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Standard Error

There appear to be two different definitions of the standard error.

The standard error of a sample of sample size n is the sample's standard deviation divided by sqrt(n). It therefore estimates the standard deviation of the sample mean based on the population mean (Press et al. 1992, p. 465). Note that while this definition makes no reference to a normal distribution, many uses of this quantity implicitly assume such a distribution.

The standard error of an estimate may also be defined as the square root of the estimated error variance sigma^^^2 of the quantity,

s_e=sqrt(sigma^^^2)

(Kenney and Keeping 1951, p. 187; Zwillinger 1995, p. 626).

See also

Estimator, Population Mean, Probable Error, Sample Mean, Standard Deviation, Standard Error of Measurement, Variance

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References

Kenney, J. F. and Keeping, E. S. "Standard Error of the Mean." §6.5 in Mathematics of Statistics, Pt. 2, 2nd ed. Princeton, NJ: Van Nostrand, pp. 110 and 132-133, 1951.Kenney, J. F. and Keeping, E. S. Mathematics of Statistics, Pt. 1, 3rd ed. Princeton, NJ: Van Nostrand, 1962.Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, 1992.Zwillinger, D. (Ed.). CRC Standard Mathematical Tables and Formulae. Boca Raton, FL: CRC Press, 1995.

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Standard Error

Cite this as:

Weisstein, Eric W. "Standard Error." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/StandardError.html

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