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31/01/2014 Page 1 of 15
C O D A-TERVUREN - C E R V A-TERVUREN
Leuvensesteenweg 17 - B 3080 Tervuren
PRO/5.4/02/DOC01/V03
VALIDATIEDOSSIER
DOSSIER DE VALIDATION
SOP/TRA/ANA/0y
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31/01/2014 Page 2 of 15
PRO/5.4/02/DOC02/V01
HISTORIEK VAN DE VALIDATIEDOSSIER / HISTORIQUE DU DOSSIER DE VALIDATION
SOP/TRA/ANA/0y
DATUM / DATE
FASE – WIJZIGING / PHASE - MODIFICATION
January 2013 – October 2013
November 2013-January 2014
Method development
Method validation, and creation of first version of the
document of validation
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PRO/5.4/02/DOC03/V01
TOEPASSINGSGEBIED VAN DE SOP / DOMAINE D’APPLICATION DE LA SOP:
This method is applicable for Se-enriched premixes for feed and for Se-enriched human food supplements.
These matrices, although they are different in end-use, are very similar as both matrices include mineral
carriers. These substrates are commonly enriched in Se with selenite, seleno-methionine or seleno-methionine
from enriched yeasts.
Precision and trueness of the method is calculated based on three different matrix-relevant samples, being: a
feed premix enriched with selenite (PREMIX), a food supplement enriched with a Se-enriched yeast (SUP1) and
another food supplement not enriched with both species (SUP2). The samples were amended with stock
solutions containing SeIV or SeMet, at three different levels, and were measured on three different days. As the
PREMIX sample is enriched with selenite, further spikings with selenite are done for this specie. The SUP1 sample
is enriched with a seleno-methionine enriched yeast so further spikings are done with seleno-methionine. Extra
spikings for both species are done in SUP2.
Definitions
Se Selenium
Se species Specific chemical form of Se defined according to e.g. its oxidation
state or its molecular structure
SeIV
Selenite
SeMet Selenomethionine
SeVI
Selenate
MeSeCys Methyl-seleno-cysteïne
Certified reference material (CRM) A certified reference material (CRM) is a material in which a specific
analyte content has been specified. In the present study the CRM SELM-
1 (seleno-yeast) is used. The material is certified for total Se and
Selenomethionine but not for other individual Se species.
Limite of quantification (LOQ) The limit of quantification (LOQ) is the minimal concentration of an
analyte which can be measured in a routine analysis. The limit of
quantification for Se species is calculated as 10 times the standard
deviation of the background signal of the chromatogram
MultiQC control chart of the type ‘Shewart’
Procedure blanc test, or value of a test, corresponding to a complete analytical cycle
(preparation+measurement), realized in conditions identical to the
sample analysis, but in the absence of the sample
Speciation analysis analytical activity which identifies and/or quantifies chemical species
Supplemented material Sample enriched with a known quantity of the analyte of interest
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VALIDATIEPARAMETERS / PARAMETRES DE VALIDATION
The method concerns a quantitative method of confirmation including the following parameters:
1. Analytical specificity
2. Robustness
3. Precision: repeatability and reproducibility
4. Trueness
5. Calibration
6. Measurement uncertainty
7. Quantification limits
8. Decisions related to the repeatability of results
9. Peak resolution
1. Analytical specificity
The measurement of 20 ‘blank’ samples, as described in PRO/5.4/02, to demonstrate analytical specificity is
not relevant for our method. Selenium is a natural constituent of the earth crust and is ubiquitous in all
biological matrices. This means that it is impossible to find ‘blank’ samples.
In trace element analysis by means of ICP-MS, analytical specificity can refer to the absence of significant
interferences during the measurements. In case of speciation analysis of selenium, the most important potential
interference is caused by the argon gas, because the 40
Ar40
Ar polyatomic ions can interfere with the detection of
Se species on mass 80. Therefore, Se is quantified on mass 78. Also at this mass there is a polyatomic
interference from 38
Ar38
Ar, although less pronounced. On VARIAN ICP-MS this interference can be counteracted
by the use of H2 as a reaction gas. During the Se speciation measurements a H
2 flow of 80mL/min is activated.
This gas can react with the polyatoms by means of a charge transfer or an atom transfer. The possible
interference that is left on the measurement will be visible as a higher background signal and will not influence
the peak height.
2. Robustness
The parameters that have to be considered are discussed in addendum 1
3. Precision (repeatability –reproducibility)
Currently no performance criteria have yet been laid down for selenium species by the Commission of the
European Communities. The performance criteria laid down in Commission Regulation 333/2007 (for amongst
others cadmium and lead) were used as a guide in the present document. According to the latter Commission
Regulation the performance criterion for precision is HORRATR < 2. The data used to calculate HORRAT
R are the
data from CRM SELM-1 (Selenium enriched-yeast; certified for total Se (2059 ± 64 mg/kg) and SeMet (1372 ±
58 mg Se/kg) but not for other Se species) between 22/11/2013 and 22/01/2014 as these data represent
reproducibility conditions. The HORRATR values are below 2 for SeMet (cfr. Table 1).
HORRATR = RSD
R (=CV% in multiQC)/RSD
R Horwitz
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Table 1. HORRATR value based on the SELM-1 (Selenium enriched-yeast)
SeMet
mg Se/kg
Mean 1296.796
SD 93.071
RSDR 7.18
RSDHorwitz
5.39
HORRATR 1.33
Repeatability and reproducibility (intermediate precision) were calculated based on the three different matrix-
relevant samples: PREMIX, SUP1 and SUP2. The first two samples were spiked with one specie and the last
sample was spiked with both species. Spikings and measurements are repeated at three different days for each
sample.
The theoretical natural level was determined as the average of the data for the unspiked samples as determined
in a preliminary experiment. This theoretical natural concentrations for Se IV and SeMet are summarized in
Table 2. The final spiking levels of SeIV and SeMet are summarized in Table3.
Table 2. Natural concentrations (mg/L) of Se IV and SeMet in different samples
mg/L PREMIX SUP1 SUP2
SeIV 12 <LOQ <LOQ
SeMet <LOQ 137 <LOQ
Table 3. Three spike levels (mg/L) of SeIV and SeMet in different samples
PREMIX SUP1 SUP2
SeIV
level 1 12 - 5
level 2 24 - 10
level 3 120 - 50
SeMet
level 1 - 137 5
level 2 - 210 13
level 3 - 280 50
The calculations can be found in the files “ValMethTerv_SeXX_XXX.xlsx” (71\ACCREDITATIE\SELENIUM
SPECIATION\VALIDATIEDOSSIER) and are added in addendum.
The long-term reproducibility (intermediate precision) will be calculated when sufficient data will be available.
Addendum 2-5:
ValMethTerv_SeIV_premix.xlsx
ValMethTerv_SeMet_sup1.xlsx
ValMethTerv_SeIV_sup2.xlsx
ValMethTerv_SeMet_sup2.xlsx
4. Accuracy/ recovery
Accuracy indicates the deviation between the mean value found and the true value. Only one certified reference
material (SELM-1, seleno-yeast) is available which is certified for SeMet. For this matrix the accuracy of SeMet is
based on the difference between the certified value and the measured value of SeMet. Over 9 timepoints, this
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accuracy was 95% on average (see file “Accuracy calculations SeSpec.xlsx” (71\ACCREDITATIE\SELENIUM\
SPECIATION\VALIDATIEDOSSIER). No CRM is available for SeIV.
The accuracy of the method for more relevant matrices is illustrated by calculating the recovery of spiked
samples. This can be determined by applying the method to samples to which known amounts of SeIV and/or
SeMet have been added. The accuracy is then calculated from the test results as a percentage of analyte
recovered.
The data that have been used to determine the accuracy in the premix/food supplement samples, are the
measurement results of spiked samples used for precision calculation (Table 4).
All calculations can be found in “Accurancy calculations SeSpec.xlsx” (71\ACCREDITATIE\SELENIUM
SPECIATION\VALIDATIEDOSSIER).
Table 4: Mean accuracy for different Se species in different matrices.
Premix SUP1 SUP2
SeIV
89% - 105%
SeMet - 97% 91%
5. Beslissingsgrens (CCα) en detectievermogen (CCβ)
As there are no legal limits for Se species in premixes and food supplements, CCα and CCβ are not relevant.
6. Calibration (Linearity of the method)
The calibration is an internal calibration of the linear type. Calibration curves for each selenium species are
presented in each analysis file. As example, the calibration curves are given for the measurement of SUP2-d3 in
figure 1-2 below (see file ‘Calibration SpecSe’ (71\ACCREDITATIE\SELENIUM\SPECIATION
\VALIDATIEDOSSIER)). Observed R2
values are > 0.99, and residuals are <15%. The random variation of the
residuals (Res%) with increasing standard concentrations supports the trueness of the linear model.
Figure 1: internal calibration curve for SeMet in a premix sample
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Figure 2: internal calibration curve for SeIV in a premix sample
7. Measurement uncertainty
The measurement uncertainty was calculated from the intra-reproducibility and from the bias (ubias
), which is
calculated from a certified reference material or recovery experiments1
:
uc = √
Uncertainties related to intra-reproducibility can be calculated from the controlchart of a matrix-matching CRM,
or they can be calculated from the repeatability (r) and intermediate precision (ip) as determined in section 3.
The bias can as well be calculated from a matrix-matching CRM, or from recovery experiments if no CRM is
available. The expanded measurement uncertainty is the product of the combined uncertainty and the coverage
factor k = 2, which corresponds to a confidence level of approximately 95%.
As there is no certified reference material available for SeIV in feed premixes and food supplements,
uncertainties related to intra-reproducibility are calculated from the repeatability and intermediate precision
data (see “ValMethTerv_SeIV_XX” files & section 3), and uncertainties related to bias are calculated from the
data from section 4 (recovery experiments for accuracy calculation). All calculations can be found in
“Measurement uncertainty SeIV.xlsx”. The expanded measurement uncertainties, calculated at different
concentration levels, are presented in Table 5.
Table 5: Expanded measurement uncertainties for SeIV in different matrices at different concentration levels.
Concentration level Premix SUP2
10 mg/kg 50% 38%
20 mg/kg 29% 34%
100 mg/kg 13% 10%
1
Calculated as described in “Procedure Bepaling van de meetonzekerheid voor kwantitatieve chemische
analyses. LAB P 508 Meetonzekerheid-v.01-nl. Goedgekeurd 03/11/2008”.
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SeMet is certified in the CRM SELM-1, which is selenium-enriched yeast. Hence this CRM can be used to
calculate the uncertainties related to intra-reproducibility and bias for SeMet in the selenium-enriched food
supplements. As the SeMet concentrations in SELM-1 are very high (1372 ± 58 mg Se/kg) and the matrix is not
quite relevant, we also chose to calculate these uncertainties by using the repeatability and intermediate
precision data (see “ValMethTerv_SeMet_XX” files & section 3) and the recovery experiment data from section 4.
All calculations can be found in “Measurement uncertainty SeMet.xlsx”. The expanded measurement uncertainty
for the determination of SeMet in food supplements or feed premixes equals 19% when calculated solely based
on the CRM. When based on the CRM (intra-reproducibility) and recovery experiments (bias), the expanded
measurement uncertainty varies from 18% in SUP1 to 19% in SUP2. The expanded measurement uncertainties,
when calculated at different concentration levels using repeatability and intermediate precision data and the
data from recovery experiments, are presented in Table 6.
Table 6: Expanded measurement uncertainty for SeMet in different matrices at different concentration levels.
Concentration level SUP1 SUP2
10 mg/kg - 19%
20 mg/kg - 14%
100 mg/kg - 10%
175 mg/kg 18% -
250 mg/kg 10% -
320 mg/kg 9% -
8. Quantification limits
The limit of quantification (LOQ) is the minimal concentration of an analyte which can be measured in a routine
analysis. The limit of quantification for each Se species corresponds to 10 times the standard deviation of the
background signal of the chromatogram. Standard deviations of the background signal of SELM-1
chromatograms were calculated in different zones of the chromatogram, because we wanted to include the
potential effect of the mobile phase gradient. For SeIV
, LOQ was based on the background signal 0.5 minutes
after SeIV
peak elution. In this region there are still small unidentified peaks present in yeast-based matrices.
Nevertheless this region is chosen to incorporate the presence of these peaks in the LOQ.
For SeMet was based on the background signal 0.5 minutes after SeMet peak elution.
Average calculated LOQ values (µg/kg) for the various species obtained on different measurement days are
shown in table 4 (values rounded to 0.5 unity).
Table 5. Calculated LOQ values in solution (µg/L) for the different Se species
SeIV
SeMet
Average signal (c/s) 355 234
Average standard deviation (c/s) 92 19
Relative standard deviation (RSD) 25% 8.1%
LOQ in solution (µg/L) 2 0.5
The calculations are detailed in the file ‘LODLOQ calculations’ (71\ACCREDITATIE\ SELENIUM
SPECIATION\VALIDATIEDOSSIER). These LOQ values translate into 4 mg/kg for SeIV
and 1 mg/kg for SeMet in
a matrix (final dilution factor of 200).
These calculated LOQ values need to be confirmed by measuring solutions with similar concentration levels.
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9. Decisions related to the repeatability of results
Because of the potential heterogeneity of biological samples, a homogenisation step is included before
subsamples are taken for analysis. Indeed, heterogeneity of the sample influences the repeatability of results
(variation among subsamples). Each analysis will therefore be performed in duplicate, and the following criteria
will be taken into account:
-Values of the reference sample need to fall within the limits specified in the file ‘Accept CRM’. These values take
into account the extended measurement uncertainty of the analysis.
-To be accepted, measurement results have to be higher than the LOQ. Results below this value will be reported
as <LOQ.
- Analyses will be performed in 2 replicates. The coefficient of variation needs to be <25%.
-When the coefficient of variation is higher than 25%, the analysis will be repeated in 3 replicates.
10. Peak resolution
Peak resolution (Rs) can be calculated according to the formula Rs= 2(Tr2-Tr1)/(W1+W2), with Tr2 en Tr1
retention times of two consecutive peaks, and W2 en W1 baseline width of the corresponding peaks.
Baseline peak width (W) corresponds to the distance between the baseline intercepts of tangent lines to the front
slope and the back slope of a peak (Figure 3). This baseline peak width, W, is considered equivalent to the peak
width at 13.4 % peak height, or for Gaussian peaks can be approached by taking 1.7* peak width at 50% peak
height.
Figure 3: Illustration of the baseline peak witdt, W, which corresponds to the distance between the baseline
intercepts of tangent lines to the front slope and the back slope of the peak.
A typical chromatogram of a 5 ppb standard solution containing a mix of the 4 Se species is presented in Figure
4. Values for retention times and peak width at 13.4% are presented in the same Figure. Using these values,
peak resolutions, Rs, can be calculated. The resolution between SeIV
and SeVI
is 5.2 and between the SeVIbis
and
SeMet is 12.4. Rs values >1.3 are characteristic for well separated peaks.
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# Name
Time
[Min]
Quantity
[ppb]
Height
[c/s]
Area
[c/s.Min]
Area %
[%]
Width
13.4% [Min]
1 Se4 3.35 10.73 25962.8 4887.8 20.247 0.28
2 Se6 5.07 10.42 13384.5 3648.6 15.114 0.38
3 MeSeCys 5.85 10.32 77319.5 6171.9 25.567 0.12
4 Se6bis 6.93 10.7 14254.5 4081.9 16.909 0.35
5 SeMet 13.36 11.68 12740.5 5350.2 22.163 0.69
Figure 4: Chromatogram of a 5 ppb standard solution containing a mix of the 4 Se species.
31/01/2014 Page 11 of 15
Addendum 1: PRO/5.4/02/DOC04/V01
FACTOREN DIE DE JUISTHEID EN BETROUWBAARHEID VAN DE BEPROEVINGEN BEÏNVLOEDEN
SOP/TRA/ANA/0y
Parameter Composants character Control
1.Equipement
and laboratorium
material
mixer
non relevant if clean and
working
mixer is cleaned with bi-distilled water after use
balances relevant
maintenance by external firm 1x/year and daily
verification
pipettes relevant
control by external firm 2x/year and
maintenance by external firm 1x/year
glassware for
standards
non relevant if clean flasks stored in bi-distilled water
ICP-MS relevant
1° maintenance by external firm 1x/year or
interventions mentioned in logbook
2° daily control of sensitivity of the apparatus by
use of a tuning solution (cfr SOP/TRA/ANA/02).
HPLC pumps relevant
intervention by firm when a pump related
problem is observed (see logbook ICP-MS)
HPLC
autosampler
non relevant if working
and injection volume
constant
check injection volume 1x/year (RSD<0.5%)
2. Products and
samples
milliQ water
non relevant if produced
daily fresh
via maintenance mentioned in logbook and
daily verification
Standards for
Se species
relevant daily fresh preparations of spike dilutions
HFBA/MeOH
solution for
mobile phase
relevant
constant use of same mark
daily fresh preparation
1° routine
samples
2° ringtest
samples
relevant
1° verification of extraction efficiency in sample
(total As in extract versus total As after
mineralisation)
2° contrôle of Z-score of PT-Test
C8 column
relevant
(physic-chemical
characteristiques of the
column)
constant use of same column mark
cleaning or replacement of column if problems
are observed (high pressure, bad peak
separation, tailing of peaks,…)
3.Method
principles
Temperature
of HPLC-
chain
non relevant because of
thermostatisation by oven
control of oven temperature 1x/year
4.Room
temperature
Room
temperature
of LC-ICP-MS
laboratory
non relevant
daily tuning of ICP-MS signal with a tuning
solution optimises signal in function of daily
conditions (cfr SOP/TRA/ANA/02)
5.Staff
Analists,
technical
responsible
relevant
first, second, third line controls
formation of people
Page 12 of 15
Addendum 2
CALCULATION of REPEATABILITY, WITHIN-LAB REPRODUCIBILITY, CCa, CCb and RECOVERY (reminder : formulas, with "E" = "sum of" :
ACCORDING TO 2002/657/EC, ISO 11843-1 and Van Loco & Beernaert (2004) SSrepl = Ed Er (Y-Ymoy(level,day))2
Srep2 = Srepl2 = MSrepl = SSrepl/(n-ndays)
DATA : RESULTS AND GRAPHS : SSdays = nrepl E(Ymoy(level,day)-Ymoy(level))2
MSdays = SSdays / (ndays-1)
Analyte : SeMet linear regression : recovery intercept R2 Sdays2 = (MSdays-MSrepl) / nrepl
Method : 103.2% 25.10 0.9863 Srw2 = Sdays2 + Srep2 )
Matrix : food supplement Se-enriched yeast warning : this is only the "repe-repro"
MRL : (Maximum Residue Limit) CCa, CCb : t(26,0.05) Yc CCa CCb part of the MU and does not include lab bias
unit : mg/kg mg/kg % of MRL mg/kg % of MRL (possibly different for different samples)
Nrepl : 3 (number of replicates) 1.706 40.90 15.31 #DIV/0! #DIV/0! #DIV/0!
Ndays : 3 (number of days or analysts)
(Nlev : 3 (number of levels)) SD, U : nom.ccn av.meas. uncertainty (k = 1) (*) U, ext. unc. (k = 2) (**) Umax. (k = 2) (***)
Measured concentrations : mg/kg mg/kg mg/kg % mg/kg % mg/kg %
(NOT corrected for recovery) : 137 165.46 7.76 4.69% 15.52 9.4% 39.4 28.8%
210 245.11 7.38 3.01% 14.77 6.0% 56.7 27.0%
conc. repl : day or analyst : 280 313.03 8.79 2.81% 17.58 5.6% 72.3 25.8%
(µg/kg) 1 2 3 4 5 6 (*) u = sd (**) U = 2 sd (***) from modif. Horwitz for Srw, HorRat < 2x2/3
level 1 : 1 162.3 177.21 167.24 224.567 SSrepl cfr Codex Alim - mth criteria - draft 14.2.08
137 2 149.7 170.59 162.81 37.428 MSrepl
3 166.67 166.48 166.14 6.118 Srepl
4 165.461 average for level
5 211.367 SSdays
6 105.684 MSdays
7 22.752 Sdays2
8 4.770 Sdays
9 7.758 Srw
10
level 2 : 1 240.28 252.94 247.44 80.671 SSrepl
210 2 238.12 250.44 238.89 13.445 MSrepl
3 236.2 249.99 3.667 Srepl
4 245.111 average for level
5 273.334 SSdays
6 136.667 MSdays
7 41.074 Sdays2
8 6.409 Sdays
9 7.384 Srw
10
level 3 : 1 305.79 317.58 318.55 270.610 SSrepl
280 2 304.62 321.45 320.71 45.102 MSrepl
3 308.07 299.99 320.46 6.716 Srepl
4 313.025 average for level
5 283.384 SSdays
6 141.692 MSdays
7 32.197 Sdays2
8 5.674 Sdays
9 8.792 Srw
10
average level 1 : 159.56 171.43 165.4 average
SumSquares 155.29 58.608 10.665 SumSquares
average level 2 : 238.2 251.69 245.44 average calculations performed by : date
SumSquares 8.3135 4.6888 67.669 SumSquares using template : ValMethTerv ver 1.72
average level 3 : 306.16 313.01 319.91 average template date : 23-sept-13
SumSquares 6.1473 261.68 2.7798 SumSquares
0
5
10
15
20
2 x Srepl 2 x Sdays 2 x Srw
Uncertainty (ug/kg) (k=2, 95% conf. int.)
137
210
280
0%
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
2 x Srepl 2 x Sdays 2 x Srw
Uncertainty (%) (k=2, 95% conf. int.)
137
210
280
135
140
145
150
155
160
165
170
175
180
1 2 3 4 5 6 7 8 9 10
0.5 x MRL
225
230
235
240
245
250
255
1 2 3 4 5 6 7 8 9 10
1 x MRL
285
290
295
300
305
310
315
320
325
1 2 3 4 5 6 7 8 9 10
1.5 x MRL
y = 7.2764x + 130.01R² = 0.5586
0
50
100
150
200
250
300
350
0.0 5.0 10.0 15.0 20.0 25.0 30.0
linear regression
Page 13 of 15
Addendum 3
CALCULATION of REPEATABILITY, WITHIN-LAB REPRODUCIBILITY, CCa, CCb and RECOVERY (reminder : formulas, with "E" = "sum of" :
ACCORDING TO 2002/657/EC, ISO 11843-1 and Van Loco & Beernaert (2004) SSrepl = Ed Er (Y-Ymoy(level,day))2
Srep2 = Srepl2 = MSrepl = SSrepl/(n-ndays)
DATA : RESULTS AND GRAPHS : SSdays = nrepl E(Ymoy(level,day)-Ymoy(level))2
MSdays = SSdays / (ndays-1)
Analyte : SeMet linear regression : recovery intercept R2 Sdays2 = (MSdays-MSrepl) / nrepl
Method : 100.0% 1.26 0.9978 Srw2 = Sdays2 + Srep2 )
Matrix : food supplement selenate warning : this is only the "repe-repro"
MRL : (Maximum Residue Limit) CCa, CCb : t(26,0.05) Yc CCa CCb part of the MU and does not include lab bias
unit : mg/kg mg/kg % of MRL mg/kg % of MRL (possibly different for different samples)
Nrepl : 3 (number of replicates) 1.706 4.69 3.44 #DIV/0! #DIV/0! #DIV/0!
Ndays : 3 (number of days or analysts)
(Nlev : 3 (number of levels)) SD, U : nom.ccn av.meas. uncertainty (k = 1) (*) U, ext. unc. (k = 2) (**) Umax. (k = 2) (***)
Measured concentrations : mg/kg mg/kg mg/kg % mg/kg % mg/kg %
(NOT corrected for recovery) : 10 10.64 0.41 3.85% 0.82 7.7% 2.9 29.3%
25 27.00 1.15 4.26% 2.30 8.5% 7.3 29.3%
conc. repl : day or analyst : 100 101.17 3.46 3.42% 6.91 6.8% 29.3 29.3%
(µg/kg) 1 2 3 4 5 6 (*) u = sd (**) U = 2 sd (***) from modif. Horwitz for Srw, HorRat < 2x2/3
level 1 : 1 10.448 11.076 10.036 0.648 SSrepl cfr Codex Alim - mth criteria - draft 14.2.08
10 2 11.324 10.752 10.274 0.108 MSrepl
3 10.733 10.596 10.545 0.329 Srepl
4 10.643 average for level
5 0.577 SSdays
6 0.288 MSdays
7 0.060 Sdays2
8 0.245 Sdays
9 0.410 Srw
10
level 2 : 1 25.743 27.91 27.81 1.002 SSrepl
25 2 26.24 27.912 26.665 0.167 MSrepl
3 25.465 28.135 27.161 0.409 Srepl
4 27.005 average for level
5 7.259 SSdays
6 3.629 MSdays
7 1.154 Sdays2
8 1.074 Sdays
9 1.149 Srw
10
level 3 : 1 101.32 100.43 102.82 71.684 SSrepl
100 2 105.64 105.11 99.105 11.947 MSrepl
3 95.684 100.66 99.726 3.456 Srepl
4 101.166 average for level
5 3.819 SSdays
6 1.910 MSdays
7 -3.346 Sdays2
8 0.000 Sdays
9 3.456 Srw
10
average level 1 : 10.835 10.808 10.285 average
SumSquares 0.3987 0.1201 0.1296 SumSquares
average level 2 : 25.816 27.986 27.212 average calculations performed by : date
SumSquares 0.3084 0.0336 0.6596 SumSquares using template : ValMethTerv ver 1.72
average level 3 : 100.88 102.07 100.55 average template date : 23-sept-13
SumSquares 49.876 13.897 7.9112 SumSquares
0
1
2
3
4
5
6
7
8
2 x Srepl 2 x Sdays 2 x Srw
Uncertainty (ug/kg) (k=2, 95% conf. int.)
10
25
100
0%
1%
2%
3%
4%
5%
6%
7%
8%
9%
2 x Srepl 2 x Sdays 2 x Srw
Uncertainty (%) (k=2, 95% conf. int.)
10
25
100
9
9.5
10
10.5
11
11.5
1 2 3 4 5 6 7 8 9 10
0.5 x MRL
24
25
26
27
28
29
1 2 3 4 5 6 7 8 9 10
1 x MRL
90
92
94
96
98
100
102
104
106
108
1 2 3 4 5 6 7 8 9 10
1.5 x MRL
y = 1.0003x + 1.2561R² = 0.9978
0
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40
60
80
100
120
0.0 20.0 40.0 60.0 80.0 100.0 120.0
linear regression
Page 14 of 15
Addendum 4
CALCULATION of REPEATABILITY, WITHIN-LAB REPRODUCIBILITY, CCa, CCb and RECOVERY (reminder : formulas, with "E" = "sum of" :
ACCORDING TO 2002/657/EC, ISO 11843-1 and Van Loco & Beernaert (2004) SSrepl = Ed Er (Y-Ymoy(level,day))2
Srep2 = Srepl2 = MSrepl = SSrepl/(n-ndays)
DATA : RESULTS AND GRAPHS : SSdays = nrepl E(Ymoy(level,day)-Ymoy(level))2
MSdays = SSdays / (ndays-1)
Analyte : Se IV linear regression : recovery intercept R2 Sdays2 = (MSdays-MSrepl) / nrepl
Method : 97.5% -1.58 0.9966 Srw2 = Sdays2 + Srep2 )
Matrix : Premix feed warning : this is only the "repe-repro"
MRL : (Maximum Residue Limit) CCa, CCb : t(26,0.05) Yc CCa CCb part of the MU and does not include lab bias
unit : mg/kg mg/kg % of MRL mg/kg % of MRL (possibly different for different samples)
Nrepl : 3 (number of replicates) 1.706 3.50 5.21 #DIV/0! #DIV/0! #DIV/0!
Ndays : 3 (number of days or analysts)
(Nlev : 3 (number of levels)) SD, U : nom.ccn av.meas. uncertainty (k = 1) (*) U, ext. unc. (k = 2) (**) Umax. (k = 2) (***)
Measured concentrations : mg/kg mg/kg mg/kg % mg/kg % mg/kg %
(NOT corrected for recovery) : 12 10.12 0.63 6.22% 1.26 12.4% 3.5 29.3%
24 21.83 1.36 6.22% 2.72 12.4% 7.0 29.3%
conc. repl : day or analyst : 120 115.43 5.58 4.84% 11.17 9.7% 35.2 29.3%
(µg/kg) 1 2 3 4 5 6 (*) u = sd (**) U = 2 sd (***) from modif. Horwitz for Srw, HorRat < 2x2/3
level 1 : 1 9.7003 10.71 10.027 1.866 SSrepl cfr Codex Alim - mth criteria - draft 14.2.08
12 2 9.4087 9.9081 10.771 0.311 MSrepl
3 10.023 11.107 9.4086 0.558 Srepl
4 10.118 average for level
5 1.132 SSdays
6 0.566 MSdays
7 0.085 Sdays2
8 0.292 Sdays
9 0.629 Srw
10
level 2 : 1 21.397 23.174 21.373 9.921 SSrepl
24 2 20.319 21.655 21.968 1.653 MSrepl
3 21.147 20.728 24.685 1.286 Srepl
4 21.827 average for level
5 4.447 SSdays
6 2.224 MSdays
7 0.190 Sdays2
8 0.436 Sdays
9 1.358 Srw
10
level 3 : 1 111.34 107.85 120.09 187.017 SSrepl
120 2 119.5 120.18 108.86 31.169 MSrepl
3 115.96 117.07 117.99 5.583 Srepl
4 115.427 average for level
5 0.700 SSdays
6 0.350 MSdays
7 -10.273 Sdays2
8 0.000 Sdays
9 5.583 Srw
10
average level 1 : 9.7105 10.575 10.069 average
SumSquares 0.1886 0.7464 0.9306 SumSquares
average level 2 : 20.954 21.852 22.676 average calculations performed by : date
SumSquares 0.6371 3.0485 6.2351 SumSquares using template : ValMethTerv ver 1.72
average level 3 : 115.6 115.03 115.65 average template date : 23-sept-13
SumSquares 33.506 82.27 71.241 SumSquares
0
2
4
6
8
10
12
2 x Srepl 2 x Sdays 2 x Srw
Uncertainty (ug/kg) (k=2, 95% conf. int.)
12
24
120
0%
2%
4%
6%
8%
10%
12%
14%
2 x Srepl 2 x Sdays 2 x Srw
Uncertainty (%) (k=2, 95% conf. int.)
12
24
120
8.5
9
9.5
10
10.5
11
11.5
1 2 3 4 5 6 7 8 9 10
0.5 x MRL
0
5
10
15
20
25
30
1 2 3 4 5 6 7 8 9 10
1 x MRL
100
102
104
106
108
110
112
114
116
118
120
122
1 2 3 4 5 6 7 8 9 10
1.5 x MRL
y = 0.9751x - 1.5784R² = 0.9966
0
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100
120
140
0.0 50.0 100.0 150.0
linear regression
Page 15 of 15
Addendum 5
CALCULATION of REPEATABILITY, WITHIN-LAB REPRODUCIBILITY, CCa, CCb and RECOVERY (reminder : formulas, with "E" = "sum of" :
ACCORDING TO 2002/657/EC, ISO 11843-1 and Van Loco & Beernaert (2004) SSrepl = Ed Er (Y-Ymoy(level,day))2
Srep2 = Srepl2 = MSrepl = SSrepl/(n-ndays)
DATA : RESULTS AND GRAPHS : SSdays = nrepl E(Ymoy(level,day)-Ymoy(level))2
MSdays = SSdays / (ndays-1)
Analyte : Se IV linear regression : recovery intercept R2 Sdays2 = (MSdays-MSrepl) / nrepl
Method : 97.6% -0.41 0.9985 Srw2 = Sdays2 + Srep2 )
Matrix : food supplement selenate warning : this is only the "repe-repro"
MRL : (Maximum Residue Limit) CCa, CCb : t(26,0.05) Yc CCa CCb part of the MU and does not include lab bias
unit : mg/kg mg/kg % of MRL mg/kg % of MRL (possibly different for different samples)
Nrepl : 3 (number of replicates) 1.706 2.40 2.87 #DIV/0! #DIV/0! #DIV/0!
Ndays : 3 (number of days or analysts)
(Nlev : 3 (number of levels)) SD, U : nom.ccn av.meas. uncertainty (k = 1) (*) U, ext. unc. (k = 2) (**) Umax. (k = 2) (***)
Measured concentrations : mg/kg mg/kg mg/kg % mg/kg % mg/kg %
(NOT corrected for recovery) : 10 9.78 0.38 3.88% 0.76 7.8% 2.9 29.3%
20 18.63 1.99 10.66% 3.97 21.3% 5.9 29.3%
conc. repl : day or analyst : 100 97.24 2.14 2.20% 4.28 4.4% 29.3 29.3%
(µg/kg) 1 2 3 4 5 6 (*) u = sd (**) U = 2 sd (***) from modif. Horwitz for Srw, HorRat < 2x2/3
level 1 : 1 9.1877 9.6449 9.6088 0.862 SSrepl cfr Codex Alim - mth criteria - draft 14.2.08
10 2 10.054 9.6729 9.6367 0.144 MSrepl
3 9.7268 10.259 10.221 0.379 Srepl
4 9.779 average for level
5 0.070 SSdays
6 0.035 MSdays
7 -0.036 Sdays2
8 0.000 Sdays
9 0.379 Srw
10
level 2 : 1 20.579 16.373 20.837 6.961 SSrepl
20 2 20.335 16.025 19.246 1.160 MSrepl
3 18.026 17.334 18.942 1.077 Srepl
4 18.633 average for level
5 19.015 SSdays
6 9.508 MSdays
7 2.783 Sdays2
8 1.668 Sdays
9 1.986 Srw
10
level 3 : 1 95.028 94.764 101.35 13.156 SSrepl
100 2 96.61 96.86 98.504 2.193 MSrepl
3 97.866 96.262 97.903 1.481 Srepl
4 97.238 average for level
5 18.685 SSdays
6 9.343 MSdays
7 2.383 Sdays2
8 1.544 Sdays
9 2.139 Srw
10
average level 1 : 9.6561 9.8589 9.8221 average
SumSquares 0.3826 0.2405 0.2387 SumSquares
average level 2 : 19.647 16.578 19.675 average calculations performed by : date
SumSquares 3.9713 0.9195 2.0699 SumSquares using template : ValMethTerv ver 1.72
average level 3 : 96.501 95.962 99.252 average template date : 23-sept-13
SumSquares 4.0451 2.3315 6.7795 SumSquares
0
1
2
3
4
5
2 x Srepl 2 x Sdays 2 x Srw
Uncertainty (ug/kg) (k=2, 95% conf. int.)
10
20
100
0%
5%
10%
15%
20%
25%
2 x Srepl 2 x Sdays 2 x Srw
Uncertainty (%) (k=2, 95% conf. int.)
10
20
100
8.6
8.8
9
9.2
9.4
9.6
9.8
10
10.2
10.4
1 2 3 4 5 6 7 8 9 10
0.5 x MRL
0
5
10
15
20
25
1 2 3 4 5 6 7 8 9 10
1 x MRL
90
92
94
96
98
100
102
1 2 3 4 5 6 7 8 9 10
1.5 x MRL
y = 0.9759x - 0.406R² = 0.9985
0
20
40
60
80
100
120
0.0 20.0 40.0 60.0 80.0 100.0 120.0
linear regression
Recommended