Consensus Mean Research Articles

Use of uncertainty information for estimation of certified values. Comparison of four approaches using data from a recent certification exercise

Four approaches for estimation of reference values and their respective uncertainties of characterisation were compared using data from the recently finalised certified reference materials ERM-EC680k and ERM-EC681k, elements in plastics. Reference values and uncertainties of characterisation were estimated as mean of laboratory means and their respective standard deviations, using equal weights and the weighting procedure of Mandel–Paule. In addition, two approaches taking into consideration uncertainty information reported by the participants, namely the consistency check and simulation procedure proposed by Cox for CCQM Key comparisons and an approach suggested by Pauwels et al. (Accred Qual Assur 3:180–184, 2000) were used. No difference between the equally-weighted and Mandel–Paule consensus means was observed and the reference value from the Cox approach was in all cases within ±2 uchar of each consensus mean. Uncertainties varied between the three approaches. Uncertainties derived from equally-weighted mean of means approach are on average 14% above uncertainties using the Mandel–Paule consensus mean, 36% above the uncertainties estimated by Pauwels et al., and 54% above the uncertainties from the Cox approach. Robustness of the uncertainty estimation against incorrect estimation of uncertainties was assessed. Assumption of a 50% uncertainty of the individual uncertainties resulted in an uncertainty of 30% of the uncertainty of characterisation. Differences between the four approaches are negligible for this dataset when combined with the uncertainty contribution from heterogeneity and stability as prescribed in ISO Guide 35.

Interlaboratory Comparison for the Determination of Five Residual Organochlorine Pesticides in Ginseng Root Samples by Gas Chromatography

An interlaboratory comparison study for the determination of 5 residual organochlorine pesticides (hexachlorobenzene and 4 hexachlorocyclohexane isomers) in ginseng root was performed. This program [Asia Pacific Laboratory Accreditation Cooperation (APLAC) T049] was the first of its kind for an herbal matrix and involved the participation of 70 laboratories from 26 countries worldwide. Consensus mean values were computed statistically from the reported results, which were eventually used to assess the performance of individual laboratories in terms of the z-scores. The distribution of analytical data was found to be widespread, with standard deviation ranging from 43.9 to 55.9%, and the result patterns obtained were similar to those residue pesticide programs using other matrixes. Although the estimation of measurement uncertainty is a crucial requirement for all quantitative tests for laboratories that meet the requirements of International Organization for Standardization/International Electrotechnical Commisssion (ISO/IEC) 17025, some laboratories in this program had difficulties and showed unfamiliarity with respect to that quality criterion. It was recommended that laboratories review and rectify the situation promptly so that they would have a better understanding of measurement uncertainty or the test service provided.

Proficiency test exercise on the determination of natural levels of radionuclides in mushroom reference material

The results from a proficiency test exercise for the determination of natural levels of radionuclides in mushroom reference material carried out by laboratories in six different countries are discussed. These laboratories submitted data on seven radionuclides, namely 134Cs, 137Cs, 40K, 90Sr, 241Am, 226Ra, and 210Po. However, only the data received for three of these radionuclides could be statistically evaluated to obtain consensus mean values and confidence intervals (at a significance level of 0.05). The contents of 134Cs, 137Cs and 40K were quantified as 4.4, 2,899 and 1,136 Bq/kg, respectively.

Effect of variability in assay bias and imprecision on external quality assessment bias and imprecision measures

External quality assessment/proficiency testing programmes that report consensus means and coefficients of variations (CVs) are a potential source of information on assay bias and imprecision. This study examined the effect of variability in assay bias and imprecision on consensus means and CVs, using a computerized spreadsheet model. A model with varying assay bias (mean and standard deviation) and assay imprecision (mean and standard deviation) was developed using a MS Excel 2003 spreadsheet with a macro to generate pseudo-random numbers from a Gaussian distribution. The means, standard deviations and CVs of these data points were considered to simulate the consensus measures reported in external quality assessment testing programmes. The simulated consensus CV was very sensitive to increases in assay bias variability, with greater effects at low levels of mean assay imprecision. Changes in assay imprecision variability had a much smaller effect on the simulated consensus CV, while the simulated consensus mean was relatively insensitive to any change in the other variables. Consensus imprecision measures from external quality assessment programmes are unreliable measures of assay imprecision. Consensus means are relatively unaffected by variability in assay bias and imprecision, and can be used as reliable measures of assay bias from a statistical standpoint.

Dissociation constants and speciation in aqueous Li 2SO 4 and K 2SO 4 from measurements of electrical conductance to 673 K and 29 MPa

The electrical conductivities of aqueous solutions of Li 2SO 4 and K 2SO 4 have been measured at 523–673 K at 20–29 MPa in dilute solutions for molalities up to 2 × 10 −2 mol kg −1. These conductivities have been fitted to the conductance equation of Turq, Blum, Bernard, and Kunz with a consensus mixing rule and mean spherical approximation activity coefficients. In the temperature interval 523–653 K, where the dielectric constant, ε, is greater than 14, the electrical conductance data can be fitted by a solution model which includes ion association to form MSO 4 - , M 2 S O 4 0 , and HSO 4 - , where M is Li or K. The adjustable parameters of this model are the first and second dissociation constants of the M 2SO 4. For the 673 K and 300 kg m −3 state point where the Coulomb interactions are the strongest (dielectric constant, ε = 5), models with more extensive association give good fits to the data. In the case of the Li 2SO 4 model, including the multi-ion associate, Li 16 ( SO 4 ) 8 0 , gave an extremely good fit to the conductance data.

Combining Data in Small Multiple-Method Studies

In this article an accurate confidence interval is derived when the results of a small number of possibly biased experimental methods are combined for the determination of an unknown quantity called the consensus mean. ANOVA and a simple hierarchical Bayesian analysis of variance with locally uniform priors result in confidence intervals too wide for precision metrology. Often when deciding on experimental methods, scientists choose methods in such a way that the truth lies between the extremes of the method means. Combining this additional information with experimental data, an interval more accurate than the ANOVA interval and the simple hierarchical Bayesian interval is obtained. The estimate obtained falls within the ISO guidelines, and the mean and standard deviation used to derive the confidence interval are shown to be the posterior mean and variance of a fully Bayesian procedure.

Electrical Conductances of Aqueous Na2SO4, H2SO4, and Their Mixtures: Limiting Equivalent Ion Conductances, Dissociation Constants, and Speciation to 673 K and 28 MPa.

The electrical conductivities of aqueous solutions of Na2SO4, H2SO4, and their mixtures have been measured at 373−673 K at 12−28 MPa in dilute solutions for molalities up to 10-2 mol kg-1. These conductivities have been fit to the conductance equation of Turq et al.1 with a consensus mixing rule and mean spherical approximation activity coefficients. Provided the concentration is not too high, all of the data can be fitted by a solution model that includes ion association to form NaSO4-, Na2SO40, HSO4-, H2SO40, and NaHSO40. The adjustable parameters of this model are the dissociation constants of the SO4- species and the H+, SO4-2, and HSO4- conductances (ion mobilities) at infinite dilution. For the 673 K and 230 kg m-3 state point with the lowest dielectric constant, e = 3.5, where the Coulomb interactions are the strongest, this model does not fit the experimental data above a solution molality of 0.016. Including the species H9(SO4)5- gave satisfactory fits to the conductance data at the higher concen...

Electrical Conductances of Aqueous Na2SO4, H2SO4, and Their Mixtures: Limiting Equivalent Ion Conductances, Dissociation Constants, and Speciation to 673 K and 28 MPa

The electrical conductivities of aqueous solutions of Na(2)SO(4), H(2)SO(4), and their mixtures have been measured at 373-673 K at 12-28 MPa in dilute solutions for molalities up to 10(-2) mol kg(-1). These conductivities have been fit to the conductance equation of Turq et al.(1) with a consensus mixing rule and mean spherical approximation activity coefficients. Provided the concentration is not too high, all of the data can be fitted by a solution model that includes ion association to form NaSO(4)(-), Na(2)SO(4)(0), HSO(4)(-), H(2)SO(4)(0), and NaHSO(4)(0). The adjustable parameters of this model are the dissociation constants of the SO(4)(-) species and the H(+), SO(4)(-2), and HSO(4)(-) conductances (ion mobilities) at infinite dilution. For the 673 K and 230 kg m(-3) state point with the lowest dielectric constant, epsilon = 3.5, where the Coulomb interactions are the strongest, this model does not fit the experimental data above a solution molality of 0.016. Including the species H(9)(SO(4))(5)(-) gave satisfactory fits to the conductance data at the higher concentrations.

Evaluation of accuracy and precision in an inter-laboratory comparison of total mercury in hair

Three round robins, involving 22 laboratories from eight countries, were conducted at six month intervals. Each of the participating laboratories analysed four samples of NIES-13 in three subsequent round robins during July 2000–October 2001. The objective of the current study was to determine accuracy and precision among participants for the analysis of total mercury. Both accuracy and precision for total mercury determinations in powder hair samples were good. The median within-laboratory (within-run) CVs ranged from 3.1 to 3.9% for four CRM samples. Most laboratories showed a proportional bias relative to the consensus mean of up to 16%. Two laboratories reported results that, on average, were almost 30% higher than the consensus mean value. Significant among-laboratory imprecision was found in the present study. Improvements are needed to reduce the analytical imprecision in a few laboratories, and attention must be focused on calibration issues and methodology-related problems.

CCQM-P13 pilot study. Metals in artificial food digest

The accuracy of elemental analyses in complex matrices is usually assessed by analysis of a suitable matrix reference material. The reference value is ascribed by consensus mean and by application of primary methods of analysis. However, the quality of this value will be affected by problems such as matrix-induced interferences, moisture corrections and heterogeneity.Pilot study CCQM-P13 was undertaken to assess the capabilities ofNational Metrology Institutes to analyse Ca, Cu and Cd in an acidic solution that simulates the digest of a food sample. This study filled the gap between the analysis of a gravimetrically prepared calibration solution and the analysis of an unknown in a complex matrix requiring extensive sample preparation. Having an independent reference value, with a small uncertainty, allowed a more rigorous estimation of the reliability of the institutes' analysis and uncertainty estimates, without including issues around sample digestion.The reference values were: 1.6617 ± 0.0020 µmol/g for Ca, 7.037 ± 0.012 nmol/g for Cu and 45.57 ± 0.10 pmol/g for Cd (expanded uncertainties are quoted with coverage factor of 2). The other elements in the matrix were: Na (~25 µg/g), K (~90 µg/g), Cl (~120 µg/g), Fe (~100 ng/g), Mg (~5 µg/g), P (~5 µg/g), Sn (~80 ng/g) and Zn (~200 ng/g).Twelve international laboratories, representing eight countries, determined the amount content of the analytes. A range of techniques that include ID-ICP-MS (high resolution and collision cell), ICP-MS, ICP-OES, AAS, voltametry and potentiometry were used. The results for this pilot study averaged: 1.654 ± 0.058 µmol/g for Ca (n = 10), 7.26 ± 0.53 nmol/g for Cu (n = 12) and 45.2 ± 5.1 pmol/g for Cd (n = 11) where the values associated with the averages are the standard deviations of n participants.Main text. To reach the main text of this paper, click on Final Report. Note that this text is that which appears in Appendix B of the BIPM key comparison database kcdb.bipm.org/.The final report has been peer-reviewed and approved for publication by theCCQM Working Group on Inorganic Analysis (IAWG), according to theprovisions of the Mutual Recognition Arrangement (MRA).

Miniature flow injection analyser for laboratory, shipboard and in situ monitoring of nitrate in estuarine and coastal waters

A miniature, submersible flow injection analyser, with solid-state spectrophotometric detection, for the in situ determination of nitrate is described. It utilises the standard laboratory chemistry of cadmium reduction followed by diazotisation. The detection limit was 2.8 μg l −1 N and the linear range could be varied from 2.8 to 100 μg l −1 N up to 100–2000 μg l −1 N to suit local environmental conditions. The versatility of the instrument is demonstrated by results from laboratory, shipboard (North Sea IMPACT Cruise) and in situ (Tamar Estuary, UK) deployments. They show the excellent temporal and spatial resolution that can be achieved for studying dynamic processes in estuarine and coastal waters. The results acquired during the IMPACT Cruise map the transport of nitrate from the Humber Estuary into the North Sea and show that nitrate uptake was more pronounced in areas of shallow and clear waters (Dogger Bank) than in the coastal mixing zone with higher suspended solids. A key feature of the analyser is its portability and ease of deployment due to the small size and weight and low buoyancy. Accuracy was assessed by participation in an international intercomparison exercise and the results were within the assigned tolerance interval of the consensus mean ( Z<2).

Long-Term Analytical Performance of Hemostasis Field Methods as Assessed by Evaluation of the Results of an External Quality Assessment Program for Antithrombin

It is important for a laboratory to know the stability of performance of laboratory tests over time. The aim of this study was to adapt from the field of clinical chemistry a method to assess the long-term analytical performance of hemostasis field methods. The linear regression model was used to compare the laboratory results with the consensus mean value of a survey. This model was applied to plasma antithrombin activity using the data for 82 laboratories, collected between 1996 and 1999 in the European Concerted Action on Thrombosis (ECAT) external quality assessment program. The long-term total, random, and systematic error were calculated. The variables introduced to define the long-term performance in this model were the long-term analytical CV (LCV(a)) and the analytical critical difference (ACD), which indicates the minimum difference necessary between two samples measured on a long-term time-scale to consider them statistically significantly different. The systematic error (bias) ranged from 4.5 to 103 units/L. The random error ranged from 24.4 to 242 units/L. For the majority of the laboratories, random error was the main component (>75%) of the total error. The LCV(a), after adjustment for the contribution of the bias, ranged from 2.8% to 48%. The ACD ranged from 78 to 1290 units/L with a median value of 190 units/L. No statistically significant differences were observed for either LCV(a) or ACD between the two different measurement principles for antithrombin activity based on the inhibition of either thrombin or factor Xa. This linear regression model is useful for assessing the total error, random error, and bias for hemostasis field methods. The LCV(a) and ACD for measurement on a long-term time-scale appear to be useful for assessing the long-term analytical performance.

Multiple Ion Association versus Redissociation in Aqueous NaCl and KCl at High Temperatures

The electrical conductivities of aqueous solutions of NaCl have been measured at 651 and 670 K at 28 MPa for molalities up to 1.0 mol kg-1. These conductivities as well as the results of Hwang et al. (High Temp. High Pres. 1970, 2, 651−669), Ritzert and Franck (Ber. Bunsen-Ges. Phys. Chem. 1968, 72, 798−808), and Mangold and Franck (Ber. Bunsen-Ges. Phys. Chem. 1969, 73, 21−27) for aqueous KCl have been fit to the conductance equation of Turq et al. (J. Phys.Chem. 1995, 99, 822−827) with a consensus mixing rule and either mean spherical approximation or Debye−Huckel activity coefficients. Except at one state point (NaCl at 670 K and 28 MPa), where the interactions are the strongest (β* = 17.8), the simplest model that fits the experimental results reasonably well (± 2−3%) at molalities up to 4.5 mol kg-1 is one with only the limiting equivalent conductance and a pair association constant adjusted. Activity coefficients calculated with either the MSA and ionic diameters or with the Debye−Huckel equation of...

Analysis of a panel of UK macroeconomic forecasts

Summary We report an exploratory analysis of an interesting and important type of forecast data set. As is common for macroeconomic variables, forecasts from a large panel are available for annual macroeconomic aggregates. Although only a few years of accumulated experience are at hand, the data set is enriched by the presence of month-to-month revisions, over a period of 24 months, of forecasts for each predicted annual outcome. We analyse the evolution of summary cross-section statistics, and most notably we find excess smoothness to be displayed in the consensus (mean) forecast. This observation is confirmed by a test for forecast efficiency. The relationship between forecaster variability and forecast errors is also examined.

High resolution ID-ICP-MS certification of an estuary water reference material (LGC 6016) and analysis of matrix induced polyatomic interferences.

Reliable trace metal analysis of environmental samples is dependent upon the availability of high accuracy, matrix reference standards. Here, we present Cd, Cu, Ni, Pb and Zn isotope dilution determination for an estuary water certified reference material (LGC 6016). This work highlights the need for high-accuracy techniques in the development of trace element CRMs rather than conventional inter-laboratory trials. Certification of the estuary water LGC6016 was initially determined from a consensus mean from 14 laboratories but this was found to be unsatisfactory due to the large discrepancies in the reported concentrations. The material was re-analysed using isotope dilution ICP-MS techniques. Pb and Cd were determined using a conventional quadrupole ICP-MS (Elan 5000). Cu, Zn and Ni were determined using a magnetic sector ICP-MS (Finnigan Element), which allowed significant polyatomic interferences to be overcome. Using the magnetic sector instrument, precise mass calibration to within 0.02 amu permitted identification of the interferences. Most interferences derived from the sample matrix. For example, the high Na content causes interferences on 63Cu, due to the formation of 40Ar23Na and 23Na2 16O1H, which in a conventional quadrupole instrument would relate to an erroneous increase in signal intensity by up to 20%. For each analyte a combined uncertainty calculation was performed following the Eurachem/GTAC and ISO guideline. For each element a combined uncertainty of 2-3% was found, which represents a 10-fold improvement compared to certification by inter-laboratory comparison. Analysis of the combined uncertainty budget indicates that the majority of systematic uncertainty derives from the instrumental isotope ratio measurements.

Consensus of Dynamical Tropical Cyclone Track Forecasts—Errors versus Spread

Abstract The relationships between consensus spread of five dynamical model tracks and the consensus mean error is explored for a western North Pacific tropical cyclone database of 381 cases. Whereas a small spread of the five tracks is often indicative of a small consensus track error, some cases with large errors also are found even though the consensus spread is small. Some of the success of the dynamical model consensus approach arises because a substantial number (21%) of the cases with a large consensus spread have reduced errors after the consensus averaging. In nearly all the cases in this sample, the best of the five models has a 72-h track error of less than 300 n mi, but no tools are available to allow the forecaster to always select this best model. It is demonstrated that the forecaster can also add value by forming a selective consensus after first eliminating one or more likely erroneous track(s) and averaging the remaining tracks. Conceptual models and symptoms in the predicted fields to a...

Quality Assurance and Proficiency Testing in the Canadian Equine Drug Control Program

ABSTRACTThe Quality Assurance Program (QAP) administered by the Canadian Pari-Mutuel Agency (CPMA) has evolved over the past 17 years, in concert with the CPMA's equine drug research program. This program consists of site inspections, reports, and a check sample program. Participating laboratories also maintain internal quality control systems and are accredited for this scope of testing.The check sample program monitors routine screening and target testing of urine and blood for drugs using thin-layer chromatography or instrumental methods. The process is based on samples obtained after administration of drugs to horses, founded on results of CPMA's research. Common drugs in equine veterinary practice, and of interest in horse racing, are monitored. These include centrally active and cardiovascular drugs, diuretics and local anesthetics, respiratory and anti-inflammatory drugs, muscle relaxants and analgesics. The QAP provides a useful measure of laboratory performance for the Canadian racing industry.More recently, as part of the CPMA's partnership with Standards Council of Canada to accredit racing laboratories to ISO/IEC Guide 25, a proficiency test specific to this scope was implemented. Each cycle consists of 10 qualitative analysis samples of lyophilized, spiked equine urine, and 2 quantitative analysis samples of frozen, spiked equine serum or urine. For quantitative analysis, laboratory results must agree within ±20% of target or consensus mean value for drugs reported in the pg/mL range, or within ±40% for drugs reported in the ng/mL range. A reference laboratory prepares samples and conducts reference analysis. To date, 5 cycles of proficiency testing have been successfully completed by the participating labs.Program design and implementation activities, and results from both quality assurance and proficiency testing programs are presented and interpreted.

Comparison of Serum and Plasma Methylmalonic Acid Measurements in 13 Laboratories: An International Study

Detection of cobalamin deficiency is increasingly important, and methylmalonic acid (MMA) appears to be a useful marker. Information on interlaboratory variation and on methodological differences for MMA in serum and plasma is limited. Using gas chromatography/mass spectrometry, 13 laboratories participated in a 2-day analysis of 8 serum and 11 EDTA-plasma specimens. Results were analyzed for imprecision, recovery, and differences among laboratories and methods. The mean among-laboratory imprecision (CV) was 19% and 21% for serum and plasma samples, respectively, and 9.3% and 7.8% for serum and plasma samples with added MMA, respectively. The mean within-laboratory (among-run) CV was 13% for both serum and plasma samples and 5.2% and 4.9% for serum and plasma samples with added MMA. Within-method imprecision was the same or higher than among-method imprecision. The mean among-laboratory recovery of MMA was 105% and 95% in serum and plasma, respectively. Most laboratories showed a proportional bias relative to the consensus mean of up to 15%. Two laboratories reported results that on average were almost 30% higher than the consensus mean. No method differences were found, but significant among-laboratory imprecision was found in the present study. Improvements are needed to reduce the analytical imprecision of most laboratories, and attention must be focused on calibration issues. Differences among laboratories can be improved by introducing high-quality reference materials and by instituting external quality assessment programs.

Non-spectroscopic suppression of zinc in ICP-MS in a candidate biological reference material (IAEA 392 Algae)

ICP-MS was used for the simultaneous determination of nine analytes in a candidate reference material, IAEA 392 Algae (Scenedesmus obliquus), following microwave digestion with nitric acid and dilution to volume with de-ionised water. For eight analytes, the results showed reasonable agreement with consensus mean results obtained from a world-wide intercomparison exercise on this material. However, the value obtained for Zn was 55.4% of the consensus mean result (69.6 versus 125.6 µg g –1 , respectively). Analysis of the same digest solutions by flame AAS gave results which were in good agreement with the consensus mean (127.1 versus 125.6 µg g –1 ), indicating that all the Zn was in solution. When the method of standard additions was employed, the result was overestimated by ≈17% by ICP-MS. A 1+9 aqueous dilution of the digests gave an acceptable result for Zn (122.0 µg g –1 ). Evidence is presented to demonstrate that the underestimation of Zn by external calibration ICP-MS is due to a non-spectroscopic suppression of the Zn in the digest solution caused by nitric acid.

Estimation of a Common Mean and Weighted Means Statistics

Measurements made by several laboratories may exhibit nonnegligible between-laboratory variability, as well as different within-laboratory variances. Also, the number of measurements made at each laboratory often differ. Questions of fundamental importance in the analysis of such data are how to form a best consensus mean, and what uncertainty to attach to this estimate. An estimation equation approach due to Mandel and Paule is often used at the National Institute of Standards and Technology (NIST), particularly when certifying standard reference materials. Primary goals of this article are to study the theoretical properties of this method, and to compare it with some alternative methods, in particular to the maximum likelihood estimator (MLE). Toward this end, we show that the Mandel-Paule solution can be interpreted as a simplified version of the maximum likelihood method. A class of weighted means statistics is investigated for situations where the number of laboratories is large. This class includes a modified MLE and the Mandel-Paule procedure. Large-sample behavior of the distribution of these estimators is investigated. This study leads to a utilizable estimate of the variance of the Mandel-Paule statistic and to an approximate confidence interval for the common mean. It is shown that the Mandel-Paule estimator of the between-laboratory variance is inconsistent in this setting. The results of numerical comparison of mean squared errors of these estimators for a special distribution of within-laboratory variances are also reported.