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Article ID
1301200103
Author Anders Kallner, Dept. of Clinical Chemistry, Karolinska
Hospital, S - 171 76 Stockholm, Sweden
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The concept uncertainty in
measurement
It is unavoidable that all decisions, all actions
and therefore all measurements harbour an inherent uncertainty. For
the lay - man/woman the term uncertainty is used in many
connections and is a frequently used concept with no scientific
meaning. However, metrologists have defined uncertainty and given
it a scientific content that is useful for all measurements. The
definition ofuncertainty in measurementaccording to ISO is:
'parameter, associated with a result of a
measurement that characterises the dispersion of the values that
could be reasonably attributed to the measurand'.
This definition may be difficult to apply to
practical work and we shall therefore expand on the definition and
explain how it can be used for describing how well a measurement
procedure performs'.
The result of a measurement shall always give
information about an interval within which the results can be
expected with a given probability. This can be reported as an
interval, as a standard deviation (SD), coefficient of variation or
standard error of the mean (SEM). Most commonly the distribution of
results is given as one SD. The SD is a description of the
precision and can always be calculated from 2 or more results but
the interpretation of this value requires knowledge of the
properties of the distribution of values. The most probable value
within a Gaussian distribution is represented by the mean. Together
with the mean, the SD fully defines the shape of a Gaussian
distribution. In these distributions the mean defines the position
of the distribution on the X - axis and the SD its width and
height. The SD is therefore a measure of the random error (the
width of the distribution). In a Gaussian distribution about 2/3 of
all results will be found between -1 SD and +1 SD counted from the
mean of the distribution. Further, about 95 % will be found within
the interval -2 SD to +2 SD and about 99 % between -3 SD and +3
SD.
All modern computers and calculators have
predefined routines for the calculation of the mean and SD.
However, the calculated properties are only estimates of the true
standard deviation and mean of the distribution. If these estimates
are made from too small a number of observations the estimate will
be non - reliable i.e. the uncertainty of the standard deviation
and mean will be large.
When characterizing a result we do not only want to
describe how precise we have managed to perform the measurement
(repeatable or reproducible) but also how correct it is i.e. the
deviation of the result from the "true value". We never know the
"true value" and it is therefore not possible to describe the
trueness of the result. This dilemma is resolved by assigning a
value and call it the "true value". This is normally called
"conventional true value" (convention is here used in the meaning
of agreement) or 'assigned value'. The difference between the mean
of many measurements of the same quantity and the conventional true
value is the "bias". The statistic "trueness" will therefore
describe the systematic error.
The precision of a result (standard error of the
mean) can be improved by increasing the number of observations
whereas the trueness of the result cannot be influenced this way.
In our role as analysts we are interested to find not only the
random error but also the systematic error. However, as a consumer
of results of measurements we would prefer a concept that would
include both the random and the systematic error for a single
measurement i.e. both the precision and the trueness. This concept
is called accuracy and in laboratory medicine often equivalent to
total error . Theconcept of uncertaintyas defined above will
offer a simple and tangible alternative to total error and will
also give us a possibility to avoid the use of "error" to describe
the variation inherent in measurements.
An accepted scientific approach to solve a problem
is to break it down into smaller entities and study each of them.
This approach can be used also to estimate the uncertainty in
measurements and is usually not too complicated. However, as in all
sciences the synthesis of results that should be performed is the
difficult part when scientists may make mistakes and end up with
grossly erroneous conclusions. The concept of uncertainty as
defined by ISO requires that all steps involved in a measurement
are defined and evaluated with regard to their uncertainty. This is
a great help in characterizing and optimising the performance of a
measurement procedure because the sources of uncertainties will be
revealed. The chemist can review the result and select the steps
that require improvement in an orderly and reproducible manner. All
steps should be included, preanalytical, e.g. sampling and sample
preparation, as well as analytical, e.g. calibrations, dilutions
and postanalytical e.g. transformations and corrections. The
accumulated data shall then be combined. The following text will
describe how these steps can be systematized and performed in a
pragmatic manner.
Formal accreditation of laboratories and
measurement procedures or methods according to the ISO standards
15189 (1) and 17025 (2) requires that the uncertainty in
measurements is estimated. The preferred method for estimation of
uncertainties is described in 'Guide to the Expression of
uncertainties n measurements' (GUM) (3).
Besides estimating the uncertainty in measurements
to identify areas in which improvements should be focused, there is
a point in estimating the uncertainty in all measurement that
produce results for the diagnosis and management of diseases. The
reason is that the uncertainty in measurements will include a
contribution from calibration etc that affect the bias as well as
estimates of the imprecision and any pre - and postanalytical
uncertainties.
The concept of uncertainty is not a statistical
concept in traditional sense i.e. it needs not be associated with a
known distribution of the data. The uncertainty shall rather be
understood as an interval within which the result can be found with
a given probability. Thus, the result will be within the interval
but all values within the interval have the same probability to
represent the result. This is quite different from other
distributions, e.g. the Gaussian distribution where the mean is the
most probable value. Therefore, there is not necessarily any
symmetry in the concept of uncertainty. There is no value that is
more probable or common than any other. It is convenient, though,
to let a number represent the distribution and one can choose any
representative value from the interval. One is as good as the other
but the central value has advantages from a presentation point of
view. By these statements we have in fact described the essential
features of a 'rectangular distribution'
The calculation or estimation of the uncertainty in
measurements is principally very simple. This is done by estimating
the uncertainty in each single step of a procedure (input
variables, X i ) and combining them in an 'uncertainty
budget'. The combination of the individual uncertainties follows
similar rules as the propagation of errors in normal statistics
giving the 'combined uncertainty' for the procedure. The combined
uncertainty is the concept that is closest to 'the total
error'.
In the examples in this document we will use a
worksheet from Excel 5.0 that simplifies these calculations and do
not require any knowledge of the mathematics behind. The worksheet
can be used for evaluation of all uncertainty budgets that deal
with independent observations.
It is essential when establishing a realistic
uncertainty budget to identify the variables that give rise to the
uncertainty and their sizes. Therefore one must have detailed
knowledge about the procedure of measurement to allow
identification and quantification of all reasonable sources.
Examples of sources of uncertainty in our field are the measurement
of volumes, weighing, reaction temperature, purity of reagents, and
value assigned to the calibrator. Also properties of the instrument
used e.g. the size and tolerance of the cuvette, if the instrument
uses more than one cuvette they may be different, the wavelength
etc. If a visual recording is made one must consider the position
of the eye in relation to the scale, i.e. one source of uncertainty
that can be referred to the operator. When a calibration function
is established one must estimate the uncertainty of the value
assigned to the calibrator. Possible sources that might influence
the calibration function are for instance the assigned value of the
calibrator, the fitting of the curve, the dilution of the
calibrators etc. When an extraction is included one must estimate
the yield. Even if all sources of bias were eliminated an
uncertainty of the success of that procedure remains and should be
estimated.
All these uncertainty sources must be evaluated and
brought into the uncertainty budget. An experienced chemist may
directly disregard some of the uncertainty sources because the
experience is that they are very small or because those remaining
are much larger.
The procedure of measurement shall then be
described in mathematical terms to illustrate how the different
variables affect each other and how their uncertainties can be
joined in a combined uncertainty. This procedure is tricky and
requires experience from establishing stochiometric calculations
i.e. the qualitative and quantitative description of a chemical
reaction and calculations of concentrations and amounts
involved.
The estimation of the size of the sources of
uncertainty can be done in two different ways called type A and
type B. The value and results of both approaches are treated
similarly but the type A is recommended whenever possible. In both
cases the 'standard uncertainty' is estimated. The standard
uncertainty is abbreviated u(x i ).
In this model the estimation is based on the
standard deviations derived from repeated measurements. The SD and
the standard uncertainty will therefore have the same size. A word
of warning: sometimes the variation is given as a coefficient of
variation (CV) or confidence interval rather than SD. That
information can also be used but it must then be corrected for what
the numbers represent e.g. multiply with the result of measurement
and divided with 100 if the CV is given in percent or multiplied
with the square root of the number of observations if the
confidence interval or SEM (standard error of the mean) is given.
One must also clarify how many SD the information refers to. As a
rule the number is one but sometimes multiples are given, for
instance two SD.
Sometimes, and particularly in complex measurement
procedures, we do not have access to or we are not able to estimate
the variation from repeated experiments, which is a prerequisite
for the estimation of the SD. The professional experience,
information in the literature or specifications from a manufacturer
will usually allow the demarcation of an interval within which a
result can reasonably be expected. For instance, it is fairly safe
to assume that the European woman is between 130 cm and 210 cm
tall, that a litre of milk costs between USD 0,1 and 2 and that one
litre of water has a mass between 994 g and 1004 g. The more one
knows about the procedure of measurement and the items measured the
better will the estimate of interval be. In laboratory medicine it
is often important to find a reasonable interval for the volume,
the mass or the reading of an instrument. For instance a 1 mL
pipette might deliver between 0.90 mL and 1.05 mL, the body mass of
a grown up man without excessive fat might be between 65 and 85 kg;
based on your experience your might even assume that it is between
69 kg and 76 kg etc.
The interval that is defined in this way will not
identify any result within the interval as being more reasonable
than any other in the same interval. Thus, the interval represents
a rectangular distribution of possible results.
Throwing a single dice will give results belonging
to a rectangular distribution. One cannot foresee the number of
dots that will come up but a reasonable (the largest possible)
interval is 1 - 6. In fact no other results can be obtained. The
probability for each result within the interval is the same,
provided the dice is fair. The mean of the interval (3.5), however,
can never be obtained!
Given an interval there is a somewhat smaller
interval within which the probability that a result will occur is
increased. This new interval is created from the half - width of
the initial interval divided by the square root of 3 (about 1.73)
in both directions from the middle of the initial interval. It is
about twice as common that results will be within this interval as
outside these limits. Using the example with the dice, the inner
interval will be from 2 to and including 5. For the dice it means
that between 2 and 5 there are four alternatives (2, 3, 4 and 5),
whereas outside there are only two, 1 and 6. It is therefore more
probable that any of the four dots 2 to 5 will show up than any of
the two outside the smaller interval. The probability that any
given number of dots within the new interval will be obtained is
the same as outside and one cannot predict which. I.e. it is more
probable than one of four given alternatives is obtained than one
of two.
The width of this inner interval is twice the
standard uncertainty 2 u(x i ).The standard uncertainty
will correspond approximately to the probability within the
interval mean � 1 SD in a Gaussian distribution where about 2/3 of
all observations will be found. You can convince yourself about
this by playing with a good dice and you would expect 2/3 of all
answers to be found between and include 2 and 5 dots.
An example from our own profession is the
estimation of the uncertainty of a measured volume using a two -
litre measurement cylinder. Suppose we want to measure 500 mL, and
assume a reasonable interval to be � 3 % or (485-515) mL. The
standard uncertainty is then 15 (half the interval) divided by the
square root of 3 i.e. 8.7 mL.
Once the sources of uncertainty have been
identified and the sizes of the uncertainties estimated then we
face the problem to combine the contributions to an uncertainty for
the entire procedure i.e. the combined uncertainty in the result y.
This is abbreviated u c (y).
Let us begin with an example:
We want to make a dilution of a sample and are only
interested in the final volume. According to the procedure we shall
take 10 mL of the sample solution and dilute that to 500 mL. We use
the measuring cylinder from the example above and measure the
sample with a pipette with a relative uncertainty of 5 %. Thus, we
now have each volume defined to its size and accompanying
uncertainty. Observe that the uncertainty of the measuring cylinder
is given as an interval whereas the uncertainty for the pipette is
given as a relative standard uncertainty.
The volumes V 1 and V 2
should be added and thus the 'reaction' could be written
The standard uncertainties are added but not as
such but as their squares:
The combined uncertainty is then obtained by taking
the square root from the sum, in this example 8.7 mL. Perform the
calculations yourself and find that the contribution from the
pipette is of minor importance in the combined uncertainty!
The standard uncertainty will thus demarcate an
interval where we can estimate that 2/3 of all the results will be
found. This is also the usual way to give the variation (usually
the standard deviation) of results in scientific literature. If we
want to find the interval that is large enough to give a 95 %
probability to cover the results in a Gaussian distribution the SD
should be multiplied with about 2 for a two - tailed distribution
(the size of the factor is depending on the number of
observations). To reach a corresponding probability for the
combined uncertainty it shall be multiplied by 2. If we wish a
larger probability then a larger factor, for instance 3 for about
99 % probability, should be used. This factor is called the
coverage factor ( k ) and the result expanded uncertainty U
y . The coverage factor shall always be given in the
answer together with the uncertainty. In case no coverage factor is
given then the combined standard uncertainty covering about 2/3 of
the result is given (k=1).
When estimating the combined uncertainty ( u
c (y)) the starting point is to define how the different
parts of the procedure interact. In our model we assume that the
uncertainty sources are independent. In the example above the two
volumes were added to reach the total volume. For additions
(subtractions), the combined uncertainty is the square root of the
sum of the squares of the ingoing standard uncertainties. In case
the variables shall be multiplied (divided) the squares of the
ingoing relative standard uncertainties shall be added. When the
square root is drawn the relative combined uncertainty is
achieved.
The mathematical expressions that describe how the
standard uncertainties shall be combined become rather complicated
when the uncertainty budget for a procedure contains all four
operators and a variable may participate as a logarithm or
exponent. The generic rule for the combination is based on partial
derivatives but we will use an approximate numerical method for
solving partial derivatives. This can conveniently be achieved by
using a spreadsheet program like Excel�.
Kragten (4) originally described the numerical
approximation of partial derivatives. The document from Eurachem
(5) describes how this method can be used in a worksheet.
All cells in the worksheet that will be filled by
calculations are protected to avoid unintentional changes in the
program. Cells that can be changed are marked with a blue border.
The number of decimals is fixed to three that will give a
sufficient presentation of results within laboratory medicine even
if it sometimes exaggerates the precision. You can perform
calculations directly in that cell where the value finally will be
placed. Never copy the contents of a cell into another, delete and
input it again or unforeseeable errors may occur.
It is suggested that you enter different data into
the given examples to see how the outcome changes.
Enter the names of the input variables in row 3 of
the worksheet. The input variables can be entered in any order. The
corresponding names will appear in column B, rows 10 to 18. Enter
actual or representative values in row 4 and the standard
uncertainty of the results in row 5 or 6 depending on if the
standard uncertainty is given in absolute (row 5) or relative terms
(row 6). Relative uncertainties shall be given as parts of 1, i.e.
1.5 % should be 0.015.
Then the interrelation between the various
components of the budget shall be entered in cell C21 ('Nominal'),
i.e. how the final result shall be calculated from the input
variables. Often this formula presents itself easily but it can
sometimes be rather complicated and require deep thoughts. It may
be helpful to establish and solve an equation that describes how to
calculate the result. In the dilution example above the expression
will be simply the volume of the original sample plus the dilution
volume. Compare example 1.
The expression which goes into cell C21 will be a
mathematical expression and shall therefore, with the Excel�
nomenclature, begin with "=" ("equal sign"). Then, enter the
algorithm and drag the contents of C21 as far to the right as
variables have been entered. Finally press "enter" and all
calculations will be carried out. Note that the cells to the right
of the last used column in row 21 shall be empty. If not, it is
safe to mark them and press delete.
Depending on how your computer has been configured
you may need to press the F9 key to trigger the calculations. If
necessary you can change the configuration to 'automatic' under
'Tools-Options-Calculation' and check 'Automatic'.
The combined uncertainty will be given on the last
row in both absolute and relative terms. Also the coverage factor
(default =2) and the uncertainty interval will be given.
Contributions from the different sources of uncertainty are shown
on row 23 and graphically in the inserted diagram. The diagram can
be freely moved within the surface if you want to study the
underlying contents of the table. The scale of the Y - axis can
also be changed to improve the presentation.
The following examples are chosen to illustrate an
increasing complexity in the calculation and originate in routine
laboratory work. The uncertainties and other numbers do not
necessarily represent reality but have been chosen to illustrate
their influences. Each example is solved on the attached diskette
where also you will also find a template for the
calculations.
Let us repeat the example above dealing with adding
two volumes and use the template.
Enter the nominations "Sample" and "Dilution" in
the correct cells in row 3 and the volumes 10 and 490 respectively
in row 4. The standard uncertainties are entered in row 5 and 6
(absolute and relative standard uncertainty, respectively). Move
the cursor to cell C21 under the label "Nominal" and enter the
formula '= C9+C10'. Copy this formula two columns to the right. The
combined uncertainty will be shown in cell C25, the relative in E25
and the interval calculated with a coverage factor 2 in the cells
K25 - L25. The expanded uncertainty is given in cell I25. compare
the result with our manually worked example.
We want to weigh NaCl on an old fashioned scale.
The empty vessel weighs 12 g. We add NaCl until 127 g. Weighing
within the given interval can be made with an uncertainty of 1,5 %.
Calculate the mass of the NaCl.
In cell C21 the formula will be:' =final
weight-weight of empty vessel (tare)'. Test the result if the
uncertainty is 0.2 g!
We shall calculate the volume of a water bath which
has a length of 35 cm, width 25 cm and height 20 cm. The edges are
measured using a ruler with an uncertainty of 2 %.
The formula in C25 will be: '=the length x width x
height'. Check the result if the uncertainty of measurement in the
interval is 0.5 cm!
Let us add a slight complication to example 3. Let
us assume that the water bath is half - filled (10 cm) and you want
to fill it up to 3 cm (the margin) from the upper rim. How much
water should be added? We make the same assumptions regarding the
uncertainty of the lengths as above, but since the vessel walls are
not quite even we must add the uncertainty this contributes. Let us
assume that this uncertainty is multiplicative and optimally 1 but
with the uncertainty 3 %.
The formula in C21 will be '"length x width x (the
height - marginal - the height at half - filled water bath) x
unevenness factor'. Test the results if the uncertainty in all
lengths is 0.2 cm!
Let us increase the complexity of example 1 above.
Assume that the sample concentration is 320 mmol/L with a standard
uncertainty of 3 %. What is the concentration in the final solution
and what is its combined uncertainty? Enter the numbers to the
template as in example 1 but add the concentration of the sample
solution in a column of its own.
The formula will be: '=sample x
concentration/(sample + dilution)'.
We want to estimate the uncertainty in an HPLC -
method. The sample is diluted 1 + 9 with a solution containing 0.25
mmol/L internal standard (IS). We inject 20 �L of the dilution. The
sample peak is 247 mm, the IS - peak is 235 mm. How much substance
did the sample contain and which is the combined uncertainty of the
result? The standard uncertainty in the sample volume is � 3 % and
for the dilution volume � 2 %. The standard uncertainty in weighing
of IS is � 1 %. Measuring of the peaks is associated with an
interval of � 2 %. The same amounts of IS and sample give the same
response on the printer with an uncertainty of � 3 %.
The relation between signal and concentration (i.e.
the calibration function) is: signal = concentration x 2-1,5; (Y=2
x X-1,5) in the concentration interval 0,5-5 units. The standard
uncertainty in the slope (b) is 2 % in the intercept (a) 5 % and in
the signal 0,01 units. Estimate the combined uncertainty in the
middle of the interval, i.e. 2,75 units.
We compare the results from measuring the same
samples on two different instruments. The results are assumed to be
identical, that is the regression function is assumed to be Y = X.
Which deviation in Y results can we expect if the standard
uncertainty in the estimation of the coefficient is 5 % and the
interval of the intercept is -0,5 - + 0,8 at the critical limit 17
mmol/L? The standard uncertainty in the reference method is 3
%.
The absorbance of a sample is measured at 580 nm.
The specific absorbance for the substance at this wavelength is
12,5, the absorbance curve is linear between 540 and 620 nm with a
slope of 0.001 absorbance units/nm. The sample was diluted 1 + 9
and the absorbance 1.35. Estimate the concentration and its
uncertainty if the standard uncertainties in the volume
measurements are 2 % and 1,5 % per sample and dilution,
respectively, the standard uncertainty of the specific absorbance
(u a ) 0,5 %, in the reading 1 %, in the slope (u
l ) 5 % and the wavelength of the filter is given as an
interval of 580 nm � 5 nm.
There are many factors involved in this example and
let us argue like this: We must somehow translate the uncertainty
in wavelength to uncertainty in specific absorbance. This can be
done by calculating the specific absorbance at another wavelength.
Let us assume 560 nm. This wavelength has no uncertainty because we
assume it is without uncertainty. At exactly 580 nm the specific
uncertainty is 0.125. We can include the uncertainty in the slope
of the absorbance curve by (580 - 560) x 0.001 � u l
. The specific absorbance at 560 nm will therefore be
(0.125 � u a -20 x 0.001 � u l ). We can then
formulate the absorbance at 580 nm � 5 nm. It will be (0.125 � u
a -20 x 0.001 � u l ) + 580 nm � 5 nm-560) x
(0.001 � u l ).
Although the wavelength has a small uncertainty
this will be the dominating source of uncertainty. Discuss what
happens if the slope increases or if the uncertainty in the volume
measurements is changed.
The concept of uncertainty can also be used for
other purposes than measurements and it can include for instance
preanalytical and post analytical sources of uncertainty. Let us
examine this example that is a simplification of an article in
"Clinical Chemistry and Laboratory Medicine" (6).
B - Glucose is used in the primary health care for
diagnosis and control of diabetes. Which is the smallest difference
in results that, with a given probability can be assumed to be
different?
The patient shall be fasting. The patient shall be
calm and relaxed to avoid that catecholamines and other hormones
will give a falsely elevated glucose concentration. The
concentration of glucose in erythrocytes is less than in plasma and
therefore one also has to control the intake of fluids to avoid
falsely low results and increased hematocrit. The capillary
sampling is difficult. One cannot avoid a varying addition of
interstitial fluid etc. There are instruments on the market that
measure P - Glucose and use an algorithm to transfer the value to B
- Glucose. The algorithm is based on the assumption that P -
Glucose is 15 % higher than B - Glucose, which however is depending
on the hematocrit of the patient. Finally we also have uncertainty
contributions from the measurement itself. All these uncertainties
shall be considered in estimating the combined uncertainty that
shall be the basis for estimating the smallest significant
difference between two results.
Let us select 6.0 mmol/L as an interesting
concentration.
Fasting and fluid intake.Just standing up can cause
to up to 15 % changes of the plasma volume. Between day variation
of the plasma volume is given in the literature (7) to � 6.5 %
based on repeated measurements. Let us assume that this includes
the variations in stress, fluid intake and fasting but excluding
whether the patient is sitting, standing or resting.
Sampling:Literature (8) postulates an uncertainty
of � 3.2 % for S - Glucose also based on repeated measurements. For
capillary sampling it is reasonable to add a little, � 5 %.
Measurement:The precision of the measurement is
related to the instrument. An instrument like Hem cue can give an
imprecision of � 3 - 5 %, many of the other instruments the same
order and magnitude if one uses the same batch of reagent strips.
Between batches the manufacturers may allow as much as up to 8 %
imprecision. Let us assume that we can manage an interval of � 5 %
uncertainty that also includes the uncertainty of
calibration.
Post analyticalIf the measurement is made with an
instrument that really measures B - Glucose this source of
uncertainty is not interesting. If, however the instrument measures
something different then one must divide with a factor. Some
literature suggests 1.17 but it is closer to 1.11 (6). Regardless
of the value of the factor it is attached to an uncertainty, let us
assume 5 %.
The smallest difference that can be called
significant is
where D is the difference, u c (y) is
the combined uncertainty and k the coverage factor. The square root
is because two values are compared. A convenient abbreviation is
D=3 x u c (y).
1. ISO/DIS 15189. Quality management in the
medical laboratory, ISO, Geneva 2000.
2. ISO/IEC IS 17025. General requirements for
the competence of testing and calibration laboratories. Geneva
1999.
1. Guide to the Expression of Uncertainty in
Measurement (GUM). ISO Geneva, Schweiz 1993 (ISBN 92 - 67 - 10188 -
9)
2. J Kragten. Calculating standard deviations
and confidence intervals with a universally applicable spreadsheet
technique. Analyst 1994; 119: 2161 - 2166.
3. Eurachem, Quantifying Uncertainty in
Analytical Measurement, LGC Information Service, Teddington
Middlesex 1995 ISBN 0 - 948926 - 08 - 2
4. A. Kallner, J Waldenstrom Does the
Uncertainty of Commonly Performed Glucose Measurements Allow
Identification of Individuals at High Risk for Diabetes? Clin Chem
Lab Med 1999;37:907 - 912
5. C Ricos et al. Current databases on
biological variation: pros, cons and progress. Scand J Clin Lab
Invest 1999;59(7):491 - 500.
6. X. Fuentes - Arderiu et al. Pre -
metrological (Pre - Analytical) Variation of some Biochemical
Quantities. Clin Chem Lab Med 1999;37:987 - 989
Three
important definitions by ISO : Trueness,agreement between the average value
from many observations and the true value
Precision,agreement between independent
results of measurement
Accuracy,agreement between the result of a
measurement and a true value of the measurand
Note the difference
betweenTruenessandAccuracy; the latter refers to one measurement
whereas the former to the mean of many measurements.
Thereforeinaccuracywill include both thebiasand theimprecision
inherent in a specific result.
Terminology and nomenclature are cornerstones
of science and a citation from L Carroll 'Alice through the looking
glass' might be appropriate to consider:
'When I use a word' Humpty Dumpty said in
rather a scornful tone, 'it means just what I choose it to mean ?
neither more nor less'
'The question is,' said Alice, 'whether you
can make words mean different things'.
'The question is, said Humpty Dumpty, ' which
is to be master ? that's all'.
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