Interlaboratory comparison study of calibration standards for foraminiferal Mg/Ca thermometry

An interlaboratory study of Mg/Ca and Sr/Ca ratios in three commercially available carbonate reference materials (BAM RS3, CMSI 1767, and ECRM 752‐1) was performed with the participation of 25 laboratories that determine foraminiferal Mg/Ca ratios worldwide. These reference materials containing Mg/Ca in the range of foraminiferal calcite (0.8 mmol/mol to 6 mmol/mol) were circulated with a dissolution protocol for analysis. Participants were asked to make replicate dissolutions of the powdered samples and to analyze them using the instruments and calibration standards routinely used in their laboratories. Statistical analysis was performed in accordance with the International Standardization Organization standard 5725, which is based on the analysis of variance (ANOVA) technique. Repeatability (RSDr%), an indicator of intralaboratory precision, for Mg/Ca determinations in solutions after centrifuging increased with decreasing Mg/Ca, ranging from 0.78% at Mg/Ca = 5.56 mmol/mol to 1.15% at Mg/Ca = 0.79 mmol/mol. Reproducibility (RSDR%), an indicator of the interlaboratory method precision, for Mg/Ca determinations in centrifuged solutions was noticeably worse than repeatability, ranging from 4.5% at Mg/Ca = 5.56 mmol/mol to 8.7% at Mg/Ca = 0.79 mmol/mol. Results of this study show that interlaboratory variability is dominated by inconsistencies among instrument calibrations and highlight the need to improve interlaboratory compatibility. Additionally, the study confirmed the suitability of these solid standards as reference materials for foraminiferal Mg/Ca (and Sr/Ca) determinations, provided that appropriate procedures are adopted to minimize and to monitor possible contamination from silicate mineral phases.


Introduction
[2] Reconstruction of past ocean temperatures from magnesium/calcium ratios in foraminiferal calcite has become an established technique during recent years [e.g., Nurnberg et al., 1996;Hastings et al., 1998;Lea et al., 1999;Mashiotta et al., 1999;Rosenthal et al., 2000;Dekens et al., 2002;Anand et al., 2003]. Mg/Ca ratios in foraminiferal calcite are now measured routinely by different laboratories and comparability of results is an important issue.
[3] A consequence of the exponential relationship between Mg/Ca and temperature in foraminiferal calcite is that in order to ensure the accuracy of calculated temperatures, the relative measurement precision, expressed as a percentage of the measured ratio, must be maintained across the range of Mg/Ca ratios from low to high values. This is contrary to the usual situation in analytical methods [Horwitz, 1982], where relative measurement precision becomes worse with decreasing values. Increasing interest in temperatures calculated from the low Mg/Ca ratios found in benthic Schrag, 2002, 2003;Martin et al., 2002;Marchitto and deMenocal, 2003;Lear et al., 2004;Elderfield et al., 2006] and cold water planktonic foraminifera [Pak et al., 2004;von Langen et al., 2005;Meland et al., 2006;Nyland et al., 2006] further emphasizes the need for compatibility of Mg/Ca measurements between different laboratories.
[4] An interlaboratory comparison study conducted by Rosenthal et al. [2004] examined the reproducibility of Mg/Ca measurements within and between laboratories in foraminiferal calcite and in synthetic standard solutions. The study additionally included Sr/Ca because of the interest in studying secular variations in seawater Sr/Ca [Martin et al., 1999;Stoll et al., 1999;Shen et al., 2001] and growing potential for fora-miniferal Sr/Ca thermometry in select genera [Mortyn et al., 2005]. Results showed that for the analyses of standard solutions, within laboratory instrumental precisions were usually better than 0.5% for measurements of both Mg/Ca and Sr/ Ca, but interlaboratory precisions were significantly worse with relative standard deviations obtained of up to 3.4% for Mg/Ca and 1.8% for Sr/Ca. Among the conclusions of that interlaboratory study were the need for standards calibration among laboratories and the desirability of developing an agreed solid standard which could be used by laboratories in a manner analogous to the way reference standards are used in isotope analyses.
[5] The accuracy of standard solutions for element ratio determinations and the potential of commercially available carbonate reference materials for application to foraminiferal Mg/Ca (and Sr/Ca) determinations were investigated by . These authors demonstrated that the errors involved in the preparation of instrument calibration standards for Mg/Ca and Sr/Ca determinations contribute significantly to interlaboratory analytical precision and proposed a limestone certified reference material (ECRM 752-1), containing Mg/Ca within the range of foraminiferal calcite (Mg/Ca = 3.75 mmol/mol), as a consistency standard which could be used within and between laboratories.
[6] Here we present the results of an interlaboratory study where three solid materials containing Mg/Ca in the range of foraminiferal calcite (0.8 mmol/mol to 6 mmol/mol) were analyzed by 25 participating laboratories. The advantage of circulating solid standards for intercalibration, rather than standard solutions, is that solid standards overcome the risk inherent in circulating small volumes of liquids that may not retain their initial compositions by the time they are analyzed. This must be balanced against stringent homogeneity and purity requirements for solid standards . Therefore, there were two objectives to the current study; first, compare instrumental standards calibrations between laboratories to assess within laboratory repeatability and between laboratory reproducibility; second, determine the suitability of the circulated solid standards as reference materials for foraminiferal Mg/Ca (and Sr/Ca) determinations.

Experimental Design
[7] This study followed the practice of previous interlaboratory studies [Rosell-Melé et al., 2001;Rosenthal et al., 2004] of maintaining anonymity by assigning random identification numbers to participating laboratories. Note that those numbers are different than the ones given for affiliations. The analytical scheme was constructed with reference to the International Union of Pure and Applied Chemistry (IUPAC) recommendations [Horwitz, , 1995 for interlaboratory comparison studies. Samples of three solid standards were sent to each participant along with a dissolution protocol which participants were requested to follow, with the aim of minimizing effects that could result from different dissolution procedures and enabling the exercise to focus on instrument calibrations. Participants were asked to make replicate dissolutions on the powder samples and to analyze them using the instruments and calibration standards routinely used in their laboratory.  Greaves et al. [2005]. The materials were certified for Mg concentrations but not for Mg/Ca ratios at the precision, or sample sizes, relevant to foraminiferal Mg/Ca thermometry. Elemental concentrations taken from the certificates of analyses are listed in Table 1 together with calculated element/ calcium ratios.

Standards
[9] Propagation of the quoted analytical errors on certified element concentrations gives errors (r.s.d.) on calculated Mg/Ca ratios of 2.7% (BAM RS3), 6.8% (ECRM 752-1) and 8.3% (CMSI 1767), insufficiently precise, with the possible exception of BAM RS3, to be directly relevant to foraminiferal Mg/Ca determinations. Foraminiferal calcite is composed of extremely pure (99%) CaCO 3 , equivalent to 39.6% Ca, with four minor elements Na, Mg, Sr and F comprising most of the remainder [Lea, 1999] and the relative purity of these materials is shown by their calcium concentrations (Table 1). The presence of Al, Fe, Mn, Si and Ti is indicative of other mineral phases. Homogeneity of the solid materials and the contribution to measured Mg/Ca from the other mineral phases were investigated in preliminary studies before circulation.

Preliminary Studies
[10] Preliminary tests of homogeneity were performed on standards BAM RS3 and CMSI 1767 at Cambridge and LSCE, respectively, following the procedure used by Greaves et al. [2005] to test the homogeneity of ECRM 752-1. Replicate aliquots were taken from a single bottle of each standard for a series of weighings in the range 10 to 250 mg. Samples were dissolved in 0.075M HNO 3 in acid cleaned HDPE or LDPE bottles, using dissolution volumes in proportion to sample weights to give [Ca 2+ ] of 400 mg/g. Solutions were analyzed both with and without centrifugation; two 0.5 mL aliquots were taken, one centrifuged for 10 min at 9000 rpm then both diluted to [Ca 2+ ] = 40 mg/g (CMSI 1767) or [Ca 2+ ] = 100 mg/g (BAM RS3) and analyzed by ICP-OES. Mg/Ca results are reported in Table 2 and illustrated in Figure 1 which shows also Fe/Ca measurements in CMSI 1767.
[11] Results for CMSI 1767 (Figure 1a) demonstrate the contribution to Mg/Ca from insoluble noncarbonate minerals within this material which is confirmed by Fe/Ca (Figure 1b). Higher and more variable Mg/Ca and Fe/Ca in noncentrifuged samples, together with consistency between the Mg/Ca and Fe/Ca data sets in Figures 1a and 1b [12] In contrast, results for BAM RS3 (Figure 1c) show good agreement between centrifuged and noncentrifuged Mg/Ca measurements. Average Mg/Ca after centrifuging of 0.796 mmol/mol (0.012 s.d., 1.56% r.s.d) on 20 measurements was influenced by two high values. Omitting these gave Mg/Ca of 0.793 mmol/mol (0.008 s.d., 0.97% r.s.d) on 18 measurements, compared to noncentrifuged Mg/Ca of 0.789 mmol/mol (0.004 s.d., 0.51% r.s.d) on 20 measurements. Fe/Ca in BAM RS3 was consistently low and in most cases below detection, with a maximum of 0.004 mmol/mol observed. Slightly higher Mg/Ca ratios and the greater variability of centrifuged compared to noncentrifuged samples may be a consequence of the additional handling involved and effect of the associated analytical blank on the low Mg/Ca of this material.
[13] Measurements of Sr/Ca in CMSI 1767 ( Figure 1d) revealed a ratio comparable to Sr/Ca in foraminiferal calcite and good homogeneity within this material from measurements both with and without centrifugation. Average Sr/Ca for samples in the 10 to 250 mg weight range was 1.542 mmol/mol (0.010 s.d., 0.66% r.s.d) on 11

Sample Preparation and Distribution
[15] All samples were prepared at LSCE from previously unopened bottles of the standards, containing 80 g CMSI 1767 (without lot number), 100 g BAM RS3 (lot number 41), 100 g ECRM 752-1 (lot number 2133). The standards were mixed well in case of settling during storage then, following the homogeneity tests detailed in the previous section, one gram portions of each standard were weighed into a series of glass sample bottles precleaned by soaking for 24 hours in 10% HNO 3 , rinsed with high-purity water and dried for 24 hours. Thus, for each standard, all samples sent to laboratories came from the same initial bottle on which homogeneity had been verified.
[16] The participating laboratories were each sent one subsample bottle of each of the three standards and requested to perform replicate analyses as described in section 2.4 except that as a check on homogeneity of the materials after subsampling, one laboratory (25) was sent five subsample bottles of each standard and asked to make a single determination from each subsample.

Protocol for Dissolution
[17] The primary objective of this Mg/Ca interlaboratory comparison was to check instrumental calibrations between laboratories and a dissolution protocol was devised with the aim of minimizing effects from noncarbonate mineral phases in the standards and from laboratories following different procedures. Participants were requested to follow the following procedure: (1) number of replicate dissolutions, 6 per standard; (2) sample weight, 50 mg; (3) dissolution volume, 50 mL; (4) dissolution acid, 0.075M HNO 3 (or as routinely used in their laboratory); (5) samples to be dissolved and analyzed on the same day; (6) a blank solution to be included; (7) solutions to be analyzed both with and without centrifuging, and (8) samples to be diluted as required for the usual instrumental procedures of each laboratory.
[18] It was intended that after initial bottle cleaning and reagent preparation, the dissolution and analyses could be completed in a single day of laboratory and instrument time. Laboratories performing analyses in solution were asked to follow, as far as possible, the protocol supplied. Laboratories doing analyses not in solution were free to investigate the materials as they saw fit. In addition to results for Mg/Ca, participants were asked to provide data for Sr/Ca and for elements indicating silicate contamination, such as Al, Fe, Mn, Si, Ti, depending on those typically measured in their laboratory. The participants were provided with the approximate Mg/Ca ratios of the three materials calculated from quoted element concentrations (Table 1), but were not informed of the Sr/Ca ratio found for CMSI 1767 in the preliminary studies, making CMSI 1767 a blind sample for the determination of Sr/Ca.

Reporting of the Results
[19] A file containing spreadsheets for returning experimental information and results using a template for each material was sent with the protocol.
On return the files were first screened to ensure that no laboratory or personal information had been included and that results were identified only by laboratory numbers before being passed to the coordinators. In this way anonymity was preserved both among participants and the coordinators when examining data. The results were tabulated in a common format by the coordinators to give a single value for each sample of material dissolved and analyzed before calculating the mean of replicate analyses by each laboratory, i.e., where some laboratories had made multiple determinations on a single dissolution of material these were combined to give a single result per analysis. The complete set of results, individual analyses, means and standard deviations of replicate dissolutions by each laboratory are presented in auxiliary material 1 Tables S1 -S3. Statistical analysis of the data followed the protocol of Horwitz [1995] and the guidelines of AOAC International [2006]. One of the criteria specified in this protocol is that only valid data should be subject to statistical analysis.
In the context of this exercise, valid Mg/Ca data are those where significant influences from other noncarbonate phases can be excluded and therefore, results for each of the three materials were examined critically, as described in section 3, to identify nonvalid data on analytical grounds as preferable to relying on statistical tests alone [Horwitz, 1995].

Outlier Testing
[20] The outcome of outlier tests depends to a large extent on the tests themselves and how they are applied. Statistical tests can identify observations which differ from the majority of others according to the rules applied, but cannot give a reason. A decision to label data as outliers should reflect scientific experience as much as the application of a statistical rule [Horwitz, 1995;Davies, 1988;Meier and Zünd, 2000]. The following tests were applied with these caveats in mind.
[21] Measurements identified as outliers for analytical reasons by individual laboratories were first excluded, then a three-sigma test (three standard deviation test) was applied to each set of data for a standard and laboratory. Data superior to the mean plus 3 sigma, or inferior to the mean minus 3 sigma, were excluded and means recalculated before data were submitted to outlier testing using Cochran and Grubbs tests [Horwitz, 1995;AOAC International, 2006]. The Cochran test is used to identify sets of results showing significantly greater variability among replicate (within-laboratory) analyses than the other laboratories for a given material. This test was applied as a 1-tail test at a probability value of 2.5%. To apply this test, we computed the within-laboratory variance for each laboratory and divided the largest of these by the sum of the variances. The resulting quotient is the Cochran statistic which indicates the presence of a removable outlier if the critical value listed in the Cochran table for P = 2.5% is exceeded. The Grubbs test is used to identify laboratories with extreme averages. This test was applied in the following order: single value test (2-tail; P = 2.5%); then if no outlier was found a pair value test was applied (2 values at the highest end and 2 values at the lowest end; then 2 values, one at each end, at an overall P = 2.5%).

Statistical Data Treatment
[22] To perform statistical data treatment, we followed the International Standardization Organization [1994], which is based on the analysis of variance (ANOVA) method. We applied a statistical scheme equivalent to that commonly used in interlaboratory analytical studies [Nilsson et al., 1997;Rosell-Melé et al., 2001;Rosenthal et al., 2004]. Summary statistics (S r , S R , RSD r , RSD R ) were calculated for the average ratios and overall method precisions for each of the three standards.
In this scheme, we focused on: the single-analyst standard deviation (S r , repeatability), the precision associated with the performance of an individual laboratory, the overall standard deviation (S R , reproducibility), the precision associated with measurements generated by a group of laboratories. The repeatability RSD r is determined from the repeatability standard deviation (S r ) and the average concentration for a particular test sample, giving an indication of the intralaboratory precision. The reproducibility RSD R , determined from the reproducibility standard deviation (S R ) and the average concentration of a particular test sample, gives an indication of the interlaboratory method precision. Equating S R to measurement uncertainty and assuming a normal distribution gives a confidence interval of 67% that the result plus and minus S R will encompass the ''true'' value. Multiplying S R by a coverage factor of 2 gives the ''expanded measurement uncertainty'' with a confidence interval of 95% that the result plus and minus 2S R will encompass the ''true'' value. The reproducibility limit (R) or repeatability limit (r) is the value less than or equal to which the absolute difference between two results obtained under reproducibility or repeatability conditions is expected to be with a probability of 95%. For a normal distribution r = 2.8S r and R = 2.8S R .

Results and Discussion
[23] The twenty-five participating laboratories each returned results of Mg/Ca determinations on one or more of the three materials, twenty-four laboratories performed analyses after dissolution and one used a flow through method [Benway et al., 2003]. Instrumental determinations were by either inductively coupled plasma optical emission spectrophotometry (ICP-OES), used by sixteen laboratories or inductively coupled plasma mass spectrometry (ICP-MS), by nine laboratories. The supplied experimental protocol was followed by most of the participants although four laboratories used significantly smaller quantities of solid material (10-20 mg) than the 50 mg proposed. Homogeneity implications of using small samples are assessed during discussion of the results. Twenty-two laboratories returned results of Sr/Ca determinations in addition to Mg/Ca. Element ratios frequently used as contamination indicators [e.g., Barker et al., 2003;Lea et al., 2005] were returned by the laboratories as follows; Mn/Ca by thirteen laboratories, Fe/Ca by eight, Al/Ca by seven, Ti/Ca by five and Si/Ca by two laboratories. Data for other trace element ratios including Ba/Ca, Cd/Ca, Nd/ Ca, U/Ca and Zn/Ca were returned by one laboratory or more with a maximum of five participants returning results of Ba/Ca determinations. Details of the procedures used and number of results reported for each material and element ratio measured are given in auxiliary material Tables S1-S3.
[24] Results for Mg/Ca, Sr/Ca and element ratios measured to indicate possible contamination from noncarbonate phases are presented and discussed for each of the three materials separately in sections 3.1 to 3.3. Comparisons between the three materials are made in section 3.4. Analytical details, individual results, means and statistics are presented in detail for each material in auxiliary material Tables S1-S3. Results for other trace metal ratios which do not relate directly to Mg/Ca are included in auxiliary material Tables S1-S3.

BAM RS3
[25] Mg/Ca was determined in BAM RS3 by all twenty-five participants on samples without centrifugation and by twenty-one laboratories after centri-  Table 3 and mean values plotted for each laboratory in Figure 2, in ascending order of uncentrifuged values, using data before statistical rejection. A single data point, flagged as contaminated by a laboratory (25) was excluded from results after centrifugation. Error bars plotted in Figure 2 are ±2 standard errors on the mean (= 2*SD/ p n) to allow for the different number of determinations by laboratories. Histograms of the individual measurements, for solutions after centrifuging, are presented in Figure 3, showing the distribution of results among laboratories ( Figure 3a) and comparing results obtained by the two instrumental techniques (Figure 3b).
[26] Within laboratory standard deviations, including all results except the determination identified as contaminated, average 0.010 mmol/mol (centrifuged) and 0.013 mmol/mol (not centrifuged) which, because of the low Mg/Ca in this material, translate into average intralaboratory precisions of 1.33% and 1.64%, respectively. The average precisions conceal a wide range in intralaboratory repeatability, from 0.17% to 4.31% for determinations after centrifuging and 0.12% to 7.58% (or 5.95% excluding the flow through technique, lab 29), for determinations without centrifuging (Table 3).
[27] Between laboratory precisions, again taking all results for Mg/Ca determinations in BAM RS3, are approximately four times worse than average within laboratory precisions at 5.4% and 5.6% for centrifuged and not centrifuged results, respectively. With the exception of laboratory 18 and to a lesser extent laboratories 3 and 19, the results with and without centrifuging are in agreement, giving overall mean Mg/Ca, before statistical analysis, from all laboratories of 0.775 mmol/mol (0.043 s.d., 5.57% r.s.d) on 25 determinations without centrifuging and 0.784 mmol/mol (0.043 s.d., 5.44% r.s.d) on 21 determinations after centrifuging (Table 3).
[28] The range of the results shown in Figures 2  and 3 could be caused by a number of analytical or geochemical factors and these are investigated here before discussing statistical analysis of the data. Three laboratories (13, 17, 26) used small (10 mg) samples for dissolution. Laboratory 13 performed analyses without centrifugation only but results of centrifuged and not centrifuged determinations from laboratories 17 and 26 are in close agreement, suggesting that homogeneity of the solid material when using 10 mg is not a major factor, in agreement with the preliminary homogeneity study described in section 2.2. If results for these laboratories, and also lab 29 which used the flow through procedure, are omitted, the between laboratory reproducibility is improved slightly but with little effect on the mean values obtained (Table 3), simply because results from laboratories 17 and 26 were above average, while those from laboratories 29 and 13 were below.
[29] The potential for magnesium contamination in analyses of BAM RS3 is significant because of its low Mg/Ca ratio. The dissolution protocol was designed to minimize the effect of the Mg blank during dissolution by producing high initial concentrations. Most laboratories adhered to this (Table 3) with a minimum initial Ca concentration, used by laboratory 13, of 120 mg/g. Calcium concentrations of the final instrumental determinations cover a very wide range from 1 to >400 mg/g, some laboratories diluting solutions before running while others ran concentrates without dilution. Although the possibility of Mg contamination can never be excluded and it may contribute to within laboratory repeatability, there is no apparent relationship between the concentrations used for final determination (Table 3) and the Mg/Ca results shown in Figure 2.
[30] Laboratories where other element ratios were determined, including Al/Ca, Fe/Ca, Mn/Ca, Si/Ca, Ti/Ca, as indicators of contamination by noncarbonate minerals found very low values in BAM RS3, confirming the results of the preliminary study and anticipated from the quoted element concentrations shown in Table 1. Similarly, Sr/Ca in this material was confirmed to be very low at approximately 0.18 mmol/mol, from both centrifuged and noncentrifuged determinations, much lower than relevant to the typical Sr/Ca range of 1.0-1.5 mmol/mol found in foraminiferal calcite. Results are included in the auxiliary material.
[31] Statistical analysis using the Cochran test rejects results from laboratories 19, 29 and 33 for analyses without centrifuging, and from laboratories 6, 18 and 22 (and 29) for analyses after centrifuging, on the basis of the within laboratory variance (Table 3 and (Table 3). Following statistical data rejection, results obtained by ICPMS are indistinguishable from those obtained by ICP-OES (Figure 3b), in agreement with the conclusions of a recent study [Andreasen et al., 2006].
[32] The mean values obtained from both noncentrifuged and centrifuged determinations, either with or without statistical data rejection, are close to the Mg/Ca ratio of 0.8 mmol/mol calculated from the certified concentrations (Table 1). The material circulated showed good homogeneity and purity and is a valuable reference material for Mg/Ca determinations. However, the spread of results shown in Figure 2 and the associated reproducibility statistics highlight the discrepancy between calibration standards used by laboratories. Results of the analysis of variance (ANOVA) are presented and discussed with those from the other two materials in section 3.4.

ECRM 752-1
[33] Results for Mg/Ca in ECRM 752-1 are presented in Table 4. Twenty-four laboratories analyzed the material without centrifugation and twenty-one laboratories after centrifuging solutions. The means were calculated using all data submitted by the participants except for one data point flagged as an outlier in results after centrifugation by the participating laboratory (24) and one data point excluded from results before centrifugation (Lab 5) on the basis that it was more than three standard deviations from the mean. The complete data set is presented in auxiliary material Tables S1-S3. Mean values obtained by each laboratory for this material are plotted in Figure 4a in ascending order of centrifuged values and individual measurements are shown in histograms in Figures 5a and 5b.
[34] Within laboratory standard deviations were similar for analyses both with and without centrifuging, averaging 0.026 and 0.027 mmol/mol, respectively, and equivalent to within laboratory precisions of 0.70% r.s.d. for this material. As found for BAM RS3, within laboratory precisions cover a wide range, from 0.18 to 1.47% for determinations after centrifuging solutions and 0.16 to 2.31% for determinations without centrifuging (Table 4). The between laboratory precisions are approximately 3.5 times worse than within laboratory precision, again reflecting the situation found for BAM RS3.
[35] It was demonstrated previously ] that silicate mineral phases within this material must be removed in order to obtain reproducible Mg/Ca results from the carbonate. Eight laboratories measured Fe/Ca as an indicator of silicate contamination ( Figure 4b) and seven measured Al/Ca (Figure 4c). Fewer participants determined Si/Ca or Ti/Ca while thirteen laboratories returned Mn/Ca measurements. The results are included in the complete data set in auxiliary material Tables S1-S3. The effect of silicate contamination on noncentrifuged Mg/Ca determinations is evident in Figure 4a and confirmed, where available, by Fe/Ca and Al/Ca (Figures 4b and 4c). Fe/Ca falls to approximately 0.07 mmol/mol on centrifuging and Al/Ca to < 0.3 mmol/mol, below or very close to detection by ICP-OES. Where laboratories did not determine either Fe/Ca or Al/ Ca it must be assumed that the centrifugation procedure used was adequate to remove any suspended undissolved silicate minerals. ICP-MS results for Al/Ca were returned by laboratory 29 using the flow through method [Benway et al., 2003] where a mean Al/Ca of 0.17 mmol/mol was found. This is close to the average Al/Ca of 0.13 mmol/mol returned by three laboratories after centrifugation ( Figure 4c) and, except for one determination (Lab 20), much lower than the average Al/Ca of 0.65 mmol/mol found without centrifugation. It would appear from this evidence to be appropriate to include results by the flow through method with centrifuged rather than noncentrifuged data. [36] Most of the participating laboratories used the 50 mg sample size requested in the dissolution protocol but smaller samples of 23 mg (Lab 4) and 10 mg (Labs 13, 17 and 26) were also used. Exclusion of results from these laboratories had little effect on the mean values and reproducibility (Table 4), confirming the homogeneity of ECRM 752-1 for sample sizes of 10 mg and above when solutions are analyzed after centrifuging .

CMSI 1767
[39] CMSI 1767 has the highest Mg/Ca ratio of the three materials circulated and contains the largest contribution from noncarbonate minerals, as shown in Table 1 and confirmed by the preliminary homogeneity study (Figure 1). Mg/Ca was determined in this material by twenty-four laboratories without centrifugation and twenty-two laboratories on solutions after centrifuging. The results of Mg/ Ca determinations in CMSI 1767 are shown in Table 5, calculated using all results with the exception of four data points. Two data points were flagged as outliers by the three sigma test in results after centrifugation; one from Lab 5, one from Lab 19, and two identified as outliers in results without centrifugation; one from Lab 16 and one from Lab 4 where anomalously high Mg/ Ca was associated with high Al/Ca, Fe/Ca and Ti/ Ca. The complete data set is included in auxiliary material Tables S1-S3. Mean Mg/Ca ratios obtained by each laboratory are plotted in Figure 6a in ascending order of centrifuged values and individual measurements for Mg/Ca determinations in solutions after centrifuging are shown in histograms in Figures 7a and 7b.
[40] Average within laboratory standard deviations for analyses of this material both with and without centrifuging were similar at 0.040 and 0.047 mmol/ mol, respectively, equivalent to within laboratory precisions of 0.71% and 0.82% r.s.d. Again, the average within laboratory precisions masked a wide range between individual laboratories, from 0.24 to 1.69% for determinations after centrifuging solutions and 0.17 to 1.88% for determinations without centrifuging (Table 5). The between laboratory precisions were approximately three times worse than average within laboratory precisions, again following the pattern found for BAM RS3 and ECRM 752-1.
[41] The high contribution of Mg from silicate mineral phases in this material gave significant differences between centrifuged and noncentrifuged determinations (Figure 6a) and emphasized the importance of concurrent measurements of other element ratios to monitor silicate contamination (e.g., Al/Ca, Fe/Ca, Si/Ca, Ti/Ca), as recommended for checking cleaning efficiency when determining Mg/Ca in foraminiferal calcite [Barker et al., 2003;Rosenthal et al., 2004;Lea et al., 2005]. The same number of laboratories determined Fe/Ca ( Figure 6b) and Al/Ca ratios ( Figure 6c) in CMSI 1767 as in ECRM 752-1, with a few participants providing results for Si/Ca and Ti/Ca and thirteen laboratories measuring Mn/ Ca. Detailed results are included in the complete data set in auxiliary material Tables S1-S3. Fe/Ca ratios >1 mmol/mol were measured in CMSI 1767 in solutions without centrifuging (Figure 6b), falling to 0.67 mmol/mol on centrifuging, in agreement with the results of the preliminary homogeneity study. Al/Ca in this material was slightly higher than in ECRM 752-1with a mean of 0.84 mmol/ mol without centrifuging, falling to 0.23 mmol/mol  Figure 4a shows interlaboratory mean and standard deviation for centrifuged analyses before statistical rejection, including flow through analysis by Lab 29. Horizontal lines in Figures 4b and 4c show mean values of not centrifuged (blue) and centrifuged (red) data, not including Lab 29 (see text). on centrifuging (Figure 6c). The flow through method (Lab 29) returned Al/Ca of 0.41 mmol/ mol, lower than all except one of the not centrifuged determinations by other laboratories, but higher than all except one of the results after centrifuging (Figure 6c).
[42] Exclusion of results from the small (< = 10 mg) sample sizes used by laboratories 13, 17 and 26 from the reproducibility calculations in Table 5    [43] Statistical analysis using the Cochran test rejects results from laboratory 6 from analyses after centrifuging, on the basis of the within laboratory variance (  (Table 5). Results of the analysis of variance (ANOVA) are presented and discussed with those from the other two materials in section 3.4. As found from analyses of the other materials, results obtained by ICPMS are statistically indistinguishable from those obtained by ICP-OES ( Figure 7b).
[44] Twenty-one laboratories returned results of Sr/ Ca determinations in CMSI 1767, twenty on solutions after centrifuging, twenty on solutions without centrifuging and one using the flow through method (Table 6). Mean values are plotted for each laboratory in Figure 8, in ascending order of centrifuged values, using data before statistical rejection. Within laboratory precisions averaged 0.54% on centrifuged solutions and 0.65% on solutions without centrifugation, excluding the flow through analyses of laboratory 29, or 0.80% including results of the flow through analysis (Table 6). Results with and without centrifuging solutions were in close agreement for all except two laboratories (18 and 30).
[45] The homogeneity of Sr/Ca within CMSI 1767 is demonstrated by results from the two laboratories where small samples (< = 10 mg) were dissolved, removal of these data having a negligible effect on the mean values shown in Table 6.
[46] Statistical analysis using the Cochran test rejected results on the basis of within laboratory variance from laboratory 29 for analyses without centrifuging, and from laboratories 6 and 23 for analyses after centrifuging (

Comparisons Between the Three Materials
[47] The results of Mg/Ca determinations in the three materials are compared in Figure 9 using the Youden plot method [Kateman and Buydens, 1993]. The Mg contents of the materials are not close enough to treat them as Youden matched pairs [Horwitz, 1995;AOAC International, 2006 Figure 6a shows interlaboratory mean and standard deviation for centrifuged analyses before statistical rejection, including flow through analysis by Lab 29. Horizontal lines in Figures 6b and 6c show mean values of not centrifuged (blue) and centrifuged (red) data, not including Lab 29 (see text).   Table 7 for comparison with results of the ANOVA method.
[49] The intralaboratory repeatabilities (RSD r %) for Mg/Ca determinations in centrifuged solutions range from 0.78% (CMSI 1767) to 1.15% (BAM RS3), becoming noticeably larger with decreasing Mg/Ca ratios. As found from the unweighted statistics, interlaboratory reproducibility (RSD R %) when calculated from analysis of variance is considerably worse than intralaboratory repeatability  (Table 7). Similarly for Sr/Ca determinations in CMSI 1767, good intralaboratory repeatability (RSD r %) was obtained, 0.52% and 0.72% for centrifuged and not centrifuged solutions, respectively, but interlaboratory reproducibility (RSD R %) was much worse at 5.05% and 5.92% for centrifuged and not centrifuged determinations, respectively.
[50] The interlaboratory reproducibilities include systematic errors from instrument calibrations within each laboratory and also any differences between the individual subsamples of material sent to the laboratories. However, the reproducibilities of determinations on material taken from five separate subsample bottles and analyzed by a single laboratory (Lab 25, Tables 3-6) show that inhomogeneity between subsamples is not significant. Interlaboratory variability is dominated by inconsistencies among instrument calibrations in the different laboratories.
[51] Conversion of the interlaboratory reproducibilities (RSD R %) to temperatures using the temperature calibration of Anand et al. [2003] gives overall reproducibilities of 0.5°C for Mg/Ca ratios of 3.76 and 5.56 mmol/mol (ECRM 752-1 and CMSI 1767) increasing to 1.0°C at Mg/Ca of 0.79 mmol/mol (BAM RS3), for a temperature sensitivity of 9% per°C [Anand et al., 2003]. The repeatability (r) and reproducibility (R) represent the 95% confidence levels that two measurements are in agreement, within and between laboratories, respectively, assuming a normal distribution. Conversion of the reproducibility (R) to temperature [Anand et al., 2003] gives ±1.4°C for Mg/Ca of 5.56 and 3.76 mmol/mol (CMSI 1767 and ECRM 752-1) increasing to ± 3°C for Mg/ Ca = 0.79 mmol/mol (BAM RS3 centrifuged) or ± 4°C when calculated from reproducibility of BAM RS3 not centrifuged.
[52] Mg/Ca results for the three materials (Tables 3-5 and 7) are lower than calculated from certified element concentrations (Table 1) because in this study small sample sizes relevant to foraminiferal calcite were used for the determination of Mg/Ca in the carbonate fraction of the materials, whereas the certified element concentrations were determined on bulk material and represent the total contribution from all minerals present. This is reflected by the trace elements (Al, Fe, Si, Ti) which are low in carbonates and high in silicate mineral phases, and demonstrated by comparison of centrifuged and noncentrifuged determinations.

Conclusions
[53] The results of Mg/Ca determinations in this study showed that repeatability (RSD r %), for Mg/ Ca determinations in solutions after centrifuging, increased with decreasing Mg/Ca, increasing from 0.78% at Mg/Ca = 5.56 mmol/mol (CMSI 1767) to 0.82% at Mg/Ca = 3.76 mmol/mol (ECRM 752-1) and 1.15% at Mg/Ca = 0.79 mmol/mol (BAM RS3) as would be predicted for most analytical methods [Horwitz, 1982]. The average intralaboratory precisions concealed a wide range among  (Tables 3-5). Interlaboratory reproducibilities (RSD R %) were noticeably worse than intralaboratory repeatabilities, again increasing at low Mg/Ca, from 4.5% at Mg/Ca = 5.56 mmol/mol and 3.76 mmol/mol (CMSI 1767 and ECRM 752-1) to 8.7% at Mg/Ca = 0.79 mmol/mol (BAM RS3), for Mg/Ca determinations in centrifuged solutions. The interlaboratory variability is dominated by inconsistencies among instrument calibrations between laboratories, which need to be addressed to improve compatibility of Mg/Ca measurements and calculated temperatures. This is particularly important when determining temperatures from the low Mg/ Ca ratios associated with benthic and cold-water planktonic species of foraminifera.
[54] This study confirmed the suitability of the circulated solid standards as reference materials for foraminiferal Mg/Ca determinations, provided that appropriate procedures are adopted in order to minimize and to monitor possible contamination from silicate mineral phases present in ECRM 752-1 and CMSI 1767. The combination of Mg/Ca determinations in ECRM 752-1 and CMSI 1767 (Figures 9b and 9d) represents an efficient way of achieving analytical consistency among laboratories, with the objective of minimizing deviations from the mean values obtained by the community. BAM RS3 was shown to be a valuable reference material for determinations at low Mg/Ca ratios, being homogenous with a pure CaCO 3 matrix. We recommend that laboratories determining low Mg/ Ca ratios report results for BAM RS3 to improve compatibility of low temperature estimates. CMSI 1767, because of its high silicate mineral content, is the most difficult of the three materials for Mg/Ca determinations but has the advantage of an ideal Sr/ Ca ratio for intercalibration of foraminiferal Sr/Ca.

Acknowledgments
[55] The manuscript was improved following constructive reviews by two anonymous reviewers and comments from the G-Cubed editor, Vincent Salters. Research funding is acknowledged in France from the IMAGES project, CNRS, the Commissariat à l'Energie Atomique, and the University Saint Quentin en Yvelines and in the UK from NERC and the Gary Comer Foundation. The project was coordinated by the first two authors, who contributed equally to this paper.