##
Guidelines for Evaluating and Expressing the
Uncertainty of NIST Measurement Results

# 2. Classification of Components of Uncertainty

**2.1** In general, the result of a measurement is only an approximation
or estimate of the value of the specific quantity subject to measurement, that
is, the **measurand**, and thus the result is complete only when accompanied
by a quantitative statement of its uncertainty.
**2.2** The uncertainty of the result of a measurement generally consists
of several components which, in the CIPM approach, may be grouped into two
categories according to the method used to estimate their numerical values:

- A. those which are evaluated by statistical methods,
- B.those which are evaluated by other means.

**2.3**
There is not always a simple correspondence between the classification of
uncertainty components into categories A and B and the commonly used
classification of uncertainty components as "random" and
"systematic." The nature of an uncertainty component is conditioned
by the use made of the corresponding quantity, that is, on how that quantity
appears in the mathematical model that describes the measurement process.
When the corresponding quantity is used in a different way, a
"random" component may become a "systematic" component
and vice versa. Thus the terms "random uncertainty" and
"systematic uncertainty" can be misleading when generally applied.
An alternative nomenclature that might be used is
- "component of uncertainty arising from a random effect,"
- "component of uncertainty arising from a systematic effect,"

where a random effect is one that gives rise to a possible random error in the
*current measurement process* and a systematic effect is one that gives
rise to a possible systematic error in the current measurement process. In
principle, an uncertainty component arising from a systematic effect may in
some cases be evaluated by method A while in other cases by method B
(see subsection 2.2), as may be an uncertainty component
arising from a random effect.
NOTE - The difference between error and uncertainty should always be
borne in mind. For example, the result of a measurement after
correction (see subsection 5.2) can
unknowably be very close to the unknown value of the measurand, and thus
have negligible error, even though it may have a large uncertainty (see
the *Guide* [2]).

**2.4** Basic to the CIPM approach is representing each component of
uncertainty that contributes to the uncertainty of a measurement result by an
estimated standard deviation, termed **standard uncertainty** with suggested
symbol *u*_{i} , and equal to the positive square root of the
estimated variance *u*_{i}^{2}.
**2.5** It follows from subsections 2.2 and 2.4 that an uncertainty
component in category A is represented by a statistically estimated
standard deviation *s*_{i}^{2} equal to the positive
square root of the statistically estimated variance
*s*_{i}^{2}, and the associated number of degrees of
freedom ν_{i }. For such a component the standard
uncertainty is *u*_{i} = *s*_{i }.

The evaluation of uncertainty by the statistical analysis of series of
observations is termed a **Type A
evaluation (of uncertainty)**.

**2.6** In a similar manner, an uncertainty component in category B
is represented by a quantity *u*_{j} , which may be considered an
approximation to the corresponding standard deviation; it is equal to the
positive square root of
*u*_{j}^{2}, which may be considered an approximation to
the corresponding variance and which is obtained from an assumed probability
distribution based on all the available information (see
section 4). Since the quantity
*u*_{j}^{2} is treated like a variance and
*u*_{j} like a standard deviation, for such a component the
standard uncertainty is simply *u*_{j} .

The evaluation of uncertainty by means other than the statistical analysis of
series of observations is termed a **Type B evaluation (of
uncertainty)**.

**2.7** Correlations between components (of either category) are
characterized by estimated covariances [see Appendix A,
Eq. (A-3)] or estimated correlation
coefficients.