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Understanding the meaning of accuracy, trueness and precision

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Antonio Menditto
Antonio Menditto
Antonio Menditto
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Marina Patriarca at Istituto Superiore di Sanità
Marina Patriarca
Bertil Magnusson at Trollboken AB
Bertil Magnusson
  • Trollboken AB
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Abstract and Figures

Clear definitions of basic terms, used to describe the quality of measurements, is essential for communication among scientists as well as when reporting measurement results to clients. Even if appropriate definitions are given in international standards and guidelines, the understanding of some basic terms sometimes proves difficult. The reasons for this are various, e.g., the same words being defined rather differently in encyclopaedias and in international standards as well as concepts, well established in some languages, that may be relatively new in other national communities and at large in the international one. Here we present a matrix intended to clarify the relationships between the type of error affecting an analytical measurement, the respective qualitative concepts (performance characteristics) and their quantitative expression.
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Accred Qual Assur (2006)
DOI 10.1007/s00769-006-0191-z DISCUSSION FORUM
Papers published in this section do not necessarily reflect the opinion of the Editors, the
Editorial Board and the Publisher.
Understanding the meaning of accuracy,
trueness and precision
Antonio Menditto
Marina Patriarca
Bertil Magnusson
Received: 6 June 2006
Accepted: 9 July 2006
C
Springer-Verlag 2006
A. Menditto ()·M. Patriarca
Department of Food Safety and Public
Veterinary Health,
Istituto Superiore di Sanit`
a,
viale Regina Elena 299,
00161 Rome, Italy
e-mail: antonio.menditto@iss.it
Tel.: +39-0649902559
Fax: +39-0649903686
B. Magnusson
SP Swedish National Testing and
Research Institute,
Bor˚
as, Sweden
Abstract Clear definitions of basic
terms, used to describe the quality of
measurements, is essential for
communication among scientists as
well as when reporting measurement
results to clients. Even if appropriate
definitions are given in international
standards and guidelines, the
understanding of some basic terms
sometimes proves difficult. The
reasons for this are various, e.g., the
same words being defined rather
differently in encyclopaedias and in
international standards as well as
concepts, well established in some
languages, that may be relatively new
in other national communities and at
large in the international one. Here
we present a matrix intended to
clarify the relationships between the
type of error affecting an analytical
measurement, the respective
qualitative concepts (performance
characteristics) and their quantitative
expression.
Keywords Terminology .
Accuracy .Trueness .Precision
The understanding of the meaning of some basic terms
(i.e. accuracy, trueness and precision), used to describe the
quality of measurements, has sometimes proven difficult,
even within the analytical community, mainly because:
a. the same words being used with conflicting meaning,
e.g. precision expresses spread within the analytical
community but in common language can be synonymous
of accuracy;1
b. the qualitative concepts of accuracy and trueness
are well established in some languages (German:
Genauigkeit and Richtigkeit, Swedish noggrannhet and
riktighet ), but relatively new in some national communi-
ties (e.g. Italian) and at large in the international one [1].
The misuse of the word accuracy in place of trueness
in most analytical publications in the field of analytical
atomic spectrometry was recently addressed [2].
In this context, it should also be mentioned the difference
existing between common usage of the word “error” and
how it is used in the GUM [3]. According to the GUM,
Error is an idealized concept and errors cannot be known
1Precision–The quality, condition or fact of being exact and accu-
rate. Pearsall, J (ed), The new Oxford Dictionary of English, Oxford
University Press 1998.
exactly [Note GUM §3.2 and further reading in Annex D].
For example, the standard deviation of the mean, some-
times indicated as standard error of the mean, expresses a
quantitative evaluation of the uncertainty of the mean de-
riving from casual effects and not the exact value of the
error of the mean, which is not known.
In addition to the appropriate definitions, given in inter-
national guidelines and standards and reported in Table 1,
the matrix presented in Fig. 1is intended to clarify the rela-
tionships between the type of error affecting an analytical
measurement, the respective qualitative concepts (perfor-
mance characteristics) and their quantitative expression.
Table 1 Definitions of qualitative terms describing the performance
characteristics of a measurement
Accuracy of
measurement
Closeness of agreement between a quantity
value obtained by measurement and the true
value of the measurand (3.5) [6]
Precision The closeness of agreement between
independent test results obtained under
stipulated conditions (3.14) [7,8]
Trueness The closeness of agreement between the
average value obtained from a large series of
test results and an accepted reference value
(3.12) [7,8]
accuracy
trueness
precision
Performance
characteristics
Type of
errors
systematic
error
(total) error
random error
bias
measurement
uncertainty
standard deviation
repeatability/
within-lab reproducibility/
reproducibility
expression of
performance
characteristics
Quantitative
Fig. 1 Relationships between type of error, qualitative performance
characteristics and their quantitative expression
For example, the effect of random errors on a measurement
is expressed as the performance characteristics “precision”,
which can be quantified as the standard deviation of re-
peated measurements on the same sample using the same
method. In more detail, precision is expressed as:
(1) repeatability, when the least changes are allowed (e.g.
assays carried out over a short period of time, by the
same analyst using the same instrument, etc.)
(2) within-laboratory reproducibility (intermediate preci-
sion) when, within the same laboratory, any relevant
influence factor is allowed to vary (e.g. assays carried
out over a longer period of time, by different analysts,
using different reagent lots, in different environmental
conditions and even using different instruments of the
same specifications)
(3) reproducibility, when the precision of the method as
applied in different laboratories is taken into account
(e.g. assays carried out according to a specified sta-
tistical design by different laboratories applying the
same analytical protocol as part of an interlaboratory
collaborative study).
In a similar way, if one or more influence quantities cause
effects on the measurement result that can be identified
as systematic components of the error (systematic error),
such effect is expressed by the performance characteristics
trueness. This can be quantified as bias, i.e. the difference
between the average of several measurements on the same
sample (e.g. a Certified Reference Material) and its (con-
ventionally) true value. The significance of such difference
must be assessed by appropriate statistical tests against
the precision of the bias measurement and the reliability
of the value chosen as reference. Therefore, experimental
precision (as the standard deviation of the mean) and the
uncertainty of the reference value are components of the
uncertainty of the bias estimate, even when no significant
bias is observed.
Since variations of influence quantities may affect a
measurement result in both random and systematic ways,
the qualitative performance characteristics of the measure-
ments – accuracy – includes both trueness and precision,
just as the general term fruits includes both apples and
oranges. It would sound peculiar to talk about fruits and
oranges and, in the same way, it is inappropriate to use the
wording accuracy and precision instead of trueness and
precision.
Accuracy is a qualitative performance characteristics, ex-
pressing the closeness of agreement between a measure-
ment result and the value of the measurand. A quantitative
estimate of the accuracy of a result is essential to define
the degree of confidence that can be placed in it and the
reliability of the decisions based on such result. Such pa-
rameter is the measurement uncertainty, which describes
“the dispersion of the values that could reasonably be at-
tributed to the measurand”, often expressed as a standard
deviation (standard uncertainty) or as an interval including
a larger fraction of such values (expanded uncertainty), ob-
tained by multiplying the combined standard uncertainty
by a specified coverage factor (k). Guidance has been pro-
vided to use both the information provided by repeata-
bility/reproducibility and trueness (bias) estimates for the
evaluation of the uncertainty of measurement [4,5]. The
broken line in Fig. 1takes into account the on-going debate
on the contribution of bias components to measurement
uncertainty.
Although the matrix in Fig. 1may not be exhaustive,
the Authors hope it can provide a simple and visual
way forward to stimulate the discussion among all those
involved in the understanding of how these basic concepts
are related and how they should be used within the
analytical community.
References
1. Inczedy J, Lengyel T, Ure AM (Eds)
(1998) IUPAC Compendium of
Analytical Nomenclature. The Orange
Book. 3rd edn. Blackwell Science,
Oxford, paragraph 18.4.3.5. Published
on-line August 2002 www.iupac.org.
Last accessed May 2006
2. Taylor A, Branch S, Halls D, Patriarca
M, White M (2003) J Anal Atom
Spectrom 18:385–428
3. BIPM, IEC, IFCC, ISO, IUPAC, IUPAP,
OIML (1995) Guide to the expression of
uncertainty in measurement. (GUM).
ISO, Geneva
4. EURACHEM/CITAC (2000)
Quantifying Uncertainty in Analytical
Measurement (QUAM). 2nd Internet
edition. 2000. www.eurachem.com, last
accessed June 2006
5. ISO (2004) ISO/TS 21748 Guidance for
the use of repeatability, reproducibility
and trueness estimates in measurement
uncertainty estimation. ISO, Geneva
6. BIPM, IEC, IFCC, ISO, IUPAC, IUPAP,
OIML (1993) International vocabulary
of basic and general terms in metrology
(VIM). 2nd edition, ISO, Geneva
7. ISO (1993) ISO 3534-1
Statistics–Vocabulary and symbols.
Probability and general statistical terms.
ISO, Geneva
8. ISO 5725-1 (1998) Accuracy (trueness
and precision) of measurement methods
and results–Part 1: General principles
and definitions. ISO, Geneva
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IUPAC Compendium of Analytical Nomenclature. The Orange Book
  • J Inczedy
  • T Lengyel
  • A M Ure
Inczedy J, Lengyel T, Ure AM (Eds) (1998) IUPAC Compendium of Analytical Nomenclature. The Orange Book. 3rd edn. Blackwell Science, Oxford, paragraph 18.4.3.5. Published on-line August 2002 www.iupac.org. Last accessed May 2006
Quantifying Uncertainty in Analytical Measurement (QUAM)
  • Jul 2000
  • Geneva 4 Iso
  • Eurachem
  • Citac
ISO, Geneva 4. EURACHEM/CITAC (2000) Quantifying Uncertainty in Analytical Measurement (QUAM). 2nd Internet edition. 2000. www.eurachem.com, last accessed June 2006
Probability and general statistical terms. ISO, Geneva 8. ISO 5725-1 (1998) Accuracy (trueness and precision) of measurement methods and results–Part 1: General principles and definitions
  • Statistics
  • Vocabulary
Statistics–Vocabulary and symbols. Probability and general statistical terms. ISO, Geneva 8. ISO 5725-1 (1998) Accuracy (trueness and precision) of measurement methods and results–Part 1: General principles and definitions. ISO, Geneva
ISO/TS 21748 Guidance for the use of repeatability, reproducibility and trueness estimates in measurement uncertainty estimation
  • Jan 2004
  • Iso
ISO (2004) ISO/TS 21748 Guidance for the use of repeatability, reproducibility and trueness estimates in measurement uncertainty estimation. ISO, Geneva
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BIPM, IEC, IFCC, ISO, IUPAC, IUPAP, OIML (1995) Guide to the expression of uncertainty in measurement. (GUM). ISO, Geneva 4. EURACHEM/CITAC (2000) Quantifying Uncertainty in Analytical Measurement (QUAM). 2nd Internet edition. 2000. www.eurachem.com, last accessed June 2006
  • Jan 2003
  • J ANAL ATOM SPECTROM
  • 385-428
  • A Taylor
  • S Branch
  • D Halls
  • M Patriarca
  • M White
Taylor A, Branch S, Halls D, Patriarca M, White M (2003) J Anal Atom Spectrom 18:385-428
ISO 3534-1 Statistics–Vocabulary and symbols. Probability and general statistical terms
  • ISO