NOTE - The NIST policy also allows the use of established and documented methods equivalent to the "RSS" method, such as the numerically based "bootstrap" (see Appendix C).

NOTES1. The uncertainty of a correction applied to a measurement result to compensate for a systematic effect is not the systematic error in the measurement result due to the effect. Rather, it is a measure of the uncertainty of the result due to incomplete knowledge of the required value of the correction. The terms "error" and "uncertainty" should not be confused (see also the note of subsection 2.3).

2. Although it is strongly recommended that corrections be applied for all recognized significant systematic effects, in some cases it may not be practical because of limited resources. Nevertheless, the expression of uncertainty in such cases should conform with these guidelines to the fullest possible extent (see the

Guide[2]).

Commonly,u_{c}, is used for reporting results of determinations of fundamental constants, fundamental metrological research, and international comparisons of realizations of SI units.

Expressing the uncertainty of NIST's primary cesium frequency standard as an
estimated standard deviation is an example of the use of *u*_{c},
in fundamental metrological research. It should also be noted that in a 1986
recommendation [9], the CIPM requested that what
is now termed combined standard uncertainty *u*_{c}, be used
"by all participants in giving the results of all international
comparisons or other work done under the auspices of the CIPM and
Comités Consultatifs."

**5.4** In many practical measurement situations, the probability
distribution characterized by the measurement result *y* and its combined
standard uncertainty *u*_{c}(*y*) is approximately normal
(Gaussian). When this is the case and *u*_{c}(*y*) itself has
negligible uncertainty (see Appendix B),
*u*_{c}(*y*) defines an interval
*y* - *u*_{c}(*y*) to
*y* + *u*_{c}(*y*) about the measurement
result *y* within which the value of the measurand *Y* estimated by
*y* is believed to lie with a level of confidence of approximately
68 percent. That is, it is believed with an approximate level of
confidence of 68 percent that
*y* - *u*_{c}(*y*) ≤ *Y* ≤
*y* + *u*_{c}(*y*) which is commonly written as
*Y* = *y* ± *u*_{c}(*y*).

The probability distribution characterized by the measurement result and its
combined standard uncertainty is approximately normal when the conditions of
the Central Limit Theorem are met. This is the case, often encountered in
practice, when the estimate *y* of the measurand *Y* is not
determined directly but is obtained from the estimated values of a significant
number of other quantities [see Appendix A,
Eq. (A-1)] describable by well-behaved
probability distributions, such as the normal and rectangular distributions;
the standard uncertainties of the estimates of these quantities contribute
comparable amounts to the combined standard uncertainty
*u*_{c}(*y*) of the measurement result *y*; and the
linear approximation implied by Eq. (A-3)
in Appendix A), is adequate.

NOTE - Ifu_{c}(y) has non-negligible uncertainty, the level of confidence will differ from 68 percent. The procedure given in Appendix B) has been proposed as a simple expedient for approximating the level of confidence in these cases.

**5.5**
The term "confidence interval" has a specific definition in
statistics and is only applicable to intervals based on *u*_{c}
when certain conditions are met, including that all components of uncertainty
that contribute to *u*_{c} be obtained from Type A evaluations.
Thus, in these guidelines, an interval based on *u*_{c} is viewed
as encompassing a fraction *p* of the probability distribution
characterized by the measurement result and its combined standard uncertainty,
and *p* is the *coverage probability* or *level of confidence*
of the interval.