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.
https://doi.org/10.1351/goldbook.