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8/12/2019 Peer Reviewed Measurement Uncertainty
1/7
Report
Measurement Uncertaintyncertainty in the broad sense is
no new concept in chemistry;
analysts have always sought to
quantify and control the accuracy of their
results. Few analysts would dispute that a
result is of little value without some
knowledge of the associated uncertainty;
clearly, without such information, inter
pretation is impossible.
Correct interpretation depends on a
good assessment of accuracy. When esti
mates of accuracy are optimistic, results
may appear irreconcilable and may be
overinterpreted; with unduly pessimistic
assessments, methods may appear unfitfor a particular purpose and may be opti
mized when it's not necessary.
In general, different methods of estimating uncertainty will lead to different values.
Most estimates of accuracy have been
based on the standard deviation of a series
of experiments or interlaboratory compari
sons,often in association with estimates of
bias in the form of recovery estimates.
When individual effects are being consid
ered, the contribution from random vari
ability can be estimated from repeatability
reproducibility or other precision mea
sures.In addition separate contributions
from several systematic or random effects
can be combined linearly or by the root
sum ofsquares.Finally, the way uncer
tainty is expressed can vary substantially.
Confidence intervals, absolute limits, stan
dard deviations, and coefficients of variance
are all in common use. Clearly, with so
many possibilities for estimating and ex
pressing such a critical parameter, a con
sensus is essential for comparability.
The most recent recommendation is
that accuracy be expressed in terms of a
quantitative estimate of uncertainty as de
scribed in the International Standards Or
ganization's (ISO)Guide to the ExpressionofUncertaintyin Measurement t1) and other
measurement authorities (2,3).The guide
is published under the auspices of several
organizations, includingISO,the Interna
tional Bureau of Weights and Measures
(BIPM) the Organization for International
and Legal Metrology (OIML) and the In
ternational Union of Pure and Applied
Chemistry (IUPAC)
The document lays out a standard ap
proach to estimating and expressing un-
Correctinterpreta
tion ofaccuracyen
sures thatresultsare
judged neitheroverly
optimistically norun
duly pessimistically.
Steve EllisonLaboratory of the Government Chemist
(U.K.)
Wolfhard WegscheiderUniversity of Leoben (Austria)
Alex WilliamsEURACHEM Working Group on
Measurement Uncertainty (U.K.)
S0003-2700(97)09035-5 CCC: $14.001997 American Chemical Society
Analytical Chemistry News & Features, October1, 1997 607 A
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certainty across manyfieldsof measure
mentand,in view ofitspedigree, is widely
accepted by accreditation and certification
agencies worldwide. This Report deals
primarily with the provisions and interpre
tation ofthisdocument, though itisrecog
nized that different approaches are used
in otherISOdocuments.
Defin i t ions
The definitionofmeasurement uncertainty
is"aparameter associated with the resultof
a measurementthatcharacterizesthedis
persion ofthe valuesthatcouldreasonably
be attributedtothe measurand"(1,4).
Thus, measurement uncertainty describes
a range or distribution ofpossiblevalues.
For example,82 5describes s rangeeo
values. Measurement uncertainty, there
fore,differs from "error", whichisdefined
as asingle valuethe difference between a
resultandthe true value.The stated range must also include the
values the measurand could reasonably
take,on the basis of the result. That
makes it quite different from measuresof
precision, which give only the range
within which the mean ofaseries of ex-
perimentswilllie. Precision makes no
allowance forbias;measurement uncer
tainty includes random components and
systematic components. Note that known
systematic errors, or bias, should be cor
rected for as fully as possible; failure to
make such a correction is simply to report
a result known to be wrong. But an uncertainty associated with each correction fac
tor remains and must be considered. This
consideration of systematic effects makes
measurement uncertainty more realistic
than measures such as standard error.
Finally, measurement uncertainty is an
estimate. Obviously, all statistical calcula
tions onfinitesamples provide estimates
of population parameters, but the estimate
goes deeper thanthis.Devising experi
ments that can accurately characterize
uncertainties in method bias and other
systematic effects is extremely difficult.For example, most derivatizations are pre
sumed to proceed to completion. How
certain can the analyst be ofthis?Unfortu
nately, statistics help little; in practice the
chemistisoften forced to make an edu
cated estimate from prior experience
However itiscrucialtorealize that the
attempt must be made the correction for
bias and the uncertainty ofthiscorrection
factor cannot simply be ignored if compa-
rability is to be established
Error and uncertainty. In common parlance, the terms error and uncer
tainty are frequently used interchange
ably. However, several significant differ
ences in the concepts are implied by the
terms defined byISO(4).Errorisdefined
as the difference between an individual
result and the true value of the measur
and. Error, therefore, has a single value
for each result. In principle, an error could
be corrected ifallthe sources of error
wereknown,though the random partof
an errorisvariable from one determina
tion to the next.Uncertainty, on the other hand, takes
the form ofarange and, if estimated for
an analytical procedure and a defined
sample type, may applytoall determina
tions so described.Nopart of uncertainty
can be corrected for. In addition, estima
tion of uncertainty does not require refer
ence to a true value, onlyto aresult and
the factors that affect theresult.This shift
in philosophy marks a concept rooted in
observable, rather than theoretical, quan-
Box 1. Calcu lati ng uncert aint y using ISO rules
Rule1:Alllontributions are eombined in the formoofsandard deviationn sSDs).
Combining as SDs allows calculating a rigorous combined SD using standard
forms. It does not imply that the underlying distribution is or needs to benormalevery distribution has an SD. It is not perfectly rigorous to deduce
a confidence interval from a combinedSD,but in most cases, especially when
three or more comparable contributions are involved, the approximation is at
least as good as most contributing estimates.
Rule2:Uncertainties are combined according to
in in whichu(y)is the uncertainty ofa valuey,lFu2,- the uncertainties ofthe independent parametersxh x2,... on which it depends, anddy/dXjis the
partial differential ofywith respectto *,-.When variables are not independent,
the relationship is extended to include a correlation term (1).
Rule2establishes the principle of combination of root sum squares. One
corollaryisthat small components are quickly swampedbylarger contributions,
making it particularly important to obtain good values for large uncertainties
and unnecessary to spend time on small components. In pictures, this looks
like a simple Pythagorean triangle. For the uncertaintiesuxandu2,the
combinationuccan be visualized.
Rule3:TheSDobtained ffom Eq. . 1neds to ob multiplied dbycoverage factor
kto obtain a range called the expanded uncertainty, which includes a large
fraction of the distribution. For most purposes,k=2 is sufficient (2)and will
give a range corresponding to an approximately95%confidence interval.
Similarly,k=3 is recommended for more demanding cases.
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titles. To further illustrate the difference,
the result ofananalysis after correction
mayby chancebe very close to the
value of the measurand, and hence have a
negligible error. The uncertainty may
nonetheless still be very large, simply be
cause the analystisunsure ofthesize of
the error.Uncertainty and quality assur-
ance.ISOexplicitly excludesgrosserrors
of procedurefrom considerationwithinan
uncertaintyassessment.Uncertainty esti
mates can realistically apply onlytowell-
established measurement processesinsta
tisticalcontrol, and thus they areastate
ment of the uncertainty expected when
proper quality control (QC) measures are
inplace. Itisthus implicit thatQCand qual
ityassurance (QA) processesbe inplace
and within specification if an uncertainty
statementis tobeat allmeaningful.
Repeatability andreproducibility
The most generally applied estimates of
uncertainty at present are those obtained
from interlaboratory comparisons, particu
larly those using the collaborative trial
protocols ofISO5725 (5) and the Associa
tion of Official Analytical Chemists
(AOAC)(6).
For legislative purposes, the collabora
tive trial reproducibility figure is the closest approach to uncertainty that attempts
to estimate the full dispersion of results
obtained by a particular metiiod, and it
has the considerable advantages of sim
plicity and generality, though at high cost.
Another substantial advantage is its objec
tivity, because itisbased entirely on ex
perimental observations inarepresenta
tive range of laboratories. Though it
serveswellin cases in which the chief
issue is comparability among particular
laboratories with a common aim several
factors leave this approach wantingReproducibility is inevitably a measure
ofprecision;although it covers a range of
laboratorybias,it cannot cover bias inher
entinthe methoditself,nor, in general,
sample matrix effects. Arguably, these
effects are not relevant for a standard
method, which may simply define a proce
dure that generatesaresult for trade or
legislative purposes. Many methods, in
deed fall into this class; even when a
metiiod purports to determine a specific
molecular species, there is no guarantee
that it determines all thatispresent or,
indeed, any particular species at all.
An example is the semiquantitative
AOACmethod for detecting cholesterol.
Though standardized and properlyac
cepted for certain trade and regulatory
purposes on the basis of collaborative trial
data showing sufficient agreement be
tween laboratories (7), subsequent work
using internal calibration (8)has shown
that method recovery is poorer than the
reproducibility figure suggests. It follows
that long-term studies of cholesterol levels
in food could be expected to misinterpretchanges in apparent level particularly
nations using different cholesterol
determination methods Reproducibility
figures will in treneral suffer from the
absence ofbiasinformation
These arguments suggest that repro
ducibilitywillgenerally underestimate
uncertaintybut not necessarily.Asingle
laboratory can have much smaller uncer
tainties for a determination than the repro
ducibility figure would indicate, which
tends to includearange of pooras wellas
good results. This issue can be put morebluntly: What does the spread of results
found byahandful of laboratories on a
specific set of samples at some time in the
past have todowith the results ofanindi
vidual laboratorytoday?Indeed, this is the
very question that mustbeanswered
quantitatively before any laboratory can
make use of collaborative trial information
inaformal uncertainty estimate. It follows
that reproducibility, although a powerful
tool, is notapanacea.
The ISO approachThe approach recommended in the ISO
guide, outlined below, is based on com
bining the uncertainties in contributory
parameterstoprovide an overall estimate
of uncertainty (Figure 1).
To begin, write down a clear statement
ofwhat isbeing measured, including the
relationship between the measurand and
the parameters (measured quantities, con
stants, calibration standards, and other
influences) on which it depends. When
Figure 1 . Uncertainty estimation process.
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Figure 2. Dioxin analysis.
possible, include corrections for known
systematic effects. Though the basic spec
ification information is normally given in
the relevant standard operating procedure
or other method description, itisoften
necessarytoadd explicit terms for factors
such as operating temperatures and ex
traction time or temperature, which will
not normally be included in the basic cal
culation given in a method description.
Then, for each parameterinthis rela
tionship, listthepossible sources of uncer
tainty, including chemical assumptions.
Measure or estimate the size of the uncer
tainty associated with each possible source
of uncertainty(orforacombinationof
sources). Combine the quantified uncer
tainty components, expressed as standard
deviations, accordingtothe appropriate
rules (seeBox onp.608 A)),ogive ecom
bined standard uncertainty, and apply theappropriate coverage factorto givean ex
panded combined uncertainty
The most important features are that
all contributing uncertainty components
are quantified as standard deviations in
the first instance, whether they arise from
random variability or systematic effects;
also, that estimates of uncertainty from
experiment, prior knowledge, and profes
sionaljudgment are treated in the same
way and given the same weight.
Quantifyingallcontributing uncertainty
componentsasstandard deviationspro
videsaparticularly simple and consistent
methodof calculationbased on standard
expressions for combining variances.It is
justified in principle because, although an
errorin aparticular casemay besystem
atic, lackof knowledgeaboutthesizeof the
errorleadstoaprobability distribution for
theerror.This distribution canbetreated
inthesame way asthat ofarandom vari
able. Treating estimatesofuncertainty fron
experiment prior knowledge and profes
sional judgmentthe same wayand giving
them the same weight ensures thatall
known factors contributingtouncertainty
are accounted forevenwhen experimental
determinationisnot possible
In principle, this approach overcomes
many ofthedeficiencies in currently used
approaches. It is much quicker and lesscostly to apply than a collaborative trial,
but it can use collaborative trial data ad
vantageously if available. The approach
covers all the effects onaresult, system
atic or random, and it takes into account
all available knowledge. In addition, it
mandates a particular form of expression,
leadingtoimproved comparability in un
certainty estimates
However, disadvantages exist. The
ISO approach, because it requires appro
priatejudgment, cannot be entirely objec
tive;to some extent it relies on the experi
ence of the analyst.Asignificant costin
time and effort isafactor; estimating un
certainties on the basis oflocalconditions
without using published data involves
more effort than simply quoting a pub
lished reproducibility figure.The lack of objectivity can be compen
sated for by third-party review, such as
quality system assessment, interlabora-
tory comparisons, in-house QC sample
results, and certified reference material
checks. Finally, it should be clear that a
decision to excludeaparticular contribu
tion entirely rather than makesomejudg
ment ofitssize represents a de facto deci
sion to allocate the contribution a size of
zero hardly an improvement.
Cost,too,may berecouped in direct or
indirect benefits. Uncertainty estimation
improves knowledge ofanalyticaltech
niques and principles, formingapowerful
adjuncttotraining.Knowing themain con
tributionstouncertainty determines the
directionof methodimprovement most
effectively. Efficiency can be improvedwith
minimal impactonmethod performance.
Finally, normalQAprocedures,such as
checking the method for use, maintaining
recordsofcalibration and statisticalQC
procedures, should provideallthe required
data;additional costshouldbe no morethan
thatofcombining the dataappropriately
Sources of uncertainty
Many factors affect analytical results, and
every one is a potential source of uncer
tainty. In sampling, effects such as ran
dom variations between different samples
and any potential for bias in the sampling
procedure are components of uncertainty
affecting thefinalresult. Recovery ofan
analyte from a complex matrix, or an in
strument response, may be affected by
other constituents ofthematrix. Analytespeciation may further compound this
effect. When a spike is used to estimate
recovery the recovery of the analyte from
the sampleiricivdiffer" from the recoverv
ofthespike Stability effects are also im-
portant but frequently are not well-known
Cross-contamination between samples
and contamination from the
laboratoryemnrrtnment are pupr nrpcpnt risk s
Though ISO does not include accidental
gross cross-contamination in its definition
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of uncertainty, as it represents loss of con
trol ofthemeasurement process, the pos
sibility of background contamination
should nonetheless be considered and
evaluated when appropriate.
Although instruments are regularly
checked and calibrated, the limits of accu
racy on the calibration constitute uncertainties. Calibration used may not accu
rately reflect the samples presented; for
example, analytical balances are com
monly calibrated using nickel check
weights, although samples are rarelyof
such high density. Though not large in
most circumstances, buoyancy effects
differ between calibration weight and sam
ple. Other factors include carry-over and
systematic truncation effects.
The molarity ofavolumetric solution is
not exactly known, even iftheparent ma
terial has been assayed, because some
uncertainty relating to the assay proce
dure exists.A widerange of ambient con
ditions, notably temperature, affects ana
lytical results. Reference materials are
also subjecttouncertainty; fortunately,
most providers of reference materials now
state the uncertainty in the manner rec
ommended in the guide.
The uncritical use of computer soft
ware can also introduce errors. Selecting
the appropriate calibration model is im
portant, and software may not permit the
best choice. Early truncation and round
ing offcanalso lead to inaccuracies in the
final result.
Operator effectsmaybe significant;
they can be evaluated either by predicting
them or by conducting experiments in
volving many operators. The latterap
proachwillnot normally detect an overall
operator bias (for example, a particular
scale reading may be taken in the same
manner byagroup of operators similarly
trained), but the scope of variation can be
estimated. "Operator effect" could reasonably be considered a proxy for a range of
poorly controlled input parameters such
as scale-reading accuracy time and dura
tion of agitation during extraction and so
on It follows thataformal mathematical
model oftheexperimental process would
not normally include "operator" as an in-
niit factor but only the specific factors un
de r ooerator
Random effects contribute to uncer
tainty in all determinations, and this en
try is usually included in the list as a
matter of course. Conceptualizing every
component of uncertainty as arising
from both systematic and random effects
is also frequently useful; this step avoids
the most common trap for the unwary
overlooking systematic effects in the
effort to obtain good precision measures.Both need to be taken into account,
though the ISO approach requires only
the overall value.
Determinands are not always com
pletely defined. For example, volumes
may or may not be defined with refer
ence to a particular set of ambient con
ditions. Similarly, the determinand may
be defined in terms ofarange of condi
tions.For example, material extracted
from an acidified aqueous solution at pH
below 3.0 allows substantial latitude.
Such incomplete definitions result in thedeterminand itself having a range of val
ues,irrespective of good analytical tech
nique, and that range constitutes an
uncertainty.
Many common analytes, such as fat,
moisture, ash, and protein, are defined not
in terms ofaparticular molecular or
atomic species but against some essen
tially arbitrary process. In effect, the re
sult is simply a response to a stated proce
dure,expressed in the most convenient
units. Such measurements are not gener
ally compared with results from other
methods; in effect, bias is neglected by
convention. However, the procedure itself
may lack full definition or permitarange
of conditions, giving rise to uncertainties.
Of course if comparison with other meth
ods is desired additional sources of un
certainty including method bias must be
taken into
Increasing confidence
The ISO guide suggests multiplying the
standard uncertainty by a coverage fac
torkto express uncertainties when a
high degree of confidence is desired.
This representation exactly mirrors the
situation in conventional statistics, in
which a confidence interval is obtainedby multiplying a standard deviation for a
parameter by a factor derived from the
Student ^-distribution for the appropriate
number of degrees of freedom.
The formal approach in the guide re
quires estimation ofasimilar parameter,
the "effective degrees of freedom", and
uses this value in the same way. Though
the details are beyond the scope of this
article, some important points can be
made.
This parameter is almost invariably
dominated by the number of degrees of
freedom in the dominant contribution to
the overall uncertainty. When the domi
nant contribution arises from sound and
well-researched information, effective de
grees of freedom remain high, normally
leadingtok= 2for near95%confidencce
Only where large uncertainty contribu
tions are based on meager datawillthe
choice ofkbecome significant.Aprag
matic approach, therefore, is simply to
adoptk = 2for routtne work ,ndk k=
when a particularly high confidence is
required(2)
The question of possible distributions
mustalsobe consideredat thepointofde
ciding coverage factors. Although the guide
usesacombination of standard deviations
based on established error propagation
theory, the step from standard deviation to
confidence involves some assumptions.
The guide takes theviewthat,in mostcir-
Table 1. Contributions to uncertainty in dioxin analysis.
Parameter u(RSD) Main contributio n3
Oss 0.02
V 0.02
Ak an d -4SS 0.09
RRFn 0.08
"lspk 0.12
Combine d uncertainty 0.17
Syringe specification; certified reference solution
uncertainty
Density (volume determined by weight)
Permitted abundance ratio range
Range permitted by method
Permined range of spike recovery
[(0.02) +(0. 02) +(0. 09) + (0.08)2 +(0.12)2]1/2
(a) Contributions are listed if they contribute more than 10% of the stated uncertainty.(b) Permitted ranges are treated as limits of rectangular distributions and adjusted to SDvalues (1)by dividing by the square root of 3.(c) Recovery of added material is not, in general, fully representative of recovery of analytematerials.
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cumstances, the centrallimittheoremwill
apply, and the appropriate distributionwill
be approximately normal. Certainlyit is
raretocalculate confidence intervals based
on other distributionsingeneral analytical
chemistry, ifonly because it isunusual to
have sufficient datatojustify other assump
tions. Nonetheless, when additional knowl
edge about underlying distributions exists,
it ismost sensible to basekonthe best
available information.
Dioxin example
The analysis ofdioxinsin the effluentof
paper and pulp mills by isotope dilution
MS (Figure2)isagood example (9). For
the sake ofdiscussion,we willconsider
only the analysis of 2,3,7,8-tetrachloro-
dibenzodioxin (2,3,7,8-TCDD) and will
ignore the normally important uncertain
ties caused by interference from other
TCDD isomers,GCintegration, and res
olution difficulties.Byway of illustration,
some minor contributions that would
not normally be included will also be
examined.
The basic equation for determining the
concentrationCxof TCDD is
Cx=AkQss/AaJiRFnVR%pk
in whichAk isthe peak area oftheana-
lyte,Qssis the amount of spike,i4ssis the
peak area ofthestandard,RRFnis the
relevant response factor for the relevant
ion13C-12, Fis the original sample vol
ume,andi?spkisthe (nominal) recoveryof
the analyte relative to added material.
Rakmerits explanation, because it is
not used in the standard. Because the13
C-12 calibration spike is added to the
slurry and is not naturally part ofthesam
ple, differential behavior is possible. If
measurable, this behavior would appear
as imperfect recovery of analyte.Acom
plete mathematical model of the system
therefore requires some representation of
the effect. Because no existing parameter
in the equation is directly influenced by
recovery the recovery term has been
added in the form ofanominal correction
factor The resultis abasic equation en
compassing all the main effects on the
result
Identification oftheremaining contri
butions to the overall uncertaintyisbest
achieved by considering the parameters
in the equation, any intermediate mea
surements from which they are derived,
and any effects that arise from particular
operations within the method (such as the
possibility of"spikepartitioning"). Table 1
lists parameters, calculated uncertainties
(as relative standard deviations), and
some contributory factors.
Informationin Table 1 showsthat uncer
tainties associated with the physical measurements of volume and mass contribute
essentially nothingtothe combined uncer
tainty and thatanyfurther study should be
directed primarilyat theremainingcompo
nents. The largest contributionarisesfrom
the extraction recovery step,in linewith
most analysts' experience.
The method studied hereisunusualin
specifying directcontrol of allthe major
factors affecting uncertainty, which makes
itrelativelyeasy toestimate uncertainty as
longasthe method isoperating withincon
trol.For most methods currentlyinuse,
however, such controllimitsarenot closely
specified.Typically,one ortwocriticalpa
rameters are given single target values, and
precision controllimitsare setIt thenfalls
to the laboratorytoestimate the contribu
tion ofits ownlevel ofcontrol tothe uncertainty, ratherthan simplydemonstrating
compliancewithan established set of fig
ures and an associated, carefully studied,
uncertainty estimate.
Legislation and compliance
Two issues are importantwhenuncer
taintyisconsidered in the context of legis
lation and enforcement. The first con
cerns the simpler problem of whether a
result constitutes evidence ofnoncompli
ance with some limit, particularly when
the limitiswithin the uncertainty quoted.The second issue is the use of uncertainty
information in setting limits.
Two instances in compliance are
clear-cut: Either the result is above the
upper limit, including its uncertainty,
which means that the result is in non
compliance (Figure 3a); or the result,
including its uncertainty, is between the
upper and lowerlimits,and is therefore
in compliance (Figure 3d). For any other
case, some interpretation is necessary
and can be made only in the light of the
and with the knowledge and
understanding of the end of the
information
For example, Figure 3b represents
probable noncompliance with the limit,
but noncompliance is not demonstrated
beyond reasonable doubt. In the case of
legislation, the precise wording needs to
be consulted; some legislation requires
that, for example, process operators dem
onstrate that they are complyingwitha
limit. In such acase,Figure 3b represents
noncompliance with the legislation; compliance has not been demonstrated be
yond doubt.
Similarly, if legislation requires clear
evidence of noncompliance withalimit
that triggers enforcement, although there
is no clear demonstration of compliance,
there is insufficient evidence of noncom
pliance to support action, as in Figure 3c.
In these situations, end-users and legisla
tors must spell out how the situation
should be handled.
Upperlimit
Lowerlimit
(a)Result above
limit plusuncertainty
(b)Result abovelimit, but limit
withinuncertainty
(c)Result belowlimit, but limit
withinuncertainty
(d)Result belowlimit minusuncertainty
Figure 3. Uncertainty and compliance limits.
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A recent editorial (10)pointed out the
need to avoid setting limits that cannot be
enforced without disproportionate effort.
An important factor to consider is the actual
uncertainty involved in determining a level
of analyte; if legislation is to be effective, the
uncertainty must be small in relation to any
limiting range. In chemistry, measurementrequirements tend to follow a "best avail
able"presumption, even when this policy is
not actually written into legislation; an ex
ample is the Delaney Clause (11).
As the state of the art improves, new
measurements become possible and are
immediately applied, leading to a situa
tion in which the best available technol
ogy is the only acceptable technology. In
such a situation, uncertainties are, inevi
tably, hard to quantify well; they will of
ten be larger than required for the pur
pose. That legislation takes into account
the full uncertainty is particularly impor
tant; failure to include significant compo
nents may unreasonably restrict enforce
ment. In particular, the possibility of sys
tematic effects being considered is vital;
legislation based on measurement of
absolute amounts of substance, as in
most new European environmental legis
lation, must consider the full range of
methods and sample matrices that may
fall within that legislation.
Another important consideration is theinterpretation of results and their relevant
uncertainties against limits. Assumptions
about the handling of experimental uncer
tainty in interpretation for enforcement
purposes must be clearly stated in the
legislation. Specifically, do limits allow for
an experimental uncertainty or not? If so,
how large is the allowance?
A fundamental factor is how well leg
islators understand uncertainty. The
need to set limits in some contexts is
easily understood, such as how much of
a toxic compound is acceptable in anenvironmental matrix. However, judging
compliance is trickier, and a better un
derstanding of analytical uncertainly is
required. The current move toward spec
ifying method performance parameters,
such as repeatability, reproducibility,
and recovery rather than the method
itself, is a step in the right direction; but
these parameters do not necessarily
cover all of the significant components of
uncertainty. What is required is the addi
tional specification of the measurement
uncertainty to meet the needs of the
legislation.
Ellison's workwassupported under contractwith the Department of Trade and Industry as
part of the National Measurement SystemValidAnalytical Measurement Programme.
References
(1) Guide to the ExpressionofUncertaintyinMeasurement;ISO:Geneva,,193;ISBN92-67-10188-9.
(2) Quantifying Uncertainty ininalyticalMeasurement;Published do nehalf foEURACHEM by Laboratory of the Government Chemist: London,1995;ISBN0-948926-08-2.
(3) Taylor,B.N.; Kuyatt, C. E.Guidelines forEvaluating and ExpressingthtUncertaintyofNISTMeasurementResults;NIST Technical Note 1297, National Institute of Stan
dards and Technology: Gaithersburg,MD,1994.
(4) International VocabularyofBasicanaGeneral Standard Termsin Metrology,ISO:Geneva,1993;ISBN 92-67-10175-1.
(5) ISO 5725:1986,PrecisionofTestMethods:DeterminationofRepeatability anaReproducibility fora Standard Method byInter-laboratoryTests;ISO:Geneva, 1987.
(6) Youden,W.H.; Steiner, E. H.StatisticalManualofthe Associationof Official Analytical ChemiststAOAC:Washington, DC,1982.
(7) Thorpe, C.W.Assoc.Anal.Chem. 1969,52,778-81.
(8) Lognay, G. C; Pearse,J.;Pocklington, D.;Boenke, A.; Schurer,B.;Wagstaffe,P.J.
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Steve Ellison is head of the analytical
quality and chemometrics section at the
Laboratory of the Government Chemist
(U.K.). His research interests include sta
tistics, validation and measurement un
certainty, and chemometrics in the con
texts of regulatory analysis and analyticalchemistry. Wolfhard Wegscheider is profes
sor of chemistry and dean of graduate
studies at the University ofLeoben (Aus
tria) and chair of EURACHEM Austria.
Alex Williams is chair of the EURACHEM
Working Group on Measurement Uncer
tainty Address correspondence about this
article to Wegscheider at Institute of Gen
eral and Analytical Chemistry University
ofLeoben A-8700 Leoben Austria
(wegschei@unileoben ac at)
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