Annex B

General metrological terms

B.1   Source of definitions

The definitions of the general metrological terms relevant to this Guide that are given here have been taken from the International vocabulary of basic and general terms in metrology (abbreviated VIM), second edition, 1993* [6], published by the International Organization for Standardization (ISO), in the name of the seven organizations that supported its development and nominated the experts who prepared it: the Bureau International des Poids et Mesures (BIPM), the International Electrotechnical Commission (IEC), the International Federation of Clinical Chemistry (IFCC), ISO, the International Union of Pure and Applied Chemistry (IUPAC), the International Union of Pure and Applied Physics (IUPAP), and the International Organization of Legal Metrology (OIML). The VIM should be the first source consulted for the definitions of terms not included either here or in the text.

NOTE   Some basic statistical terms and concepts are given in Annex C, while the terms “true value”, “error”, and “uncertainty” are further discussed in Annex D.

B.2   Definitions

As in Clause 2, in the definitions that follow, the use of parentheses around certain words of some terms means that the words may be omitted if this is unlikely to cause confusion.

The terms in boldface in some notes are additional metrological terms defined in those notes, either explicitly or implicitly (see Reference [6]).

B.2.1
(measurable) quantity
attribute of a phenomenon, body or substance that may be distinguished qualitatively and determined quantitatively

NOTE 1   The term quantity may refer to a quantity in a general sense (see Example 1) or to a particular quantity (see Example 2).

EXAMPLE 1   Quantities in a general sense: length, time, mass, temperature, electrical resistance, amount‑of‑substance concentration.

EXAMPLE 2   Particular quantities:

NOTE 2   Quantities that can be placed in order of magnitude relative to one another are called quantities of the same kind.

NOTE 3   Quantities of the same kind may be grouped together into categories of quantities, for example:

NOTE 4   Symbols for quantities are given in ISO 31**.

[VIM:1993, definition 1.1]
B.2.2
value (of a quantity)
magnitude of a particular quantity generally expressed as a unit of measurement multiplied by a number

EXAMPLE 1   Length of a rod: 5,34 m or 534 cm.

EXAMPLE 2   Mass of a body: 0,152 kg or 152 g.

EXAMPLE 3   Amount of substance of a sample of water (H2O): 0,012 mol or 12 mmol.

NOTE 1   The value of a quantity may be positive, negative or zero.

NOTE 2   The value of a quantity may be expressed in more than one way.

NOTE 3   The values of quantities of dimension one are generally expressed as pure numbers.

NOTE 4   A quantity that cannot be expressed as a unit of measurement multiplied by a number may be expressed by reference to a conventional reference scale or to a measurement procedure or to both.

[VIM:1993, definition 1.18]
B.2.3
true value (of a quantity)
value consistent with the definition of a given particular quantity

NOTE 1   This is a value that would be obtained by a perfect measurement.

NOTE 2   True values are by nature indeterminate.

NOTE 3   The indefinite article “a”, rather than the definite article “the”, is used in conjunction with “true value” because there may be many values consistent with the definition of a given particular quantity.

[VIM:1993, definition 1.19]

Guide Comment: See Annex D, in particular D.3.5, for the reasons why the term “true value” is not used in this Guide and why the terms “true value of a measurand” (or of a quantity) and “value of a measurand” (or of a quantity) are viewed as equivalent.

B.2.4
conventional true value (of a quantity)
value attributed to a particular quantity and accepted, sometimes by convention, as having an uncertainty appropriate for a given purpose

EXAMPLE 1   At a given location, the value assigned to the quantity realized by a reference standard may be taken as a conventional true value.

EXAMPLE 2   The CODATA (1986) recommended value for the Avogadro constant: 6,022 136 7 × 1023 mol−1.

NOTE 1   “Conventional true value” is sometimes called assigned value, best estimate of the value, conventional value or reference value. “Reference value”, in this sense, should not be confused with “reference value” in the sense used in the Note to VIM:1993, definition 5.7.

NOTE 2   Frequently, a number of results of measurements of a quantity is used to establish a conventional true value.

[VIM:1993, definition 1.20]

Guide Comment: See the Guide Comment to B.2.3.

B.2.5
measurement
set of operations having the object of determining a value of a quantity

NOTE   The operations may be performed automatically.

[VIM:1993, definition 2.1]
B.2.6
principle of measurement
scientific basis of a measurement

EXAMPLE 1   The thermoelectric effect applied to the measurement of temperature.

EXAMPLE 2   The Josephson effect applied to the measurement of electric potential difference.

EXAMPLE 3   The Doppler effect applied to the measurement of velocity.

EXAMPLE 4   The Raman effect applied to the measurement of the wave number of molecular vibrations.

[VIM:1993, definition 2.3]
B.2.7
method of measurement
logical sequence of operations, described generically, used in the performance of measurements

NOTE   Methods of measurement may be qualified in various ways such as:


[VIM:1993, definition 2.4]
B.2.8
measurement procedure
set of operations, described specifically, used in the performance of particular measurements according to a given method

NOTE   A measurement procedure is usually recorded in a document that is sometimes itself called a “measurement procedure” (or a measurement method) and is usually in sufficient detail to enable an operator to carry out a measurement without additional information.

[VIM:1993, definition 2.5]
B.2.9
measurand
particular quantity subject to measurement

EXAMPLE   Vapour pressure of a given sample of water at 20 °C.

NOTE   The specification of a measurand may require statements about quantities such as time, temperature and pressure.

[VIM:1993, definition 2.6]
B.2.10
influence quantity
quantity that is not the measurand but that affects the result of the measurement

EXAMPLE 1   Temperature of a micrometer used to measure length.

EXAMPLE 2   Frequency in the measurement of the amplitude of an alternating electric potential difference.

EXAMPLE 3   Bilirubin concentration in the measurement of haemoglobin concentration in a sample of human blood plasma.

[VIM:1993, definition 2.7]

Guide Comment: The definition of influence quantity is understood to include values associated with measurement standards, reference materials, and reference data upon which the result of a measurement may depend, as well as phenomena such as short‑term measuring instrument fluctuations and quantities such as ambient temperature, barometric pressure and humidity.

B.2.11
result of a measurement
value attributed to a measurand, obtained by measurement

NOTE 1   When a result is given, it should be made clear whether it refers to:

and whether several values are averaged.

NOTE 2   A complete statement of the result of a measurement includes information about the uncertainty of measurement.

[VIM:1993, definition 3.1]
B.2.12
uncorrected result
result of a measurement before correction for systematic error
[VIM:1993, definition 3.3]
B.2.13
corrected result
result of a measurement after correction for systematic error
[VIM:1993, definition 3.4]
B.2.14
accuracy of measurement
closeness of the agreement between the result of a measurement and a true value of the measurand

NOTE 1   “Accuracy” is a qualitative concept.

NOTE 2   The term precision should not be used for “accuracy”.

[VIM:1993, definition 3.5]

Guide Comment: See the Guide Comment to B.2.3.

B.2.15
repeatability (of results of measurements)
closeness of the agreement between the results of successive measurements of the same measurand carried out under the same conditions of measurement

NOTE 1   These conditions are called repeatability conditions.

NOTE 2   Repeatability conditions include:

NOTE 3   Repeatability may be expressed quantitatively in terms of the dispersion characteristics of the results.

[VIM:1993, definition 3.6]
B.2.16
reproducibility (of results of measurements)
closeness of the agreement between the results of measurements of the same measurand carried out under changed conditions of measurement

NOTE 1   A valid statement of reproducibility requires specification of the conditions changed.

NOTE 2   The changed conditions may include:

NOTE 3   Reproducibility may be expressed quantitatively in terms of the dispersion characteristics of the results.

NOTE 4   Results are here usually understood to be corrected results.

[VIM:1993, definition 3.7]
B.2.17
experimental standard deviation
for a series of n measurements of the same measurand, the quantity s(qk) characterizing the dispersion of the results and given by the formula:
eqn18
qk being the result of the kth measurement and q‾‾ being the arithmetic mean of the n results considered

NOTE 1   Considering the series of n values as a sample of a distribution, q‾‾ is an unbiased estimate of the mean μq, and s2(qk) is an unbiased estimate of the variance σ2, of that distribution.

NOTE 2   The expression s(qk)⁄√n‾‾‾ is an estimate of the standard deviation of the distribution of q‾‾ and is called the experimental standard deviation of the mean.

NOTE 3   “Experimental standard deviation of the mean” is sometimes incorrectly called standard error of the mean.

NOTE 4   Adapted from VIM:1993, definition 3.8.

Guide Comment: Some of the symbols used in the VIM have been changed in order to achieve consistency with the notation used in 4.2 of this Guide.

B.2.18
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 can also 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.

[VIM:1993, definition 3.9]

Guide Comment: It is pointed out in the VIM that this definition and the notes are identical to those in this Guide (see 2.2.3).

B.2.19
error (of measurement)
result of a measurement minus a true value of the measurand

NOTE 1   Since a true value cannot be determined, in practice a conventional true value is used [see VIM:1993, definitions 1.19 (B.2.3) and 1.20 (B.2.4)].

NOTE 2   When it is necessary to distinguish “error” from “relative error”, the former is sometimes called absolute error of measurement. This should not be confused with absolute value of error, which is the modulus of the error.

[VIM:1993, definition 3.10]

Guide Comment: If the result of a measurement depends on the values of quantities other than the measurand, the errors of the measured values of these quantities contribute to the error of the result of the measurement. Also see the Guide Comment to B.2.22 and to B.2.3.

B.2.20
relative error
error of measurement divided by a true value of the measurand

NOTE   Since a true value cannot be determined, in practice a conventional true value is used [see VIM:1993, definitions 1.19 (B.2.3) and 1.20 (B.2.4)].

[VIM:1993, definition 3.12]

Guide Comment: See the Guide Comment to B.2.3.

B.2.21
random error
result of a measurement minus the mean that would result from an infinite number of measurements of the same measurand carried out under repeatability conditions

NOTE 1   Random error is equal to error minus systematic error.

NOTE 2   Because only a finite number of measurements can be made, it is possible to determine only an estimate of random error.

[VIM:1993, definition 3.13]

Guide Comment: See the Guide Comment to B.2.22.

B.2.22
systematic error
mean that would result from an infinite number of measurements of the same measurand carried out under repeatability conditions minus a true value of the measurand

NOTE 1   Systematic error is equal to error minus random error.

NOTE 2   Like true value, systematic error and its causes cannot be completely known.

NOTE 3   For a measuring instrument, see “bias” (VIM:1993, definition 5.25).

[VIM:1993, definition 3.14]

Guide Comment: The error of the result of a measurement (see B.2.19) may often be considered as arising from a number of random and systematic effects that contribute individual components of error to the error of the result. Also see the Guide Comment to B.2.19 and to B.2.3.

B.2.23
correction
value added algebraically to the uncorrected result of a measurement to compensate for systematic error

NOTE 1   The correction is equal to the negative of the estimated systematic error.

NOTE 2   Since the systematic error cannot be known perfectly. the compensation cannot be complete.

[VIM:1993, definition 3.15]
B.2.24
correction factor
numerical factor by which the uncorrected result of a measurement is multiplied to compensate for systematic error

NOTE   Since the systematic error cannot be known perfectly, the compensation cannot be complete.

[VIM:1993, definition 3.16]

*   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).


**   Footnote to the 2008 version:
The ISO 31 series is under revision as a series of ISO 80000 and IEC 80000 documents. (Some of these documents have already been published.)