Symmetric confidence limits
() about the estimated mean, which cover the population mean with
probability. The quantity
is calculated by the formula:
Here
, is the critical value from the
- (or Student) distribution function corresponding to the
confidence level
and
degrees of freedom. The symbol
represents the percentile (or percentage point) of the
-distribution. For 1-sided intervals,
; for 2-sided intervals,
. In each case, the
confidence level is
. The confidence interval is given as
.
Note:
If the population
standard deviation is known, confidence limits about a single result may be calculated with the formula:
The
coefficient, is the limiting value of the
-distribution function for
at
confidence level.
This is identical to
, the
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
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.