Almost all the participants (96 %) reported the expanded uncertainties (k=2) with their results for at least some of their results (Table 3, Appendix 9). The range of the reported uncertainties varied between the measurands and the sample types, and thus the harmonization of the uncertainty’s estimation should be continued. It was evident, that for pH some uncertainties had been reported erroneously, not as relative values (%) as the provider of this proficiency test had requested (Table 3).
Table 3. The range of the expanded measurement uncertainties (k=2, Ui%) reported by the participants.
Measurement Sample The range of Ui %
Cl2, comb U1K 10-40
U2K 10-40
Cl2, free U1K 10-25
U2K 10-25
Cl2, total U1K 10-27
U2K 10-27
KMnO4 U1P 9-32
U2P 9-41
NO3 U1N 6-29
U2N 6-22
pH U1H 0.1-5
U2H 0.1-5
Turbidity U1S 6-30
U2S 6-30
Urea A1U 12-30
UE2 12-25
UK2 15-30
Several approaches were used for estimating the measurement uncertainty (Appendix 13).
The most used estimation approach was based on using the internal quality control data (Appendix 13). At maximum eight participants used MUkit measurement uncertainty software for the estimation of their uncertainties [8]. The free software is available on the webpage:
www.syke.fi/envical/en. Generally, the used approach for estimating measurement uncertainty did not make definite impact on the uncertainty estimates.
4 Evaluation of the results
The performance evaluation of the participants was based on the z scores, which were calculated using the assigned values and the standard deviation for the performance assessment (Appendix 7). The z scores were interpreted as follows:
Criteria Criteria
Performance Performance
z 2 Satisfactory
2 < z < 3 Questionable
| z 3 Unsatisfactory
In total, 88 % of the results were satisfactory when total deviation of 10–25 % and 0.2 pH units from the assigned values were accepted. 96 % of participants used accredited analytical methods at least for a part of the measurands and 89 % of the results were satisfactory. The summary of the performance evaluation and comparison to the previous performance is presented in Table 4.
In the previous similar PT, SPW 01/2019, the performance was satisfactory for 93 % of the results [6]. All samples passed the stability test and, thus, no estimation was needed for the effect of increased temperature during the sample transportation.
14 Proftest SYKE SPW 01/20
Table 4. Summary of the performance evaluation in the proficiency test SPW 01/2020.
Measurand 2 x spt% Satisfactory
results, % Remarks
Cl2, comb 20-25 88
In the SPW 01/2019 the performance was satisfactory for 92 % of the results, with the same range of standard deviation for performance assessment [6].
Cl2, free 15 85 In the SPW 01/2019 the performance was satisfactory for 97 % of the
results, when accepting the deviation of 20 % from the assigned value [6].
Cl2, total 10 95 Good performance. In the SPW 01/2019 the performance was
satisfactory for 100 % of the results, with the same range of standard deviation for performance assessment [6].
KMnO4 20 85 In the SPW 01/2019 the performance was satisfactory for 93 % of the results, when accepting the deviation of 15-20 % from the assigned value [6].
NO3 10 91 Good performance. In the SPW 01/2019 the performance was satisfactory for 88 % of the results, with the same range of standard deviation for performance assessment [6].
pH 2.6-3.0 91
Good performance. In the SPW 01/2019 the performance was satisfactory for 98 % of the results, when accepting the deviation of 2.7-3.4 % from the assigned value [6].
Turbidity 25 80 In the SPW 01/2019 the performance was satisfactory for 90 % of the results, with the same range of standard deviation for performance assessment [6].
Urea
A1U 15 100
Excellent performance. In the SPW 01/2019 the performance was satisfactory for 93 % of the results, with the same range of standard deviation for performance assessment [6].
Enzymatic, UE2 15 78
Difficulties in measurements of the sample, <80 % satisfactory results.
The recovery is in average 106 % of the calculated value. Based on the PT the method is suitable for urea measurements of swimming pool waters. In the SPW 01/2019 the performance was satisfactory for 71 % of the results with the same range of standard deviation for performance assessment [6].
Koroleff, UK2 20 71
Approximate performance evaluation.
Difficulties in measurements of the sample, <80 % satisfactory results.
The recovery is in average 56 % of the calculated value and 53 % of the results obtained by enzymatic method. Usage of the method for swimming pool waters requires method validation where the matrix effect needs to be taken into consideration. In the SPW 01/2019 the performance was satisfactory for 71 % of the results with the same range of standard deviation for performance assessment [6].
The recovery for urea in the swimming water sample was calculated from the mean concentrations of different methods (recovery% = 100 × mean of results / calculated value). The recovery for the enzymatic method was 106 %, while for the Koroleff’s method it was 56 %. The recovery percentage for the results obtained by Koroleff’s method is in the same range as in the previous similar proficiency test SPW 01/2019 (56 %) [6]. In Finland, the national supervisory authority for welfare and health (Valvira) has considered the differences between urea concentrations obtained by Koroleff’s method and enzymatic photometric method in the national guide for quality and monitoring of swimming pool waters [9]. The participants are encouraged to continue reporting more results obtained by the enzymatic photometric method for better method comparison.
5 Summary
Proftest SYKE carried out the proficiency test (PT) for analysis of combined chlorine, free chlorine, total chlorine, permanganate index (KMnO4), nitrate, pH, turbidity, and urea from swimming pool waters in January-February 2020 (SPW 01/2020). In total, 26 participants joined in this proficiency test.
The evaluation of the performance was based on the z scores, which were calculated using the assigned value and standard deviation for proficiency assessment at 95 % confidence level. In this PT 88 % of the data evaluated based on the z scores was regarded satisfactory when the results were accepted to deviate 10 to 25 % or 0.2 pH units from the assigned value. The calculated value was used as the assigned value for the urea measurements of the synthetic sample (A1U) and of the sample UE2 (enzymatic method). The robust mean of the results reported by participants was used as the assigned value for the other measurements, except for urea measurement with the Koroleff’s method (sample UK2), where the median value was used (nstat<12).
It should be noted that there is a clear difference between the urea results of the swimming pool water sample (U2U) measured with the Koroleff’s method and with the enzymatic photometric method. The reported results obtained with the Koroleff’s method were about 56 % of the calculated concentration, while the reported results obtained with the enzymatic method were in the vicinity of the calculated value. It is recommended to use the enzymatic photometric method for the urea measurements of the swimming pool waters or to validate the Koroleff’s method for the urea determination of the swimming pool waters.
16 Proftest SYKE SPW 01/20
6 Summary in Finnish
Proftest SYKE järjesti tammi-helmikuussa 2020 pätevyyskokeen uima-allasvesiä analysoiville laboratorioille (SPW 01/2020). Pätevyyskokeessa testattiin allasvesien kloori-, KMnO4-, NO3-, pH-, sameus- ja ureamäärityksiä. Ureamääritystä varten toimitettiin myös synteettinen näyte.
Pätevyyskokeeseen osallistui yhteensä 26 laboratoriota.
Pätevyyden arvioimisessa käytettiin pääsääntöisesti z-arvoa ja sitä laskettaessa tuloksille sallit-tiin pH-määrityksessä 0,2 pH-yksikön ja muissa määrityksissä 10–25 %:n poikkeama vertailu-arvosta. Laskennallista pitoisuutta käytettiin vertailuarvona synteettisen näytteen (A1U) sekä näytteen UE2 (entsymaattinen menetelmä) ureamäärityksissä. Muissa määrityksissä vertailu-arvona käytettiin osallistujien tulosten robustia keskiarvoa, poikkeuksena näytteen UK2 (Koroleffin menetelmä) ureamääritys, missä käytettiin tulosaineiston mediaania (nstat<12).
Hyväksyttäviä tuloksia oli kokonaisuudessaan 88 %.
Uima-allasvesinäytteiden ureatuloksissa havaittiin ero Koroleffin menetelmän ja entsymaattisen spektrometrisen menetelmän välillä. Vastaava ero on havaittu myös aikaisemmissa pätevyys-kokeissa. Koroleffin menetelmään perustuvalla määrityksellä saadut tulokset poikkesivat huomattavasti laskennallisista pitoisuuksista. Koroleffin menetelmällä saadut ureapitoisuudet olivat noin 56 % laskennallisesta vertailuarvosta, kun entsymaattisella testillä määritetyt tulokset ovat lähellä laskennallista arvoa. Onkin suositeltavaa käyttää entsymaattista spektrometristä menetelmää uima-allasvesien ureapitoisuuksien määrittämisessä. Käytettäessä Koroleffin menetelmää uima-allasvesien ureapitoisuuden määrittämiseen tulisi näytetyypin vaikutus tuloksiin selvittää paremmin.
R EF ERENCES
1. SFS-EN ISO 17043, 2010. Conformity assessment – General requirements for Proficiency Testing.
2. ISO 13528, 2015. Statistical methods for use in proficiency testing by interlaboratory comparisons.
3. Thompson, M., Ellison, S. L. R., Wood, R., 2006. The International Harmonized Protocol for the Proficiency Testing of Analytical Chemistry laboratories (IUPAC Technical report). Pure Appl. Chem. 78: 145-196, www.iupac.org.
4. STM asetus 315/2002 Uimahallien ja kylpylöiden allasvesien laatuvaatimuksia ja valvontatutkimuksia (in Finnish).
5. Proftest SYKE Guide for laboratories: www.syke.fi/proftest/en → Current proficiency test www.syke.fi/download/noname/%7B3FFB2F05-9363-4208-9265-1E2CE936D48C%7D/39886. 6. Leivuori, M., Tyrväinen, S., Sarkkinen, M., Koivikko, R., Tervonen, K., Lanteri, S.,
Väisänen, R. ja Ilmakunnas, M., 2019. Interlaboratory Proficiency Test 01/2019, Swimming pool water analysis. Reports of the Finnish Environment institute 14/2019, 58 p, Helsinki.
http://hdl.handle.net/10138/300660.
7. Koroleff, F. 1983. Determination of urea. In Methods of Seawater Analysis (Grasshoff, K., Erhardt, M. & Kremling K., eds.). Verlag Chemie, Weinheim, pp. 158-162.
8. Näykki, T., Virtanen, A. and Leito, I., 2012. Software support for the Nordtest method of measurement uncertainty evaluation. Accred. Qual. Assur. 17: 603-612. MUkit website:
www.syke.fi/envical.
9. Valvira, 2017. Allasvesiasetuksen soveltamisohje, Uima-allasveden laatu ja valvonta. Ohje 2/2017. pp 89 (In Finnish, http://www.valvira.fi/-/allasvesiasetuksen-soveltamisohje).
10. Magnusson B., Näykki T., Hovind H., Krysell M., Sahlin E., 2017. Handbook for Calculation of Measurement Uncertainty in Environmental Laboratories. Nordtest Report TR 537 (ed. 4).
(http://www.nordtest.info)
APPENDIX 1 (1/1)
18 Proftest SYKE SPW 01/20
: Participants in the proficiency test
Country Participant Belgium Brulabo
Finland Eurofins Ahma Oy Seinäjoki
Eurofins Ahma Oy, Rovaniemi
Eurofins Environment Testing Finland Oy, Lahti HSY Käyttölaboratorio Pitkäkoski Helsinki
KVVY Tutkimus Oy, Tampere
KVVY-Botnialab, Vaasa
Kymen Ympäristölaboratorio Oy
Lounais-Suomen vesi- ja ympäristötutkimus Oy, Turku
LUVYLab Oy Ab
MetropoliLab Oy
Saimaan Vesi- ja Ympäristötutkimus Oy, Lappeenranta Savo-Karjalan Ympäristötutkimus Oy, Joensuu Savo-Karjalan Ympäristötutkimus Oy, Kajaani Savo-Karjalan Ympäristötutkimus Oy, Kuopio
ScanLab Oy
SeiLab Oy Haapaveden toimipiste SeiLab Oy Seinäjoen toimipiste Snellmans Köttförädling, Laboratorium
SYKE Oulun toimipaikka
ÅMHM laboratoriet, Jomala, Åland
Germany Eigenbetrieb Stadtentwässerung Stuttgart (SES)
Romania Directia de Sanatate Publica
Sweden Eurofins Water Testing Sweden AB
Switzerland Amt fr Lebensmittelsicherheit und Veterinärwesen Basel-Landschaft PCAM - Division protection des eaux (PRE)
APPENDIX 2 (1/1)
: Sample preparation
Measurand/Sample U1K U2K
Cl2, comb Initial concentration, mg/l 0.14 0.14
Added compound (producer) Addition, mg/l
Added compound (producer)
Addition, mg/l NaClO (BHD)
0.90 NaClO (BHD)
0.50
Assigned value, mg/l 0.88 0.49
Cl2, total Initial concentration, mg/l 0.32 0.32
Addition, mg/l 1.25 1.06
Assigned value, mg/l 1.26 1.08
U1P U2P
KMnO4 Initial concentration, mg/l 2.71 2.71
Added compound (producer) Addition, mg/l
NO3 Initial concentration, mg/l 29.1 29.1
Dilution 5 : 1 1 : 5
Assigned value, mg/l 24.3 4.91
U1H U2H
pH Initial concentration 7.52 7.52
pH adjustment C8H5KO4 (Radiometer, pH4.0) -
Assigned value 6.72 7.71
U1S U2S
Turbidity Initial concentration, FNU 0.1 0.1
Added compound (producer) Addition, FNU
Formazin (Hach) 0.79
Added compound (producer)
Addition, mg/l CO(NH2)2 (Merck)
0.72 CO(NH2)2 (Merck)
0.54
Assigned value, mg/l 0.72 0.54/0.30
A = Synthetic sample U = Swimming pool water
APPENDIX 3 (1/1)
20 Proftest SYKE SPW 01/20
: Homogeneity of the samples
Homogeneity was tested from duplicate measurements of selected measurement from four or six samples of each sample types.
Criteria for homogeneity:
sanal/spt<0.5 and ssam2<c, where
spt = standard deviation for proficiency assessment
sanal = analytical deviation, standard deviation of the results in a sub samples
ssam = between-sample deviation, standard deviation of the results between sub samples
c = F1 × sall2 + F2 × sanal2, where sall2 = (0.3 × spt)2
F1 and F2 are constants of F distribution derived from the standard statistical tables for the tested number of samples [2, 3].
Measurand/Sample Concentration
mg/l or FNU n spt% spt sanal sanal/spt sanal/spt<0.5? ssam ssam2 c ssam2<c?
KMnO4 / U1P 7.93 4 10 0.79 0.19 0.24 Yes 0 0 0.25 Yes
KMnO4 / U2P 10.8 4 10 1.08 0.35 0.33 Yes 0.30 0.09 0.62 Yes
NO3 / U1N 24.5 4 5 1.22 0.03 0.02 Yes 0.09 0.009 0.35 Yes
NO3 / U2N 4.93 4 5 0.25 0.008 0.03 Yes 0.02 0.0004 0.01 Yes
pH / U1H 6.73 6 1.5 0.10 0.009 0.09 Yes 0.02 0.0005 0.002 Yes
pH / U2H 7.75 6 1.3 0.10 0.006 0.06 Yes 0.02 0.0002 0.002 Yes
Turbidity / U1S 0.90 4 12.5 0.11 0.01 0.11 Yes 0 0 0.003 Yes
Turbidity / U2S 0.62 4 12.5 0.08 0.008 0.10 Yes 0.01 0.001 0.002 Yes
Urea / U2U 0.59 4 10 0.06 0.006 0.10 Yes 0.008 0.00007 0.0009 Yes
Conclusion: All criteria for homogeneity were fulfilled and the samples could be considered homogenous.
APPENDIX 4 (1/2)
: Stability of the samples
The samples were delivered to the participants 27 or 28 January 2020 and they arrived at the participants mainly on 29 January 2020. The samples were requested to be measured on 30 January 2020. Stability of pH, Cl2,free, Cl2,comb, Cl2,tot and urea was tested by analyzing the samples stored at the temperatures 4 °C and 20 ºC.
Criterion for stability: D < 0.3 × spt, where
D = |the difference of results measured from the samples stored at the temperatures 4 °C and 20 °C|
spt = standard deviation for proficiency assessment Cl2, comb
Sample Result, mg/l Sample Result, mg/l Date 30.1.
(20 ºC) 30.1.
(4 ºC) Date 30.1.
(20 ºC) 30.1.
(4 ºC)
U1K 0.410 0.427 U2K 0.649 0.634
D 0.017 D 0.015
0.3×spt 0.014 0.3×spt 0.018
D <0.3 × spt? No1) D <0.3 × spt? Yes
Cl2, free
Sample Result, mg/l Sample Result, mg/l Date 30.1.
(20 ºC) 30.1.
(4 ºC) Date 30.1.
(20 ºC) 30.1.
(4 ºC)
U1K 0.898 0.900 U2K 0.457 0.500
D 0.002 D 0.04
0.3×spt 0.02 0.3×spt 0.01
D <0.3 × spt? Yes D <0.3 × spt? No1)
Cl2, total
Sample Result, mg/l Sample Result, mg/l Date 30.1.
(20 ºC) 30.1.
(4 ºC) Date 30.1.
(20 ºC) 30.1.
(4 ºC)
U1K 1.308 1.330 U2K 1.108 1.130
D 0.023 D 0.022
0.3×spt 0.019 0.3×spt 0.016
D <0.3 × spt? No1) D <0.3 × spt? No1)
pH
Sample Result Sample Result
Date 30.1.
(20 ºC) 30.1.
(4 ºC) Date 30.1.
(20 ºC) 30.1.
(4 ºC)
U1H 6.69 6.77 U2H 7.58 7.68
D 0.08 D 0.10
0.3×spt 0.03 0.3×spt 0.03
D <0.3 × spt? No1) D <0.3 × spt? No1)
APPENDIX 4 (2/2)
22 Proftest SYKE SPW 01/20
Urea
Sample Result, mg/l Sample Result, mg/l Date 31.1.
(20 ºC) 31.1.
(4 ºC) Date 31.1.
(20 ºC) 31.1.
(4 ºC)
A1U 0.736 0.732 U2U 0.579 0.587
D 0.0008 D 0.008
0.3×spt 0.016 0.3×spt 0.012
D <0.3 × spt? Yes D <0.3 × spt? Yes
1) The difference is within the analytical error
Conclusion: According to the test results, the pH or the chlorine concentration could slightly change in some samples during transport and storage if the sample temperature rises. Participants did not report higher than 12 ºC control sample temperatures.
Furthermore, all the differences are within the analytical error and, thus, all the samples were considered stable.
APPENDIX 5 (1/2)
: Feedback from the proficiency test FEEDBACK FROM THE PARTICIPANTS
Participant Comments on technical excecution Action / Proftest SYKE 9 The ordered sample U1S was not delivered to the
participant.
The provider apologized the happened.
The sample was delivered to the participant after the information.
24 The participant informed receiving the samples one day after the estimated delivery day.
The used distributor (Posti) did not deliver the samples according to the agreed schedule.
All The cover letter of the samples contained a couple of mistakes.
The provider contacted the participants by email. The letter was corrected and uploaded to ProftestWEB.
All The preliminary result report was not available from ProftestWEB.
The provider apologized the happened.
The provider attached the report immediately after the note.
Participant Comments to the results Action / Proftest SYKE 1 The participant informed that they reported their pH result
erroneously.
The corrected result was:
U1H 6.64
The result was outlier in the statistical treatment, and thus did not affect the performance evaluation. If the result had been reported correctly, the result would have been satisfactory. The participant can re-calculate the z score according to the Guide for participants [5].
14 The participant informed that their turbidity result for the
sample U2S was incorrect it the preliminary report. The participant reported their turbidity result for the sample U2S with a typo (two commas). Thus, the used statistical program could not read the data correctly.
The value was corrected, and the
performance evaluation is given in this final report.
16 The participant informed additional measured results after the preliminary results:
pH U1H 6.75, pH U2H 7.68
Clcomb U1K 0.37 mg/l, U2K 0.62 mg/l Clfree U1K 0.85 mg/l, U2K 0.48 mg/l Cltotal U1K 1.22 mg/l, U2K 1.10 mg/l
The participant did not inform that their reported results were erroneous.
Nevertheless, these additional results, if reported as official results, would have been satisfactory. The participant can calculate the z scores according to the Guide for participants [5].
17 The participant informed that they reported KMnO4 results in the wrong unit.
Their corrected values were:
U1P 8.377 mg/l U2P 10.590 mg/l
The results were outliers in the statistical treatment, and thus did not affect the performance evaluation. If the results had been reported correctly, the results would have been satisfactory. The participant can re-calculate the z scores according to the Guide for participants [5].
24 The participant reported the results for total chlorine erroneously as combined chlorine.
The corrected total chlorine results were:
U1K 1,24 mg/l U2K 1,05 mg/l
The results were outliers in the statistical treatment, and thus did not affect the performance evaluation. If the results had been reported correctly, the results would have been satisfactory. The participant can re-calculate the z scores according to the
APPENDIX 5 (2/2)
24 Proftest SYKE SPW 01/20
FEEDBACK TO THE PARTICIPANTS Participant Comments
1, 7, 8, 10, 22 The participants did not return the sample arrival document to the provider. Thus, their
information of the sample arrival temperature missed as well. The participants should follow the instructions of the provider.
4, 16, 18 The participants did not report the expanded measurement uncertainties for some
measurands. Participants are accredited laboratories, whom should report uncertainties with their results.
1 The participant reported absolute measurement uncertainty for their pH results, but the request from the provider was to report the relative measurement uncertainty. The participant should follow the instructions of the provider.
11, 23 The participant did not inform the accreditation status of their method for some measurands.
The participants should follow the instructions of the provider.
26 The participant did not report the replicate result for turbidity, thus these results were not included in the statistical calculations. The participant should follow the instructions of the provider.
APPENDIX 6 (1/1)
: Evaluation of the assigned values and their uncertainties
Measurand Sample Unit Assigned value Upt Upt, % Evaluation method of assigned value upt/spt
Cl2, comb U1K mg/l 0.38 0.03 8.5 Robust mean 0.34
U2K mg/l 0.59 0.03 5.1 Robust mean 0.26
Cl2, free U1K mg/l 0.88 0.03 3.0 Robust mean 0.20
U2K mg/l 0.49 0.02 4.1 Robust mean 0.27
Cl2, total U1K mg/l 1.26 0.04 2.8 Robust mean 0.28
U2K mg/l 1.08 0.02 2.0 Robust mean 0.20
KMnO4 U1P mg/l 7.82 0.51 6.5 Robust mean 0.33
U2P mg/l 10.0 0.6 6.1 Robust mean 0.31
NO3 U1N mg/l 24.3 0.4 1.8 Robust mean 0.18
U2N mg/l 4.91 0.16 3.3 Robust mean 0.33
pH U1H 6.71 0.05 0.8 Robust mean 0.27
U2H 7.70 0.04 0.5 Robust mean 0.19
Turbidity U1S FNU 0.86 0.06 6.9 Robust mean 0.28
U2S FNU 0.59 0.05 7.8 Robust mean 0.31
Urea A1U mg/l 0.72 0.00 0.6 Calculated value 0.04
UE2 mg/l 0.54 0.00 0.6 Calculated value 0.04
UK2 mg/l 0.30 0.03 9.6 Median 0.48
Upt = Expanded uncertainty of the assigned value
Criterion for reliability of the assigned value upt/spt < 0.3, where spt= the standard deviation for proficiency assessment upt= the standard uncertainty of the assigned value
If upt/spt < 0.3, the assigned value is reliable and the z scores are qualified.
APPENDIX 7 (1/1)
26 Proftest SYKE SPW 01/20
: Terms in the results tables
Results of each participant
Measurand The tested parameter
Sample The code of the sample
z score Calculated as follows:
z = (xi - xpt)/spt, where
xi = the result of the individual participant
xpt = the assigned value
spt = the standard deviation for proficiency assessment Assigned value The value attributed to a particular property of a proficiency test item 2 × spt % The standard deviation for proficiency assessment (spt) at the 95 %
confidence level
Participant’s result The result reported by the participant (the mean value of the replicates)
Md Median
s Standard deviation
s % Standard deviation, %
nstat Number of results in statistical processing Summary on the z scores
S – satisfactory ( -2 z 2)
Q – questionable ( 2< z < 3), positive error, the result deviates more than 2 × spt from the assigned value q – questionable ( -3 < z < -2), negative error, the result deviates more than 2 × spt from the assigned value U – unsatisfactory (z ≥ 3), positive error, the result deviates more than 3 × spt from the assigned value u – unsatisfactory (z ≤ -3), negative error, the result deviates more than 3 × spt from the assigned value
Robust analysis
The items of data are sorted into increasing order, x1, x2, xi,…,xp. Initial values for x* and s* are calculated as:
x* = median of xi (i = 1, 2, ...., p)
s* = 1.483 × median of ׀xi – x*׀ (i = 1, 2, ...., p)
The mean x* and s* are updated as follows:
Calculate φ = 1.5 × s*. A new value is then calculated for each result xi (i = 1, 2, …, p):
{ x* - φ, if xi < x* - φ xi* = { x* + φ, if xi > x* + φ
{ xi otherwise The new values of x* and s*are calculated from:
The robust estimates x* and s* can be derived by an iterative calculation, i.e. by updating the values of x* and s* several times, until the process convergences [2].
p x x* =
i*/
− −=
1.134 (x x )2/(p 1)
s i
APPENDIX 8 (1/9)
: Results of each participant
Participant 1
Measurand Unit Sample z score Assigned value 2×spt % Participant's result Md Mean s s % nstat
Cl2, comb mg/l U1K 1.12 0.38 25 0.43 0.37 0.38 0.05 14.6 19
mg/l U2K 0.18 0.59 20 0.60 0.58 0.59 0.05 8.1 18
Cl2, free mg/l U1K 0.42 0.88 15 0.91 0.89 0.89 0.03 3.8 20
mg/l U2K -0.48 0.49 15 0.47 0.49 0.49 0.03 6.9 18
Cl2, total mg/l U1K 1.27 1.26 10 1.34 1.27 1.25 0.07 5.4 21
mg/l U2K -0.09 1.08 10 1.08 1.08 1.08 0.04 3.9 21
KMnO4 mg/l U1P -0.65 7.82 20 7.31 8.08 7.81 0.77 9.9 17
mg/l U2P -0.56 10.0 20 9.4 9.9 10.0 1.0 10.3 18
pH U1H -4.67 6.71 3 6.24 6.69 6.72 0.10 1.4 22
U2H 0.20 7.70 2,6 7.72 7.70 7.71 0.05 0.7 22
Turbidity FNU U1S -0.01 0.86 25 0.86 0.86 0.84 0.10 12.1 20
FNU U2S -0.39 0.59 25 0.56 0.57 0.57 0.07 11.7 18
Urea mg/l A1U 1.46 0.72 15 0.80 0.75 0.74 0.04 5.6 15
Urea mg/l UK2 2.17 0.30 20 0.37 0.30 0.32 0.04 12.7 7
Participant 2
Measurand Unit Sample z score Assigned value 2×spt % Participant's result Md Mean s s % nstat
Cl2, comb mg/l U1K 1.16 0.38 25 0.44 0.37 0.38 0.05 14.6 19
mg/l U2K 0.59 0.59 20 0.63 0.58 0.59 0.05 8.1 18
Cl2, free mg/l U1K -0.53 0.88 15 0.85 0.89 0.89 0.03 3.8 20
mg/l U2K -0.95 0.49 15 0.46 0.49 0.49 0.03 6.9 18
Cl2, total mg/l U1K 0.32 1.26 10 1.28 1.27 1.25 0.07 5.4 21
mg/l U2K 0.00 1.08 10 1.08 1.08 1.08 0.04 3.9 21
KMnO4 mg/l U1P -1.88 7.82 20 6.35 8.08 7.81 0.77 9.9 17
mg/l U2P -1.08 10.0 20 8.9 9.9 10.0 1.0 10.3 18
NO3 mg/l U1N -0.25 24.3 10 24.0 24.3 24.3 0.7 2.9 17
mg/l U2N 2.69 4.91 10 5.57 4.85 4.92 0.32 6.5 17
pH U1H 2.19 6.71 3 6.93 6.69 6.72 0.10 1.4 22
U2H 0.80 7.70 2,6 7.78 7.70 7.71 0.05 0.7 22
Turbidity FNU U1S -0.37 0.86 25 0.82 0.86 0.84 0.10 12.1 20
FNU U2S -0.34 0.59 25 0.57 0.57 0.57 0.07 11.7 18
Urea mg/l A1U 1.20 0.72 15 0.79 0.75 0.74 0.04 5.6 15
Urea mg/l UE2 2.22 0.54 15 0.63 0.57 0.57 0.05 8.4 9
Participant 3
Measurand Unit Sample z score Assigned value 2×spt % Participant's result Md Mean s s % nstat
Cl2, comb mg/l U1K -0.21 0.38 25 0.37 0.37 0.38 0.05 14.6 19
mg/l U2K -0.51 0.59 20 0.56 0.58 0.59 0.05 8.1 18
Cl2, free mg/l U1K -0.08 0.88 15 0.88 0.89 0.89 0.03 3.8 20
mg/l U2K 0.27 0.49 15 0.50 0.49 0.49 0.03 6.9 18
Cl2, total mg/l U1K -0.24 1.26 10 1.25 1.27 1.25 0.07 5.4 21
mg/l U2K -0.37 1.08 10 1.06 1.08 1.08 0.04 3.9 21
KMnO4 mg/l U1P 0.46 7.82 20 8.18 8.08 7.81 0.77 9.9 17
mg/l U2P 1.20 10.0 20 11.2 9.9 10.0 1.0 10.3 18
-3 0 3
-3 0 3
-3 0 3
APPENDIX 8 (2/9)
APPENDIX 8 (3/9)
Participant 6
Measurand Unit Sample z score Assigned value 2×spt % Participant's result Md Mean s s % nstat
NO3 mg/l U1N 0.74 24.3 10 25.2 24.3 24.3 0.7 2.9 17
mg/l U2N 1.38 4.91 10 5.25 4.85 4.92 0.32 6.5 17
pH U1H 0.60 6.71 3 6.77 6.69 6.72 0.10 1.4 22
U2H 0.90 7.70 2,6 7.79 7.70 7.71 0.05 0.7 22
Turbidity FNU U1S 0.30 0.86 25 0.89 0.86 0.84 0.10 12.1 20
FNU U2S 1.49 0.59 25 0.70 0.57 0.57 0.07 11.7 18
Urea mg/l A1U -0.86 0.72 15 0.67 0.75 0.74 0.04 5.6 15
Urea mg/l UE2 0.02 0.54 15 0.54 0.57 0.57 0.05 8.4 9
Participant 7
Measurand Unit Sample z score Assigned value 2×spt % Participant's result Md Mean s s % nstat
Cl2, comb mg/l U1K -2.74 0.38 25 0.25 0.37 0.38 0.05 14.6 19
mg/l U2K -0.13 0.59 20 0.58 0.58 0.59 0.05 8.1 18
Cl2, free mg/l U1K 1.21 0.88 15 0.96 0.89 0.89 0.03 3.8 20
mg/l U2K -1.22 0.49 15 0.45 0.49 0.49 0.03 6.9 18
Cl2, total mg/l U1K -0.79 1.26 10 1.21 1.27 1.25 0.07 5.4 21
mg/l U2K -0.97 1.08 10 1.03 1.08 1.08 0.04 3.9 21
KMnO4 mg/l U1P 0.14 7.82 20 7.93 8.08 7.81 0.77 9.9 17
mg/l U2P 0.32 10.0 20 10.3 9.9 10.0 1.0 10.3 18
NO3 mg/l U1N -0.22 24.3 10 24.0 24.3 24.3 0.7 2.9 17
mg/l U2N -0.24 4.91 10 4.85 4.85 4.92 0.32 6.5 17
pH U1H -0.20 6.71 3 6.69 6.69 6.72 0.10 1.4 22
U2H 0.60 7.70 2,6 7.76 7.70 7.71 0.05 0.7 22
Turbidity FNU U1S 2.14 0.86 25 1.09 0.86 0.84 0.10 12.1 20
FNU U2S 3.25 0.59 25 0.83 0.57 0.57 0.07 11.7 18
Urea mg/l A1U 1.57 0.72 15 0.81 0.75 0.74 0.04 5.6 15
Urea mg/l A1U 1.57 0.72 15 0.81 0.75 0.74 0.04 5.6 15