage.
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In other words, the margin of error is half the width of the confidence interval. The margin of error for a particular statistic of interest is usually defined as the radius or half the width of the confidence interval for that statistic. In media reports of poll results, the term usually refers to the maximum margin of error for any percentage from that poll. For a simple random sample from a large population, the maximum margin of error is a simple re-expression of the sample size n. The numerators of these equations are rounded to two decimal places. If an article about a poll does not report the margin of error, but does state that a simple random sample of a certain size was used, the margin of error can be calculated for a desired degree of confidence using one of the above formulae.
A random sample of size will give a margin of error of 0. While the margin of error typically reported in the media is a poll-wide figure that reflects the maximum sampling variation of any percentage based on all respondents from that poll, the term margin of error also refers to the radius of the confidence interval for a particular statistic. The margin of error for a particular individual percentage will usually be smaller than the maximum margin of error quoted for the survey. The formula above for the margin of error assume that there is an infinitely large population and thus do not depend on the size of the population of interest.
According to sampling theory , this assumption is reasonable when the sampling fraction is small. FPC can be calculated using the formula: . To adjust for a large sampling fraction, the FPC factored into the calculation of the margin of error, which has the effect of narrowing the margin of error. It holds that the FPC approaches zero as the sample size n approaches the population size N , which has the effect of eliminating the margin of error entirely.
Analysts should be mindful that the samples remain truly random as the sampling fraction grows, lest sampling bias be introduced. Confidence intervals can be calculated, and so can margins of error, for a range of statistics including individual percentages, differences between percentages, means, medians,  and totals.
No Margin for Error
The margin of error for the difference between two percentages is larger than the margins of error for each of these percentages, and may even be larger than the maximum margin of error for any individual percentage from the survey. In a plurality voting system , where the winner is the candidate with the most votes, it is important to know who is ahead. The terms "statistical tie" and "statistical dead heat" are sometimes used to describe reported percentages that differ by less than a margin of error, but these terms can be misleading.
The survey results also often provide strong information even when there is not a statistically significant difference. When comparing percentages, it can accordingly be useful to consider the probability that one percentage is higher than another. This may not be a tenable assumption when there are more than two possible poll responses. For more complex survey designs, different formulas for calculating the standard error of difference must be used. The standard error of the difference of percentages p for Kerry and q for Bush, assuming that they are perfectly negatively correlated, follows:.
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Her exciting follow-up to Boots, Belts, Berets and On the Double takes an incisive look at the patriots who risk it all to stand in the line of fire. About the author Tanushree Podder is a self-confessed word-a-holic and a traveller.
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A true maverick, she stumbled through many career choices before settling on writing. No Margin for Error is her ninth novel. After leading a nomadic life for several decades, thanks to the Indian Army, she has finally grown roots at Pune.
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No margin for error
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