IUPAC Gold Book - confidence limits (about the mean)

confidence limits (about the mean)

Symmetric confidence limits ( $Math - text$ ) about the estimated mean, which cover the population mean with probability $Math - ei$ . The quantity $Math - text$ is calculated by the formula:

$Math - e$

Here $Math - text$ , is the critical value from the $Math - text$ - (or Student) distribution function corresponding to the confidence level $Math - ei$ and degrees of freedom $Math - text$ . The symbol $Math - text$ represents the percentile (or percentage point) of the $Math - text$ -distribution. For 1-sided intervals, $Math - ei$ ; for 2-sided intervals, $Math - ei$ . In each case, the confidence level is $Math - ei$ . The confidence interval is given as $Math - ei$ .

Note:

If the population standard deviation $Math - note$ is known, confidence limits about a single result may be calculated with the formula:

$Math - e$

The coefficient $Math - note$ , is the limiting value of the $Math - note$ -distribution function for $Math - ei$ at confidence level $Math - ei$ . This is identical to $Math - note$ , the $Math - note$ th percentage point of the standard normal variate.

Source:

PAC, 1994, 66, 595 (Nomenclature for the presentation of results of chemical analysis (IUPAC Recommendations 1994)) on page 601

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Cite as:
IUPAC. Compendium of Chemical Terminology, 2nd ed. (the "Gold Book"). Compiled by A. D. McNaught and A.Wilkinson. Blackwell Scientific Publications, Oxford (1997). XML on-line corrected version: http://goldbook.iupac.org (2006-) created by M. Nic, J. Jirat, B. Kosata; updates compiled by A. Jenkins. ISBN 0-9678550-9-8. doi:10.1351/goldbook.

Last update: 2008-10-07; version: 2.0.2.

DOI of this term: doi:10.1351/goldbook.C01247.

Original PDF version (may be out of date): http://www.iupac.org/goldbook/C01247.pdf.

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