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confidence limits (about the mean)

Symmetric confidence limits (± C) about the estimated mean, which cover the population mean with probability1 − α. The quantity C is calculated by the formula:
C = t p , v S n
Here t p , v, is the critical value from the t- (or Student) distribution function corresponding to the confidence level1 − α and degrees of freedomv. The symbol p represents the percentile (or percentage point) of the t-distribution. For 1-sided intervals, p = 1 − α; for 2-sided intervals, p = 1 − α 2. In each case, the confidence level is 1 − α. The confidence interval is given as x _ ± C.
Note:
If the population standard deviationσ is known, confidence limits about a single result may be calculated with the formula:
C = t p , ∞ σ
The coefficientt p , ∞, is the limiting value of the t-distribution function for v = ∞ at confidence level1 − α. This is identical to z p, the pth 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: 2014-02-24; version: 2.3.3.
DOI of this term: doi:10.1351/goldbook.C01247.
Original PDF version: http://www.iupac.org/goldbook/C01247.pdf. The PDF version is out of date and is provided for reference purposes only. For some entries, the PDF version may be unavailable.
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