# 2   Definitions

## 2.1   General metrological terms

The definition of a number of general metrological terms relevant to this Guide, such as “measurable quantity”, “measurand”, and “error of measurement”, are given in Annex B. These definitions are taken from the International vocabulary of basic and general terms in metrology (abbreviated VIM)* [6]. In addition, Annex C gives the definitions of a number of basic statistical terms taken mainly from International Standard ISO 3534‑1 [7]. When one of these metrological or statistical terms (or a closely related term) is first used in the text, starting with Clause 3, it is printed in boldface and the number of the subclause in which it is defined is given in parentheses.

Because of its importance to this Guide, the definition of the general metrological term “uncertainty of measurement” is given both in Annex B and 2.2.3. The definitions of the most important terms specific to this Guide are given in 2.3.1 to 2.3.6. In all of these subclauses and in Annexes B and C, the use of parentheses around certain words of some terms means that these words may be omitted if this is unlikely to cause confusion.

## 2.2   The term “uncertainty”

The concept of uncertainty is discussed further in Clause 3 and Annex D.

2.2.1   The word “uncertainty” means doubt, and thus in its broadest sense “uncertainty of measurement” means doubt about the validity of the result of a measurement. Because of the lack of different words for this general concept of uncertainty and the specific quantities that provide quantitative measures of the concept, for example, the standard deviation, it is necessary to use the word “uncertainty” in these two different senses.

2.2.2   In this Guide, the word “uncertainty” without adjectives refers both to the general concept of uncertainty and to any or all quantitative measures of that concept. When a specific measure is intended, appropriate adjectives are used.

2.2.3   The formal definition of the term “uncertainty of measurement” developed for use in this Guide and in the VIM [6] (VIM:1993, definition 3.9) is as follows:

uncertainty (of measurement)
parameter, associated with the result of a measurement, that characterizes the dispersion of the values that could reasonably be attributed to the measurand

NOTE 1   The parameter may be, for example, a standard deviation (or a given multiple of it), or the half‑width of an interval having a stated level of confidence.

NOTE 2   Uncertainty of measurement comprises, in general, many components. Some of these components may be evaluated from the statistical distribution of the results of series of measurements and can be characterized by experimental standard deviations. The other components, which also can be characterized by standard deviations, are evaluated from assumed probability distributions based on experience or other information.

NOTE 3   It is understood that the result of the measurement is the best estimate of the value of the measurand, and that all components of uncertainty, including those arising from systematic effects, such as components associated with corrections and reference standards, contribute to the dispersion.

2.2.4   The definition of uncertainty of measurement given in 2.2.3 is an operational one that focuses on the measurement result and its evaluated uncertainty. However, it is not inconsistent with other concepts of uncertainty of measurement, such as

• a measure of the possible error in the estimated value of the measurand as provided by the result of a measurement;
• an estimate characterizing the range of values within which the true value of a measurand lies (VIM:1984, definition 3.09).

Although these two traditional concepts are valid as ideals, they focus on unknowable quantities: the “error” of the result of a measurement and the “true value” of the measurand (in contrast to its estimated value), respectively. Nevertheless, whichever concept of uncertainty is adopted, an uncertainty component is always evaluated using the same data and related information. (See also E.5.)

## 2.3   Terms specific to this Guide

In general, terms that are specific to this Guide are defined in the text when first introduced. However, the definitions of the most important of these terms are given here for easy reference.

NOTE   Further discussion related to these terms may be found as follows: for 2.3.2, see 3.3.3 and 4.2; for 2.3.3, see 3.3.3 and 4.3; for 2.3.4, see Clause 5 and Equations (10) and (13); and for 2.3.5 and 2.3.6, see Clause 6.

2.3.1
standard uncertainty
uncertainty of the result of a measurement expressed as a standard deviation
2.3.2
Type A evaluation (of uncertainty)
method of evaluation of uncertainty by the statistical analysis of series of observations
2.3.3
Type B evaluation (of uncertainty)
method of evaluation of uncertainty by means other than the statistical analysis of series of observations
2.3.4
combined standard uncertainty
standard uncertainty of the result of a measurement when that result is obtained from the values of a number of other quantities, equal to the positive square root of a sum of terms, the terms being the variances or covariances of these other quantities weighted according to how the measurement result varies with changes in these quantities
2.3.5
expanded uncertainty
quantity defining an interval about the result of a measurement that may be expected to encompass a large fraction of the distribution of values that could reasonably be attributed to the measurand

NOTE 1   The fraction may be viewed as the coverage probability or level of confidence of the interval.

NOTE 2   To associate a specific level of confidence with the interval defined by the expanded uncertainty requires explicit or implicit assumptions regarding the probability distribution characterized by the measurement result and its combined standard uncertainty. The level of confidence that may be attributed to this interval can be known only to the extent to which such assumptions may be justified.

NOTE 3   Expanded uncertainty is termed overall uncertainty in paragraph 5 of Recommendation INC‑1 (1980).

2.3.6
coverage factor
numerical factor used as a multiplier of the combined standard uncertainty in order to obtain an expanded uncertainty

NOTE   A coverage factor, k, is typically in the range 2 to 3.

*   Footnote to the 2008 version:
The third edition of the vocabulary was published in 2008, under the title JCGM 200:2008, International vocabulary of metrology — Basic and general concepts and associated terms (VIM).