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 , standard deviation , and sample size , the margin of error (for a normal distribution) is

where  is the inverse erf function.

REFERENCES:

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