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Margin of Error

The margin of error is an estimate of a confidence interval for a given measurement, result, etc. and is frequently cited in statistics.

While phrases such as, "The poll has a margin of error of plus or minus 3.1 percentage points" are commonly heard, an additional qualification such as "at a 95 percent confidence level" is also needed in order to precisely indicate what the error refers to.

For a given confidence interval CI, standard deviation sigma, and sample size n, the margin of error (for a normal distribution) is

sqrt(2/n)sigmaerf^(-1)(CI),

where erf^(-1)(x) is the inverse erf function.

See also

Confidence Interval, Error, Inverse Erf, Standard Deviation

Portions of this entry contributed by Ed Pegg, Jr. (author's link)

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References

Moore, D. S. and McCabe G. P. Introduction to the Practice of Statistics. New York: W. H. Freeman, p. 443, 1999.

Referenced on Wolfram|Alpha

Margin of Error

Cite this as:

Pegg, Ed Jr. and Weisstein, Eric W. "Margin of Error." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MarginofError.html

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