An Interlaboratory Investigation of the 

Effect of Material Granularity 

and Sample Processing on 

Measurement Variability: 

Nutritional Elements in Cereals 

Katrice A. Lippa

Laura J. Wood

Stefan D. Leigh

N. Alan Heckert

http://dx.doi.org/10.6028/NIST.IR.7927

NISTIR 7927
NISTIR 7927

An Interlaboratory Investigation of the Effect of Material 

Granularity and Sample Processing on Measurement 

Variability: Nutritional Elements in Cereals

Katrice A. Lippa 

Laura J. Wood

Chemical Sciences Division

Material Measurement Laboratory

Stefan D. Leigh 

N. Alan Heckert

Statistical Engineering Division

Information Technology Laboratory

http://dx.doi.org/10.6028/NIST.IR.7927

May 2013

U.S. Department of Commerce

Rebecca M. Blank, Acting Secretary

National Institute of Standards and Technology

Patrick D. Gallagher, Under Secretary for Standards and Technology and Director
ABSTRACT

This interlaboratory study was specifically designed to determine the effects of material

granularity and sample processing techniques on the measurement variability (i.e. precision) of 

nutritional elements in various cereal materials. Participants were asked to determine in triplicate 

the levels of iron, calcium and zinc in six breakfast cereals (three wheat-based, two rice-based 

and one wheat/rice mixture). Processing of the three ground materials (ground and homogenized 

wheat, ground wheat and ground rice) was anticipated to be relatively straightforward, whereas 

the two flake materials (wheat flake and rice flake) were expected to require appropriate 

processing prior to subsampling to limit measurement variability. The final material (wheat/rice 

mixture with a hand-crushed granularity) was anticipated to be a ‘challenge’ material due to its 

inherent heterogeneity both in content and in granularity. In general, approximately 25 % of the 

laboratories processed and analyzed the suite of six cereal materials with adequate to exemplary 

measurement precision. Another 60 % of the laboratories experienced measurement issues 

related only to a specific type of cereal matrix (e.g., wheat vs. rice or the ‘challenge’ wheat/rice 

sample), or for only a select element (e.g., Fe vs. Ca or Zn). A small number (≈ 15 %) of 

laboratories experienced significant sample processing and/or measurement problems. It should 

be noted that this study is a precursor to possible future exercises that will assess method 

precision using commercially available nutritional products that will contain more varied 

ingredients and thus exhibit significant heterogeneity. 

INTRODUCTION

The Nutrition Labeling and Education Act of 1990 requires nutrition labels to report the Ca and 

Fe content of processed foods, including ready-to-eat cereal, that will be sold within the U.S. 

Nutrients such as Zn with an established reference daily intake value may also be listed. The 

nutritional elements study is designed to elucidate the effect of sample size/sample preparation as 

well as the individual testing laboratory comparability by analyzing a set of samples that range in 

granularity. This interlaboratory study was specifically designed to determine the effects of both 

the material granularity and the sample processing techniques on measurement variability as well 

as to provide individual laboratories information on their performance relative to the other 

participants (comparability information). 

Six wheat-based and rice-based fortified breakfast cereals were selected as study materials 

(Figure 1) and were specifically prepared to represent a series of various granularities and 

fortification levels, as well as a range of fiber and protein content. Table 1 provides the nominal 

levels of the proximates (fats, protein, carbohydrates, etc.) as well as the levels of Fe, Ca and Zn.

As shown in Table 1, the rice-based cereal was fortified with Fe only but had naturally occurring 

levels of Ca and Zn. Each laboratory was provided with the six cereal samples and asked to 

report values for triplicate measurements of Fe, Ca and Zn in each of the six samples. 

Laboratories were also asked to provide details regarding their sample processing techniques, 

amount of study material that was processed and the amount of subsample that was used in the 

analysis. 

1
As this study was designed to compare material granularities and sample processing techniques, 

a complete statistical assessment of between- and within-laboratory variabilities was conducted

to determine the consistency of the data across the multiple sample processing approaches. The 

relative variabilities of triplicate measurements for Fe, Ca and Zn for each of the six materials 

were assessed and compared with the sample processing information provided by each 

laboratory. Comparison with the sample processing information is important because the various 

matrices of this suite of cereal samples may respond differently to differing sample preparation 

techniques (e.g., mechanical grinding, hand-crushing), influencing an individual laboratory’s 

ability to provide reproducible results for each material.

SOURCE OF MATERIAL 

Cereal A (SRM 3233 Fortified Breakfast Cereal) was the only study material used that has NIST 

assigned values for Fe, Ca and Zn and therefore the only material for which the measurement 

results can be assessed for trueness (or relative proximity to the NIST certified values). 

Cereals B and C were prepared from the same source of commercially available fortified wheat 

flake cereal originating from two production lots that were well mixed prior to packaging (21 kg 

in total). Cereals D and E were prepared from the same source of commercially available 

partially fortified rice flake cereal originating from a single production lot (13 kg in total) 

(Figure 1). For both the wheat and rice cereals, half of the production lot was packaged directly 

as the flake material and the remainder was ground using a Teflon disc mill. Cereal F was 

prepared from a hand-crushed 50:50 mixture (by weight) of the wheat flake and rice flake 

cereals. While this material was well mixed, a visual examination of the individual packages of 

Cereal F suggested inhomogeneity with respect to both flake size and texture. 

SAMPLE DISTRIBUTION

Duplicate samples from each of the six separate containers of cereals (Cereals A-F) containing 

approximately 30 g were provided to each participant and were distributed by the NIST 

laboratory in Charleston, SC to each of 20 laboratories (including NIST Gaithersburg, MD) 

during the week of April 12, 2010. These six cereals included three ground breakfast cereals, 

two whole flake breakfast cereals, and one partially crushed breakfast cereal. The ground and 

partially crushed materials were provided in sealed amber bottles, while the whole flake 

materials were supplied in sealed plastic bags. 

Participants were advised to store samples at room temperature (≈ 23 °C) away from direct light 

prior to analysis. Participants were also advised about the general nutritional element levels in 

the samples, which were described as containing significantly varying Ca levels ranging from 

300 mg/kg to 40000 mg/kg, Fe levels from 250 mg/kg to 800 mg/kg, and Zn levels from 30 

mg/kg to 700 mg/kg.

2
EVALUATION OF EXERCISE RESULTS 

Establishment of the Exercise Values

Laboratory data submission: Each laboratory was requested to provide triplicate values for Ca, 

Fe and Zn for each of the six materials (Cereals A-F). Participants were advised to report data 

for all six samples and it was specified that it was preferred that the data be reported for all three 

analytes (a total of 18 values reported). However, if it was not feasible for a particular laboratory 

to provide the complete data, then it was requested they provide data for only a single element 

across all six materials rather than for a random selection of materials (e.g., it was sufficient to 

report Fe data for the six samples, rather than report all elements for only three samples). 

Laboratories were also asked to provide all sample preparation data to determine the effects of 

sample size and sample pretreatment. An example of the reporting sheet for the sample 

preparation data is provided in Appendix A. 

A summary of the sample processing techniques used by each laboratory for processing of the 

flake and hand-crushed cereals C, E and F is provided in Table 2. Reported sample processing 

techniques included mortar and pestle, metal mechanical grinder, non-metal mechanical grinder,

hammer and hand crushing. Approximately half (45 %) of the laboratories used a mortar and 

pestle, while 40 % of the participating laboratories used a metal mechanical grinder. There were 

only three laboratories (15 % of participating laboratories) that used other techniques: hand 

crushing, a hammer and a non-metal mechanical grinder. The majority (90 %) of laboratories 

processed the study material before subsampling for triplicate analyses. The amount of study 

material that was processed ranged from 1 g to 60 g (2 packages processed together). For only 

the three textured samples (Cereals C, E and F), the range of subsample size used for triplicate 

analysis was 0.2 g to 10 g, with a median value of 0.5 g. 

Determination of laboratory analyte means and standard deviation: For each laboratory, the 

analyte mean and standard deviation of the three sample results were calculated for Ca, Fe and 

Zn in each of the six materials (Cereal A-F). This data is provided in Table 3. In a few 

instances, laboratories provide identical values for the triplicate measurements therefore a 

standard deviation was labeled as “not applicable” or n/a. For laboratories that did not provide 

data for a particular analyte, the data was labeled as “not determined” or n/d. 

Data distribution assessment: Normal probability plots for each material/analyte combination 

were generated to test if each dataset is normally distributed (Appendix B). Normal probability 

plot correlation coefficients (PPCC) and the 5 % critical values (CV) were determined for each 

material/analyte combination. Normality is rejected at the 5 % level if the PPCC value is less 

than the critical value. These plots were used as a data screening tool only and were used 

primarily to identify outlying laboratories. 

Comparison to material NIST values: The NIST value for Cereal A (SRM 3233 Fortified 

Breakfast Cereal) was provided based on a combination of results from inductively coupled 

plasma optical emission spectrometry (ICP-OES) measurements made at NIST and from 

determinations made by external collaborating measurement laboratories. The mean value of the 

NIST measurements was combined with the median of the means of the collaborating 

3
laboratories to provide the NIST value. SRM 3233 was not certified at the time of this study 

therefore the study values may differ from the certified values. A comparison of participant’s 

results for Ca, Fe and Zn in Cereal A (SRM 3233 Fortified Breakfast Cereal) to the NIST value 

at the time of this study is provided in Figure 2. Twenty laboratories participated in the 

nutritional elements in breakfast cereals sampling exercise including NIST. Participants used 

both ICP-OES and inductively coupled plasma mass spectrometry (ICP-MS) as the analytical 

techniques for the determination of these three elements. Fourteen of the non-NIST laboratories 

used ICP-OES and five used ICP-MS. 

Determination of variability between- and within-laboratories: The triplicate data for Fe, Ca and 

Zn for all six materials were analyzed with respect to between-laboratory (using an h-consistency 

statistic) and within-laboratory (using a k-consistency statistic) components of variance using the 

established ASTM E691 protocol for the determination of precision of a test method.1

 Briefly, 

the between-laboratory consistency statistic (h) is:

h = d/sx

where d is the individual laboratory deviation (deviation of the average of the individual 

laboratory (i.e., cell) values from the average of all the laboratories averages) and sx is the 

standard deviation of the laboratory (cell) averages. The within-laboratory consistency statistic 

(k) is:

k = s/sr

where s is the standard deviation for an individual laboratory and sr is the repeatability standard 

deviation of the material, simply determined as:

sr = �∑ s2/p p

1

with p = the number of laboratories evaluated. The values of the h-consistency and kconsistency statistics determined for each data set are then compared to critical values of h and k

at the 5 % significance level.

The complete set of h-consistency statistic and k-consistency statistic plots for Fe, Ca and Zn in 

both sets of materials (Cereals A, B, C and Cereals E, D, F) together with a tabular data output 

are provided in Appendix C.

REPORTED RESULTS

An overview of the variability of the participating laboratories’ performance for all 18 

nutrient/cereal pairs is summarized in Table 4. The variability is tabulated as the median of the

relative standard deviations (RSDs) of the results observed in each laboratory, where the relative 

standard deviation is defined as the standard deviation divided by the absolute value of the mean. 

The median RSD summary results illustrate that half (50 %) of laboratories analyzed the

4
triplicate samples with reasonable precision, having RSDs of 5 % or less. For some laboratories, 

however, the results are less precise, with RSDs of 10 % or greater, and in some cases, RSDs as 

high as 45 %. 

Figure 2 compares the participant’s results for Ca, Fe, and Zn to the independently measured

NIST reference values for Cereal A. As shown in Figure 2, 15 out of 19 participating 

laboratories (79 %) have sample mean values that fall within within the 95 % confidence bounds 

(± 2u) for the NIST value for Fe. For Ca, 9 out of 19 participating laboratories (47 %) fall within 

the 95 % confidence bounds and for Zn, 7 out of 20 participating laboratories (35 %) fall within 

the 95 % confidence bounds. The uncertainty associated with Fe for the NIST value was greater 

than for Ca or Zn.6-8 The larger uncertainty associated with the NIST value for Fe, with a 

relative expanded uncertainty of 12 %, afforded the participants a greater opportunity of falling 

within the target range. The relative expanded uncertainties associated with the NIST values for 

Ca and Zn were 2 % and 4 % respectively. 

Normal probability plots for each material/analyte combination (Appendix B) were assessed to 

evaluate if each dataset were normally distributed. Specifically for the Ca data, the cereal A 

measured mass fractions are approximately normally distributed. For cereals B and C (wheat 

ground and wheat flake), the PPCC values are just below the 5 % critical value, so the departure 

from normality is mild. For cereal B, a number of laboratories have slightly higher than 

expected mass fractions while for cereal C there are 4 laboratories with somewhat lower than 

expected mass fractions. Cereals D, E, and F (rice ground, rice flake, rice/wheat crushed) have 

PPCC values that are well below the 5 % critical value. For cereals D and E (rice ground and 

rice flake), there are several laboratories with slightly higher than expected mass fractions and 

three laboratories with much higher than expected mass fraction values. It is notable that these 

two materials have considerably lower mass fraction of Ca (nearly 100-fold) than the other 

materials. The source of calcium in these rice cereals originates from its naturally-occurring 

form within the cereal matrix, calcium caseinate, which is added to the cereal for protein

fortification. Notably, this amount of calcium added does not provide a significant amount of Ca 

with respect to the recommended daily allowances per serving size of 30 g. This is in contrast to 

the wheat cereals in which Ca fortification is achieved by the direct addition of calcium 

carbonate. 

For the Fe data, only cereal D (rice ground) appears to be approximately normal. Cereals A and 

B (superground wheat and ground wheat) have a number of laboratories with much lower than 

expected mass fractions (more severe for cereal A). Cereals E and F (rice flake and rice/wheat 

crushed) have lower than expected mass fractions in the lower half of the data.

Lastly for Zn, cereals A, B, and F are approximately normal. The PPCC value for cereal C is 

just below the 5 % critical value, so the departure from normality is mild (there is one lab with a 

much lower than expected mass fraction). Cereals D and E (rice ground and rice flake) have 

several laboratories with much lower than expected mass fractions and several laboratories with 

much higher than expected mass fractions. Similar to the Ca data, the mass fraction of Zn in 

these two materials is considerably lower (nearly 20-fold) than the other cereals and is present in 

only its naturally-occurring form within the cereal matrix. 

5
Examples of h and k plots for the determination of Zn in the ground and flake wheat cereals (A, 

B and C) are shown in Figure 3. In the top figure, laboratories considered to be significantly 

different relative to the other laboratories (h-consistency statistic) will approach or fall above or 

below the critical value of |2.56| (5 % significance level). For laboratories that have not 

adequately processed all samples, a greater between-laboratory variance would be expected for 

Cereal C (wheat flake) in comparison to Cereals A and B (wheat ground with homogenization 

and wheat ground, respectively) because the variability of values determined for Cereal C are 

more dependent on the completeness of sample processing. The data given in the top figure

indicate, however, that most laboratories have similar h-consistency statistics for the three wheat 

materials, implying that all samples were adequately processed and that the method of processing 

the material is not contributing significantly to the overall measurement variability for Zn.

In the bottom figure, the k-consistency statistics of laboratories that approach or fall above the 

critical value of 2.21 (5 % significance level) denote significantly greater within-laboratory 

variability for these measurements. However, while small k values are indicative of small 

variability, very small k values (near zero) may also indicate measurement problems (i.e. 

measurement insensitivity).2, 3 For laboratories that have not adequately processed all samples, 

a greater within-laboratory variance (k-consistency statistic) would be expected for Cereal C 

(wheat flake) in comparison to Cereals A and B (wheat ground and homogenized and wheat 

ground, respectively). The data given in the bottom figure indicate, however, that most 

laboratories have similar k-consistency statistics for the three wheat materials, reinforcing the hconsistency conclusion (top figure) that most samples were adequately processed and that the 

method of processing the material is not contributing significantly to the overall measurement 

variability for Zn.

Six sets of h- and k-consistency plots similar to Figures 3a and 3b were generated (one for each 

element and material combination) and are provided in Appendix C. A summary of those data 

that were above the critical line (5 % significance level) are provided in Table 5. This summary 

table (Table 5) illustrates which laboratories are outliers with respect to the h and k indicators for 

the three elements (Fe, Ca and Zn) across the six materials investigated. The several h indicators 

for Zn in Cereal F may be representative of sample heterogeneity. The few h indicators 

randomly scattered across materials and elements could indicate anything from improper sample 

handling or preparation to an error in data processing. The clusters of k indicators around labs 

and materials are sometimes inconsistent and were used only to flag outlying data. 

Figure 4 represents exemplar consensus plots for Zn in the ground and flake wheat cereals 

(Cereal B and Cereal C, respectively) using DerSimonian-Laird (DSL) weighted consensus 

means and multiples of Horn-Horn-Duncan (HHD) standard uncertainty lines. The DSL 

weighted mean is a method commonly used in the biostatistical literature to determine a 

consensus value from many different participating laboratories’ measurements. The DSL 

weighted consensus mean accounts for both the within- and between-laboratory variance 

components and is used to determine interlaboratory consensus values.4

 Horn-Horn-Duncan 

(HHD) is a related method used to estimate consensus uncertainty of the mean.5

 The examples 

in Figure 4 show the relationship of each laboratory’s three individual Zn values to the 

consensus mean. The solid line connecting the median value illustrates the replicate variability 

within a laboratory. 

6
A complete set of eighteen DSL consensus plots are provided for each element (Fe, Ca and Zn) 

in each of the six materials (Cereals A-F) in Appendix D. The results of these consensus plots 

were compiled by generating summary consensus plots that represent the performance of each 

individual laboratory with respect to the overall exercise results. The individual laboratorycustomized plots are provided in Appendix E with explanatory details intended to provide useful 

feedback regarding each laboratory’s performance in this study. 

DISCUSSION

A few general observations were found based on results obtained from the 20 participants in this 

study. While each participant’s data is unique to his or her own laboratory, there are a variety of 

patterns and trends that are identifiable based on results obtained from the 20 participants. 

Technical guidelines can be recommended for good laboratory practices based on these 

observations. 

It was observed that laboratories processing samples in their entirety produced a more 

homogeneous material that could be subsequently subsampled for further analysis. In general, 

the optimal procedure is to process (i.e., grind, crush) the entire sample received first (i.e., the 

entire bottle or package) then subsample for analysis after processing the sample. Also, when 

analyzing food and dietary supplements, complete digestions are required to ensure that all 

elements are in solution in order to obtain accurate results. Leachate-type digestions will not 

produce complete digestions for food or dietary supplements and results for these types of 

digestions were found to be below the NIST target value. 

The use of calibration standards, obtained from a reliable source, must still be confirmed for 

quality before use. Determination of the approximate mass fraction of the working solutions will 

allow calibration points to be made that closely surround the working solutions, ensuring that 

calibration points are linear in the measurement range allowing for more accurate measurements. 

Along with unknown samples, an appropriate Certified Reference Material (CRM) or traceable 

in-house control should be prepared and carried through the entire experiment for quality 

assurance.

Some initial comparisons can be made with this data of the sampling processes that were used by 

each laboratory (Table 2). While it is not readily apparent that the sample processing method

grossly affects analytical outcome, it does appear that both when the processing was employed 

(grinding before or after subsampling for analysis) and the amount of sample used for grinding 

can influence the between- and within-laboratory variability. Between-laboratory differences (hconsistency statistic) observed in flake materials may be an indication of material inhomogeneity 

potentially caused by improper sample processing, sampling a very small amount or processing 

the sample after it has been subsampled for analysis. When extreme values are observed (hconsistency statistics) for both ground and flake materials, this may be an indication of a 

potential calibration or dilution error. The majority of laboratories (70 %) indicated that the 

entire bottle or package was used for grinding prior to subsampling. Partitioning the original 

sample into relatively small subsamples prior to grinding and homogenization may result in 

7
obtaining replicate subsamples that differ in granularity, nutrient and thus elemental content. 

When outliers are observed due to variability within a laboratory’s measurements (k-consistency 

statistic), methodological sources of error such as improper sample processing, sample analysis, 

improper calibration or incomplete digestion are possible. These factors can contribute to a 

significant increase in variability. 

The greatest variability was observed for measurement of Ca in cereals D, E, and F, which are

rice-based materials that contained native levels of Ca. Likewise, Cereal F is comprised of 50 % 

of the rice-based cereal (Cereal D/E) with the other 50 % comprised of the wheat-based cereal

(Cereal B/C). Cereals D and E also contained a higher protein content and this particular material 

and element combination may have caused more difficulty for some laboratories with respect to

sampling and/or chemical analysis. In contrast to Ca, most laboratories sampled and analyzed Fe 

with essentially the same degree of precision independent of the sample matrix (similar across 

the six materials). Some laboratories had difficulty with Fe for all of the sample matrices, which 

may be attributable to the fact that Fe contamination is more prevalent than either Ca or Zn in a 

typical laboratory environment. Such contamination could have occurred during either the 

sample processing or chemical analysis steps and care should be taken to avoid Fe 

contamination. The variability of Zn measurement was similar to that of Ca measurement in the 

wheat based materials and appeared more manageable to the laboratories with respect to their 

overall precision with observed RSDs typically less than 6.5%. 

Increased variability may also be a product of material heterogeneity, as in Cereal F. Betweenlaboratory results for the overall Fe, Ca and Zn levels in Cereal F may thus be more variable 

among the participating laboratories, with some laboratories reporting much higher (or lower) 

nutrient levels for Cereal F depending on whether the mixture contained more of Cereal C or 

Cereal E. As a case in point, this material heterogeneity may explain why some of the laboratory 

results (including NIST’s) for Cereal F for all three nutrients (Fe, Ca and Zn) were considerably 

different from the consensus value. Nonetheless, Cereal F is a practical example of a material 

that laboratories may be required to evaluate, in which values from replicate bottles or packages 

do not agree as a result of material inhomogeneity. An important consideration when faced with 

inhomogeneity is determination of an appropriate sample size. For instance, if the sample to be 

measured were granola bars, one bar would most likely not constitute a representative sample. 

An entire box of granola bars may not even constitute a representative sample. Laboratories 

must determine on a case-by-case basis the amount of material needed to have a representative 

sample for evaluation. In this cereal study, between-laboratory results tended to be more 

variable for Cereal F. Within-laboratory results for triplicate measurements should not be 

affected if appropriate sample processing and subsampling techniques are employed.

Acknowledgments

The time and effort of the analysts and management of the participating laboratories are 

gratefully acknowledged. We thank Rebecca S. Pugh, Amanda J. Moors, and Lauren B. Rust of 

the Hollings Marine Laboratory for preparation and shipping of the cereal samples to the 

participants. We also thank David L. Duewer for invaluable data visualization advice and 

8
Catherine A. Rimmer, Melissa M. Philips and Katherine E. Sharpless for their helpful 

suggestions and editorial advice. 

Disclaimer

Certain commercial equipment, instruments, or materials are identified in this report to specify 

adequately the experimental procedure. Such identification does not imply recommendation or 

endorsement by the National Institute of Standards and Technology, nor does it imply that the 

materials or equipment identified are the best available for the purpose.

References

1. ASTM E691-99: Standard practice for conducting an interlaboratory study to determine 

the precision of a test method. 1999.

2. Mandel, J. Evaluation of control measurements, New York: Marcel Dekker, 1991.

3. Rukhin, A. L. Weighted means statistics in interlaboratory studies. Metrologia, 46 

(2009), 323-331.

4. DerSimonian, R., Laird, N. Meta-analysis in clinical trials. Control. Clin. Trials, 7 

(1986), 177-188.

5. Horn, R.A., Horn, S.A., Duncan, D.B. Estimating heteroscedastic variance in linear 

models. J. Am. Stat. Assoc., 70 (1975), 380-385.

6. Sharpless, K. E. NIST Material Measurement Laboratory, Analytical Chemistry Division 

Report of Analysis 839.00-09-118.

7. Sharpless, K. E. NIST Material Measurement Laboratory, Analytical Chemistry Division 

Report of Analysis 839.00-09-118a.

8. Francini, L, Wood, L., NIST Material Measurement Laboratory, Analytical Chemistry 

Division Report of Analysis 839-01-033.

9
Figure 1. Overview of the preparation and relative matrix differences for the six cereals (A-F) 

10
Figure 2. A comparison of participant results with independently measured NIST reference 

values for Ca, Fe and Zn (mg/kg) in “Cereal A” Superground Wheat (SRM 3233 Fortified 

Breakfast Cereal). The mean value for the triplicate data are represented as circles (•) with the 

corresponding vertical lines representing the range of the values (min to max) for each individual 

laboratory. The NIST reference values are represented by dark solid lines with corresponding ±

1, 2, 3, 4, 5, 6 standard uncertainty (u) lines. The approximate 95% confidence interval (± 2u) 

about the NIST value is highlighted with a red-shaded box. 

11
Figure 2 (cont’d). 

12
Figure 3. Plots represent both the h-consistency statistics (between-laboratory) and kconsistency statistics (within-laboratory) for Zn in wheat cereals A, B and C (wheat ground and 

homogenized, wheat ground and wheat flake, respectively). The 5 % significance levels (critical 

values) are denoted by a dashed horizontal line for each plot.

13
Figure 4. Consensus plots for Zn in Cereal B: wheat ground and Cereal C: wheat flake. The 

DerSimonian-Laird (DSL) consensus means are represented by the dark solid lines with ± 1, 2, 3, 

4, 5, 6 Horn-Horn-Duncan (HHD) standard uncertainty lines. The median value for the triplicate 

data are represented as circles (•) with the corresponding lines representing the range of the 

values (min-max) for each individual laboratory. Laboratory data that were flagged with a kconsistency statistic are labeled in red.

14
Table 1. Nominal nutrient levels for the six cereals (A-F).

Nutrient

Cereal A: 

Wheat 

Ground 

(SRM 3233)

Cereal B: 

Wheat 

Ground

Cereal C: 

Wheat 

Flake

Cereal D: 

Rice

Ground

Cereal E: 

Rice

Flake

Cereal F: 

Wheat/Rice 

Crushed

Fiber (mg/g) 100 100 100 33 33 67

Protein (mg/g) 67 67 67 200 200 133

Carbohydrates 

(mg/g) 770 770 770 770 770 770

Ca (mg/kg) 36500 35000 35000 200 200 17500

Fe (mg/kg) 750 800 800 500 500 650

Zn (mg/kg) 600 700 700 20 20 350

15
Table 2. Sample preparation details for the three textured (non-ground) cereals (C, E, F).

a

Sample processing method (choices included: hammer, hand crushing, metal mechanical grinder, non-metal mechanical grinder, 

and mortar and pestle)

b

Stage when processing of the sample was performed, i.e., before or after subsampling for analysis

c All of the original sample was used for processing (i.e., grinding, crushing, etc.) into subsamples for analysis. This includes labs 

which used all material from one package or combined all material from both packages.

Lab 

Code

Sample Processing 

Methoda Whenb

Subsample 

Amount (g) 

for Analyses

Cereal C: 

Wheat 

Flake

Processed (g)

Cereal E: 

Rice

Flake

Processed (g)

Cereal F:

Wheat/Rice 

Crushed 

Processed (g)

E509 metal mechanical grinder before 10 60 60 30

E510 metal mechanical grinder after 0.2 60 30 30

E511 metal mechanical grinder before 2.2 allc allc allc

E520 metal mechanical grinder before n/a 30 30 30

E522 metal mechanical grinder before 0.5 30 40 30

E526 metal mechanical grinder before 0.5 allc allc n/a

E529 metal mechanical grinder before 3-5 30 30 30

E540 metal mechanical grinder before 0.5 allc allc n/a

E530 mortar & pestle before 0.5 5 5 5

E531 mortar & pestle after 0.25 5 5 5

E533 mortar & pestle before 1 to 2.2 n/a n/a n/a

E534 mortar & pestle before 0.5 allc allc allc

E537 mortar & pestle before 0.5 30 30 30

E538 mortar & pestle before n/a 1 1 n/a

E539 mortar & pestle before 0.25 10 10 10

E541 mortar & pestle before 1 30 30 30

E543

(NIST) mortar & pestle before 0.5 30 30 30

E502 non-metal 

mechanical grinder before 2 60 60 60

E513 hammer before 1 all all all

E515 hand before 0.5 n/a n/a n/a

16
Table 3. Mean and standard deviation of the three sample results for Ca, Fe and Zn mass fractions (mg/kg) in each of the six cereals 

(A-F).

Ca

Cereal A: 

Wheat Ground

(SRM 3233)

Cereal B: 

Wheat Ground

Cereal C: 

Wheat Flake

Cereal D:

Rice Ground

Cereal E:

Rice Flake

Cereal F: 

Wheat/Rice Crushed

Lab Code Mean SD Mean SD Mean SD Mean SD Mean SD Mean SD

E543

(NIST) 37248 336 34617 162 34502 496 282.3 10.5 279.4 4.8 21131 920

E502 37334 203 35756 262 35628 409 195.9 1.0 196.5 5.0 18259 171

E509 35100 854 34000 n/a 33800 721 196.7 11.5 206.7 5.8 16700 1212

E510 32853 648 32010 331 30737 786 195.3 7.4 232.6 43.2 16297 346

E511 36633 1115 34433 924 34833 1012 196.0 6.0 198.7 7.6 17700 600

E513 37000 1000 34000 1000 34667 1155 180.0 n/a 180.0 n/a 16667 577

E515 35319 306 33266 384 34156 699 233.3 2.3 238.3 9.9 13128 1103

E520 41728 565 38718 223 38892 654 171.3 3.5 161.3 5.5 16120 538

E522 37253 338 35070 306 34858 455 144.7 3.5 146.3 2.1 17255 304

E526 36183 58 34417 126 34783 76 183.3 5.8 190.0 n/a 16433 176

E529 38820 272 34707 353 37047 259 201.1 44.7 229.6 35.8 18417 1500

E531 38907 3290 37237 2622 37867 2137 263.3 23.1 213.3 23.1 18013 1213

E533 37533 252 35100 173 35433 723 233.3 11.5 216.7 5.8 16400 2805

E534 39700 529 37000 1308 37367 971 224.0 18.7 216.7 12.7 20667 1305

E537 40618 969 34166 782 37849 756 176.3 7.5 170.7 2.5 17364 228

E538 36602 1529 34323 1440 34974 1485 1247.9 314.3 960.3 435.3 19439 1760

E539 36700 458 34933 987 35500 608 154.3 17.0 390.0 91.3 19733 1436

E540 37133 379 34233 252 34800 346 460.0 20.0 440.0 10.0 18267 153

E541 40242 939 37811 297 39917 526 235.0 39.6 294.7 62.9 25932 5254

17
Table 3 (cont’d). Mean and standard deviation of the three sample results for Ca, Fe and Zn mass fractions (mg/kg) in each of the six 

cereals (A-F).

Fe

Cereal A: 

Wheat Ground

(SRM 3233)

Cereal B: 

Wheat Ground

Cereal C: 

Wheat Flake

Cereal D:

Rice Ground

Cereal E:

Rice Flake

Cereal F: 

Wheat/Rice Crushed

Lab Code Mean SD Mean SD Mean SD Mean SD Mean SD Mean SD

E543

(NIST) 785.3 10.1 844.7 21.4 838.5 7.3 524.0 15.7 533.7 17.2 738.3 10.1

E502 700.3 8.0 704.5 34.0 771.1 20.6 489.4 10.8 494.2 9.9 610.3 14.3

E509 720.0 26.5 786.7 25.2 820.0 20.0 453.3 5.8 426.7 30.6 603.3 15.3

E510 682.8 9.4 731.7 14.1 666.9 96.0 459.5 24.5 384.1 32.6 499.8 24.5

E511 747.0 25.1 805.7 23.0 818.3 29.4 516.3 12.4 506.0 8.0 654.0 22.0

E513 743.3 5.8 773.3 5.8 800.0 10.0 513.3 11.5 500.0 n/a 660.0 10.0

E515 805.0 14.4 899.3 11.9 908.3 15.0 472.3 13.1 487.0 35.0 622.7 9.7

E520 860.7 21.1 912.0 7.0 937.7 13.1 572.0 11.5 577.0 15.5 703.0 9.2

E522 744.0 10.8 786.7 42.7 845.0 20.9 492.3 7.6 490.3 11.0 652.7 5.9

E526 747.0 5.8 826.0 1.7 847.7 42.6 506.7 7.2 501.3 4.7 667.0 6.2

E529 n/d n/d n/d n/d n/d n/d n/d n/d n/d n/d n/d n/d

E530 374.9 35.5 697.0 64.6 438.7 50.3 461.0 41.9 331.7 30.8 346.7 69.0

E531 773.3 28.9 823.3 87.4 816.7 11.5 513.3 20.8 500.0 60.8 706.7 35.1

E533 690.0 20.0 753.3 28.9 793.3 5.8 460.0 10.0 466.7 11.5 583.3 32.1

E534 849.0 32.4 880.0 29.6 900.3 11.0 539.7 16.9 536.7 18.8 730.0 25.5

E537 716.3 7.5 782.7 19.4 746.0 14.0 517.0 8.9 513.3 4.9 627.3 16.9

E538 476.7 78.6 555.9 106.5 560.6 109.8 440.5 54.1 459.4 26.2 523.6 49.2

E539 782.0 11.4 855.0 14.5 849.7 40.1 513.3 62.3 570.7 34.8 733.7 13.5

E540 790.0 26.5 846.7 15.3 856.7 11.5 556.7 11.5 543.3 5.8 706.7 15.3

E541 706.3 7.1 779.0 7.5 800.0 2.0 508.3 13.1 501.3 11.6 685.3 7.4

18
Table 3 (cont’d). Mean and standard deviation of the three sample results for Ca, Fe and Zn mass fractions (mg/kg) in each of the six 

cereals (A-F).

Zn

Cereal A: 

Wheat Ground

(SRM 3233)

Cereal B: 

Wheat Ground

Cereal C: 

Wheat Flake

Cereal D:

Rice Ground

Cereal E:

Rice Flake

Cereal F: 

Wheat/Rice Crushed

Lab Code Mean SD Mean SD Mean SD Mean SD Mean SD Mean SD

E543 

(NIST) 625.7 1.8 694.4 4.8 695.6 6.1 21.1 1.3 21.5 0.6 448.3 18.7

E502 631.1 0.6 716.3 5.6 715.6 5.2 23.6 0.1 23.7 0.1 396.6 3.0

E509 546.7 11.5 610.0 10.0 820.0 20.0 19.3 0.6 19.3 0.6 313.3 15.3

E510 536.4 30.0 587.4 37.5 521.6 66.0 20.5 0.7 17.7 1.9 284.2 7.1

E511 609.0 18.5 675.0 17.3 688.3 22.2 20.2 0.6 20.2 0.6 357.3 4.7

E513 533.3 5.8 573.3 5.8 586.7 5.8 18.3 0.6 18.3 0.6 320.0 17.3

E515 648.3 3.2 723.3 21.0 756.0 13.1 26.0 n/a 25.3 0.6 299.0 25.5

E520 675.3 6.8 730.0 5.0 743.3 10.4 7.9 1.0 7.2 0.9 316.7 12.5

E522 620.0 6.6 687.7 6.1 699.3 10.5 19.4 n/a 19.6 0.1 357.7 3.5

E526 607.6 10.7 679.3 4.0 709.3 7.0 20.6 0.2 20.2 0.3 342.7 2.9

E529 587.7 6.1 686.0 7.0 681.7 6.5 13.5 3.3 19.0 0.1 366.3 23.6

E530 590.2 4.7 674.0 3.0 646.7 25.0 23.3 2.7 20.8 1.2 318.8 6.7

E531 676.7 41.6 793.3 40.4 683.3 55.1 20.0 n/a 20.0 n/a 426.7 20.8

E533 573.3 5.8 650.0 36.1 706.7 20.8 30.0 n/a 30.0 n/a 326.7 50.3

E534 581.7 3.5 622.3 15.9 601.0 16.4 16.9 0.9 16.7 0.6 358.0 31.0

E537 618.7 3.2 660.3 8.1 652.7 11.2 20.2 0.3 20.0 0.3 310.0 11.8

E538 577.1 22.7 619.6 17.4 627.5 28.4 20.6 0.7 20.4 1.3 391.6 33.7

E539 612.7 0.6 684.3 7.0 701.7 26.8 19.0 1.4 25.1 1.3 416.3 34.2

E540 653.3 11.5 706.7 5.8 713.3 5.8 38.3 1.5 40.7 4.9 416.7 5.8

E541 553.0 1.7 609.7 1.2 624.0 2.0 18.7 0.6 19.3 1.5 357.7 4.7

19
Table 4. Summary of overall exercise laboratory results and relative standard deviation (%RSD) 

for the triplicate measurement results for the eighteen cereal/nutrient combinations

Cereal Description N* Median†

mg/kg

Median‡

RSD

Range

RSD

Fe

A Wheat

“Superground” 19 37248 1.3 0.2 to 8.5

B Wheat Ground 18 34617 1.0 0.4 to7.0

C Wheat Flake 19 34974 2.0 0.2 to 5.6

D Rice Ground 18 196 4.3 0.5 to 25.2

E Rice Flake 17 216 3.8 1.4 to 45.3

F Wheat/Rice 

Crushed 19 17700 4.4 0.8 to 20.3

Ca

A Wheat

“Superground” 19 744 1.8 0.8 to 16.5

B Wheat Ground 19 787 2.5 0.2 to 19.2

C Wheat Flake 19 818 1.9 0.3 to 19.6

D Rice Ground 19 508 2.4 1.3 to 12.3

E Rice Flake 18 500 3.0 0.9 to 12.2

F Wheat/Rice 

Crushed 19 654 2.3 0.9 to 19.9

Zn

A Wheat

“Superground” 20 608 1.0 0.1 to 6.1

B Wheat Ground 20 677 1.0 0.2 to 6.4 

C Wheat Flake 20 692 1.7 0.3 to 12.7

D Rice Ground 16 20 3.4 0.4 to 24.4 

E Rice Flake 18 20 3.2 0.4 to 12.5

F Wheat/Rice 

Crushed 20 358 4.1 0.8 to 15.4

 *N= total number of laboratories summarized 

 †

Median of laboratory mean values and ‡median RSD of the three sample results (Table 3)

20
Table 5. Summary of consistency statistics (h and k) that exceeded the critical value at 5 % 

significance level.

Lab Code

E543(NIST)

E502

E509

E510 k

E511

E513

E515

E520

E522

E526

E529

E530 h h h h,k

E531 k k k k k k

E533

E534

E537

E538 h,k h,k h

E539 k k

E540 h h,k

E541 h,k

Cereal: A B C D E F A B C D E F A B C D E F

Element: Ca Fe Zn

h = h-consistency statistic > critical value (significantly different with respect to between-laboratory variability).

k = k-consistency statistic > critical value (significantly different with respect to within-laboratory variability).

Gray-filled segments denote non-participation.

21
Appendices for NISTIR 7927

An Interlaboratory Investigation of the Effect of Material 

Granularity and Sample Processing on Measurement 

Variability: Nutritional Elements in Cereals

22
APPENDIX A Sample Reporting Sheet

Sample preparation reporting sheet provided to participants

An exemplar sample preparation reporting sheet for Laboratory E543 (NIST) results:

Cereal A Cereal B Cereal C Cereal D Cereal E Cereal F

Mass taken from original package (≈ g) 0 0 0 0 0 0

Did you grind/crush the material? Select (Y/N): Select (Y/N): Select (Y/N): Select (Y/N): Select (Y/N): Select (Y/N):

If 'Yes', When? (Select from List): (Select from List): (Select from List): (Select from List): (Select from List): (Select from List):

If 'Yes', How? (Select from List): (Select from List): (Select from List): (Select from List): (Select from List): (Select from List):

Did you grind/crush again? Select (Y/N): Select (Y/N): Select (Y/N): Select (Y/N): Select (Y/N): Select (Y/N):

If 'Yes', When? (Select from List): (Select from List): (Select from List): (Select from List): (Select from List): (Select from List):

If 'Yes', How? (Select from List): (Select from List): (Select from List): (Select from List): (Select from List): (Select from List):

Mass of Subsamples (approx. avg of 3) (≈ g) 0 0 0 0 0 0

 Same for Fe

 Same for Zn

 Did you further process the material? If 'Yes', then please continue. If 'No', then please enter only the Mass of Subsamples.

 Please check boxes if you used the same processing to prepare subsamples for the other elements. If needed, separate spreadsheets for Fe, Zn are available.

Elements in Cereals (Ca) - Sample Preparation Information

Additional information:

Primary 

Processing

Secondary 

Processing

Cereal A Cereal B Cereal C Cereal D Cereal E Cereal F

Mass taken from original package (≈ g) 0 0 30 0 30 30

Did you grind/crush the material? No No Yes No Yes Yes 

If 'Yes', When? (Select from List): (Select from List): Before replicates (processed 

together) (Select from List): Before replicates (processed together)

Before replicates (processed 

together)

If 'Yes', How? (Select from List): (Select from List): Manual-type Mortar & Pestle (Select from List): Manual-type Mortar & Pestle Manual-type Mortar & Pestle

Did you grind/crush again? Select (Y/N): Select (Y/N): No Select (Y/N): No No

If 'Yes', When? (Select from List): (Select from List): (Select from List): (Select from List): (Select from List): (Select from List):

If 'Yes', How? (Select from List): (Select from List): (Select from List): (Select from List): (Select from List): (Select from List):

Mass of Subsamples (approx. avg of 3) (≈ g) 0 0 0.5 0 0.5 0.5

 Same for Ca

 Same for Zn

Elements in Cereals (Fe) - Sample Preparation Information

 Please check boxes if you used the same processing to prepare subsamples for the other elements. If needed, separate spreadsheets for Ca, Zn are available.

Additional information:

Primary 

Processing

Secondary 

Processing Did you further process the material? If 'Yes', then please continue. If 'No', then please enter only the Mass of Subsamples.

23
APPENDIX B Normal Probability Distribution Plots

The following 18 plots are normal probability distributions for the individual mass fraction (or concentration) data for Ca, Fe and Zn 

(mg/kg) in the six materials (Cereals A-F). Probability plot correlation coefficients (PPCC) are provided with the 5 % critical values 

(CV). 

24
25
26
27
APPENDIX C h-Consistency and k-Consistency Statistics Plots

The following 6 sets of plots represent both the h-consistency statistics (between-laboratory) and kconsistency statistics (within-laboratory) for Ca, Fe and Zn in Wheat (cereals A, B and C) and Ca, 

Fe and Zn in Rice (cereals D, E and F). The 5 % significance levels (critical values) are denoted by 

a dashed horizontal line for each plot. Also provided with each set of h- and k-plots are tabulated 

results from the corresponding interlaboratory analysis that includes the important determined 

E691parameters (d, h, k). 

28
29
Ca

Initial Preparation of Test Result Data for Material: 1 (Cereal A)

Laboratory

Number

Cell

Mean

Cell

SD d h k

1 37247.67 335.50 -408.30 -0.20 0.33

2 37334.00 203.27 -321.96 -0.15 0.20

10 32853.33 647.87 -4802.63 -2.30 0.63

11 36633.33 1115.05 -1022.63 -0.49 1.08

13 37000.00 1000.00 -655.96 -0.31 0.97

15 35319.00 305.78 -2336.96 -1.12 0.30

20 41728.33 565.23 4072.37 1.95 0.55

22 37252.67 337.59 -403.30 -0.19 0.33

26 36183.33 57.74 -1472.63 -0.71 0.06

29 38820.00 272.21 1164.04 0.56 0.26

31 38906.67 3289.82 1250.70 0.60 3.19

33 37533.33 251.66 -122.63 -0.06 0.24

34 39700.00 529.15 2044.04 0.98 0.51

37 40618.33 969.25 2962.37 1.42 0.94

38 36601.67 1529.35 -1054.30 -0.51 1.48

39 36700.00 458.26 -955.96 -0.46 0.44

40 37133.33 378.59 -522.63 -0.25 0.37

41 40242.33 939.26 2586.37 1.24 0.91

Average of cell averages = 37655.96296 

Standard Deviation of cell averages = 2087.27832 

Repeatability Standard Deviation = 1030.14276 

Reproducibility Standard Deviation = 2250.37631 

Ca

Initial Preparation of Test Result Data for Material: 2 (Cereal B)

Laboratory

Number

Cell

Mean

Cell

SD d h k

1 34617.00 161.61 -482.80 -0.29 0.18

2 35755.33 262.15 655.54 0.40 0.29

10 32010.00 330.61 -3089.80 -1.86 0.36

11 34433.33 923.76 -666.46 -0.40 1.01

13 34000.00 1000.00 -1099.80 -0.66 1.10

15 33265.67 383.67 -1834.13 -1.11 0.42

20 38718.33 223.35 3618.54 2.18 0.25

22 35069.67 305.90 -30.13 -0.02 0.34

26 34416.67 125.83 -683.13 -0.41 0.14

29 34706.67 353.03 -393.13 -0.24 0.39

31 37236.67 2622.33 2136.87 1.29 2.88

33 35100.00 173.21 0.20 0.00 0.19

34 37000.00 1307.67 1900.20 1.15 1.44

37 34166.00 781.88 -933.80 -0.56 0.86

38 34323.00 1440.40 -776.80 -0.47 1.58

39 34933.33 986.58 -166.46 -0.10 1.08

40 34233.33 251.66 -866.46 -0.52 0.28

41 37811.33 297.38 2711.54 1.64 0.33

Average of cell averages = 35099.79630 

Standard Deviation of cell averages = 1657.89789 

Repeatability Standard Deviation = 910.32472 

Reproducibility Standard Deviation = 1816.88914 

Ca

Initial Preparation of Test Result Data for Material: 3 (Cereal C)

Laboratory

Number

Cell

Mean

Cell

SD d h k

1 34501.67 495.66 -1265.54 -0.60 0.56

2 35628.33 409.16 -138.87 -0.07 0.46

10 30736.67 786.21 -5030.54 -2.39 0.89

11 34833.33 1011.60 -933.87 -0.44 1.14

13 34666.67 1154.70 -1100.54 -0.52 1.30

15 34156.00 698.67 -1611.20 -0.77 0.79

20 38892.33 654.30 3125.13 1.49 0.74

22 34857.67 454.57 -909.54 -0.43 0.51

26 34783.33 76.38 -983.87 -0.47 0.09

29 37046.67 259.29 1279.46 0.61 0.29

31 37866.67 2137.32 2099.46 1.00 2.41

33 35433.33 723.42 -333.87 -0.16 0.82

34 37366.67 971.25 1599.46 0.76 1.10

30
37 37849.33 756.08 2082.13 0.99 0.85

38 34973.67 1484.55 -793.54 -0.38 1.67

39 35500.00 608.28 -267.20 -0.13 0.69

40 34800.00 346.41 -967.20 -0.46 0.39

41 39917.33 526.34 4150.13 1.97 0.59

Average of cell averages = 35767.20370 

Standard Deviation of cell averages = 2101.51320 

Repeatability Standard Deviation = 886.98024 

Reproducibility Standard Deviation = 2222.80162 

Ca-h

Material

Laboratory 1 2 3

1 -0.20 -0.29 -0.60

2 -0.15 0.40 -0.07

10 -2.30 -1.86 -2.39

11 -0.49 -0.40 -0.44

13 -0.31 -0.66 -0.52

15 -1.12 -1.11 -0.77

20 1.95 2.18 1.49

22 -0.19 -0.02 -0.43

26 -0.71 -0.41 -0.47

29 0.56 -0.24 0.61

31 0.60 1.29 1.00

33 -0.06 0.00 -0.16

34 0.98 1.15 0.76

37 1.42 -0.56 0.99

38 -0.51 -0.47 -0.38

39 -0.46 -0.10 -0.13

40 -0.25 -0.52 -0.46

41 1.24 1.64 1.97

Critical Value = 2.53000 

Ca-k

Material

Laboratory 1 2 3

1 0.33 0.18 0.56

2 0.20 0.29 0.46

10 0.63 0.36 0.89

11 1.08 1.01 1.14

13 0.97 1.10 1.30

15 0.30 0.42 0.79

20 0.55 0.25 0.74

22 0.33 0.34 0.51

26 0.06 0.14 0.09

29 0.26 0.39 0.29

31 3.19 2.88 2.41

33 0.24 0.19 0.82

34 0.51 1.44 1.10

37 0.94 0.86 0.85

38 1.48 1.58 1.67

39 0.44 1.08 0.69

40 0.37 0.28 0.39

41 0.91 0.33 0.59

Critical Value = 2.20000 

Ca-Precision Statistics

Material Xbar sx sr sR r R

1 37655.96 2087.28 1030.14 2250.38 2884.40 6301.05

2 35099.80 1657.90 910.32 1816.89 2548.91 5087.29

3 35767.20 2101.51 886.98 2222.80 2483.54 6223.84

31
32
Fe

Initial Preparation of Test Result Data for Material: 1 (Cereal A)

Laboratory

Number

Cell

Mean

Cell

SD d h k

1 785.33 10.12 64.60 0.56 0.39

2 700.27 8.01 -20.47 -0.18 0.31

9 720.00 26.46 -0.74 -0.01 1.01

10 682.77 9.41 -37.97 -0.33 0.36

11 747.00 25.06 26.26 0.23 0.96

13 743.33 5.77 22.60 0.19 0.22

15 805.00 14.42 84.26 0.72 0.55

20 860.67 21.13 139.93 1.20 0.81

22 744.00 10.82 23.26 0.20 0.41

26 747.03 5.84 26.30 0.23 0.22

30 374.93 35.47 -345.80 -2.97 1.35

31 773.33 28.87 52.60 0.45 1.10

33 690.00 20.00 -30.74 -0.26 0.76

34 849.00 32.45 128.26 1.10 1.24

37 716.33 7.51 -4.40 -0.04 0.29

38 476.67 78.62 -244.07 -2.10 3.00

39 782.00 11.36 61.26 0.53 0.43

40 790.00 26.46 69.26 0.60 1.01

41 706.33 7.09 -14.40 -0.12 0.27

Average of cell averages = 720.73684 

Standard Deviation of cell averages = 116.24638 

Repeatability Standard Deviation = 26.24053 

Reproducibility Standard Deviation = 118.20434 

Fe

Initial Preparation of Test Result Data for Material: 2 (Cereal B)

Laboratory

Number

Cell

Mean

Cell

SD d h k

1 844.67 21.36 52.91 0.64 0.53

2 704.50 34.04 -87.26 -1.05 0.85

9 786.67 25.17 -5.09 -0.06 0.63

10 731.67 14.06 -60.09 -0.72 0.35

11 805.67 23.03 13.91 0.17 0.57

13 773.33 5.77 -18.43 -0.22 0.14

15 899.33 11.93 107.57 1.30 0.30

20 912.00 7.00 120.24 1.45 0.17

22 786.67 42.74 -5.09 -0.06 1.06

26 826.00 1.73 34.24 0.41 0.04

30 697.00 64.65 -94.76 -1.14 1.61

31 823.33 87.37 31.57 0.38 2.17

33 753.33 28.87 -38.43 -0.46 0.72

34 880.00 29.61 88.24 1.06 0.74

37 782.67 19.43 -9.09 -0.11 0.48

38 555.93 106.52 -235.83 -2.84 2.65

39 855.00 14.53 63.24 0.76 0.36

40 846.67 15.28 54.91 0.66 0.38

41 779.00 7.55 -12.76 -0.15 0.19

Average of cell averages = 791.75965 

Standard Deviation of cell averages = 82.97406 

Repeatability Standard Deviation = 40.24783 

Reproducibility Standard Deviation = 89.24472 

Fe

Initial Preparation of Test Result Data for Material: 3 (Cereal C)

Laboratory

Number

Cell

Mean

Cell

SD d h k

1 838.53 7.29 48.25 0.40 0.18

2 771.13 20.57 -19.15 -0.16 0.51

9 820.00 20.00 29.71 0.25 0.50

10 666.90 96.01 -123.39 -1.03 2.40

11 818.33 29.37 28.05 0.23 0.73

13 800.00 10.00 9.71 0.08 0.25

15 908.33 15.04 118.05 0.98 0.38

20 937.67 13.05 147.38 1.22 0.33

22 845.00 20.88 54.71 0.45 0.52

26 847.67 42.57 57.38 0.48 1.06

30 438.67 50.29 -351.62 -2.92 1.25

33
31 816.67 11.55 26.38 0.22 0.29

33 793.33 5.77 3.05 0.03 0.14

34 900.33 11.02 110.05 0.91 0.27

37 746.00 14.00 -44.29 -0.37 0.35

38 560.57 109.84 -229.72 -1.91 2.74

39 849.67 40.08 59.38 0.49 1.00

40 856.67 11.55 66.38 0.55 0.29

41 800.00 2.00 9.71 0.08 0.05

Average of cell averages = 790.28772 

Standard Deviation of cell averages = 120.37809 

Repeatability Standard Deviation = 40.08184 

Reproducibility Standard Deviation = 124.74742 

Fe-h

Material

Laboratory 1 2 3

1 0.56 0.64 0.40

2 -0.18 -1.05 -0.16

9 -0.01 -0.06 0.25

10 -0.33 -0.72 -1.03

11 0.23 0.17 0.23

13 0.19 -0.22 0.08

15 0.72 1.30 0.98

20 1.20 1.45 1.22

22 0.20 -0.06 0.45

26 0.23 0.41 0.48

30 -2.97 -1.14 -2.92

31 0.45 0.38 0.22

33 -0.26 -0.46 0.03

34 1.10 1.06 0.91

37 -0.04 -0.11 -0.37

38 -2.10 -2.84 -1.91

39 0.53 0.76 0.49

40 0.60 0.66 0.55

41 -0.12 -0.15 0.08

Critical Value = 2.54000 

Fe-k

Material

Laboratory 1 2 3

1 0.39 0.53 0.18

2 0.31 0.85 0.51

9 1.01 0.63 0.50

10 0.36 0.35 2.40

11 0.96 0.57 0.73

13 0.22 0.14 0.25

15 0.55 0.30 0.38

20 0.81 0.17 0.33

22 0.41 1.06 0.52

26 0.22 0.04 1.06

30 1.35 1.61 1.25

31 1.10 2.17 0.29

33 0.76 0.72 0.14

34 1.24 0.74 0.27

37 0.29 0.48 0.35

38 3.00 2.65 2.74

39 0.43 0.36 1.00

40 1.01 0.38 0.29

41 0.27 0.19 0.05

Critical Value = 2.20000 

Fe-Precision Statistics

Material Xbar sx sr sR r R

1 720.74 116.25 26.24 118.20 73.47 330.97

2 791.76 82.97 40.25 89.24 112.69 249.89

3 790.29 120.38 40.08 124.75 112.23 349.29

34
35
Zn

Initial Preparation of Test Result Data for Material: 1 (Cereal A)

Laboratory

Number

Cell

Mean

Cell

SD d h k

1 625.67 1.82 22.78 0.53 0.13

2 631.07 0.65 28.18 0.66 0.05

9 546.67 11.55 -56.22 -1.32 0.80

10 536.40 30.04 -66.49 -1.56 2.09

11 609.00 18.52 6.11 0.14 1.29

13 533.33 5.77 -69.56 -1.63 0.40

15 648.33 3.21 45.44 1.06 0.22

20 675.33 6.81 72.44 1.70 0.47

22 620.00 6.56 17.11 0.40 0.46

26 607.63 10.72 4.74 0.11 0.75

29 587.67 6.11 -15.22 -0.36 0.43

30 590.20 4.70 -12.69 -0.30 0.33

31 676.67 41.63 73.78 1.73 2.90

33 573.33 5.77 -29.56 -0.69 0.40

34 581.67 3.51 -21.22 -0.50 0.24

37 618.67 3.21 15.78 0.37 0.22

38 577.13 22.63 -25.76 -0.60 1.58

39 612.67 0.58 9.78 0.23 0.04

40 653.33 11.55 50.44 1.18 0.80

41 553.00 1.73 -49.89 -1.17 0.12

Average of cell averages = 602.88833 

Standard Deviation of cell averages = 42.67365 

Repeatability Standard Deviation = 14.36604 

Reproducibility Standard Deviation = 44.25641 

Zn

Initial Preparation of Test Result Data for Material: 2 (Cereal B)

Laboratory

Number

Cell

Mean

Cell

SD d h k

1 694.40 4.83 25.25 0.47 0.28

2 716.23 5.56 47.09 0.87 0.32

9 610.00 10.00 -59.14 -1.10 0.57

10 587.40 37.51 -81.75 -1.51 2.15

11 675.00 17.35 5.86 0.11 0.99

13 573.33 5.77 -95.81 -1.78 0.33

15 723.33 20.98 54.19 1.00 1.20

20 730.00 5.00 60.86 1.13 0.29

22 687.67 6.11 18.52 0.34 0.35

26 679.33 4.04 10.19 0.19 0.23

29 686.00 7.00 16.86 0.31 0.40

30 674.00 3.00 4.86 0.09 0.17

31 793.33 40.41 124.19 2.30 2.31

33 650.00 36.06 -19.14 -0.35 2.06

34 622.33 15.95 -46.81 -0.87 0.91

37 660.33 8.08 -8.81 -0.16 0.46

38 619.53 17.36 -49.61 -0.92 0.99

39 684.33 7.02 15.19 0.28 0.40

40 706.67 5.77 37.52 0.70 0.33

41 609.67 1.15 -59.48 -1.10 0.07

Average of cell averages = 669.14500 

Standard Deviation of cell averages = 53.96865 

Repeatability Standard Deviation = 17.47966 

Reproducibility Standard Deviation = 55.82389 

Zn

Initial Preparation of Test Result Data for Material: 3 (Cereal C)

Laboratory

Number

Cell

Mean

Cell

SD d h k

1 695.57 6.12 16.85 0.26 0.25

2 715.63 5.18 36.92 0.56 0.21

9 820.00 20.00 141.28 2.15 0.82

10 521.63 65.97 -157.08 -2.39 2.71

11 688.33 22.23 9.62 0.15 0.91

13 586.67 5.77 -92.05 -1.40 0.24

15 756.00 13.11 77.28 1.17 0.54

20 743.33 10.41 64.62 0.98 0.43

22 699.33 10.50 20.62 0.31 0.43

36
26 709.33 7.02 30.62 0.47 0.29

29 681.67 6.51 2.95 0.04 0.27

30 646.67 25.01 -32.05 -0.49 1.03

31 683.33 55.08 4.62 0.07 2.26

33 706.67 20.82 27.95 0.42 0.85

34 601.00 16.37 -77.72 -1.18 0.67

37 652.67 11.24 -26.05 -0.40 0.46

38 627.50 28.46 -51.22 -0.78 1.17

39 701.67 26.76 22.95 0.35 1.10

40 713.33 5.77 34.62 0.53 0.24

41 624.00 2.00 -54.72 -0.83 0.08

Average of cell averages = 678.71667 

Standard Deviation of cell averages = 65.79795 

Repeatability Standard Deviation = 24.36753 

Reproducibility Standard Deviation = 68.74024 

Zn-h

Material

Laboratory 1 2 3

1 0.53 0.47 0.26

2 0.66 0.87 0.56

9 -1.32 -1.10 2.15

10 -1.56 -1.51 -2.39

11 0.14 0.11 0.15

13 -1.63 -1.78 -1.40

15 1.06 1.00 1.17

20 1.70 1.13 0.98

22 0.40 0.34 0.31

26 0.11 0.19 0.47

29 -0.36 0.31 0.04

30 -0.30 0.09 -0.49

31 1.73 2.30 0.07

33 -0.69 -0.35 0.42

34 -0.50 -0.87 -1.18

37 0.37 -0.16 -0.40

38 -0.60 -0.92 -0.78

39 0.23 0.28 0.35

40 1.18 0.70 0.53

41 -1.17 -1.10 -0.83

Critical Value = 2.56000 

Zn-k

Material

Laboratory 1 2 3

1 0.13 0.28 0.25

2 0.05 0.32 0.21

9 0.80 0.57 0.82

10 2.09 2.15 2.71

11 1.29 0.99 0.91

13 0.40 0.33 0.24

15 0.22 1.20 0.54

20 0.47 0.29 0.43

22 0.46 0.35 0.43

26 0.75 0.23 0.29

29 0.43 0.40 0.27

30 0.33 0.17 1.03

31 2.90 2.31 2.26

33 0.40 2.06 0.85

34 0.24 0.91 0.67

37 0.22 0.46 0.46

38 1.58 0.99 1.17

39 0.04 0.40 1.10

40 0.80 0.33 0.24

41 0.12 0.07 0.08

Critical Value = 2.21000 

Zn-Precision Statistics

Material Xbar sx sr sR r R

1 602.89 42.67 14.37 44.26 40.22 123.92

2 669.14 53.97 17.48 55.82 48.94 156.31

3 678.72 65.80 24.37 68.74 68.23 192.47

37
38
Ca

Initial Preparation of Test Result Data for Material: 4 (Cereal D)

Laboratory

Number

Cell

Mean

Cell

SD d h k

1 282.33 10.50 -0.69 0.00 0.13

2 196.00 1.00 -87.02 -0.34 0.01

9 196.67 11.55 -86.35 -0.33 0.15

10 195.33 7.64 -87.69 -0.34 0.10

11 196.00 6.00 -87.02 -0.34 0.08

15 233.33 2.31 -49.69 -0.19 0.03

20 171.33 3.51 -111.69 -0.43 0.04

22 144.67 3.51 -138.35 -0.53 0.04

29 201.33 44.60 -81.69 -0.32 0.57

31 263.33 23.09 -19.69 -0.08 0.29

33 233.33 11.55 -49.69 -0.19 0.15

34 224.00 18.68 -59.02 -0.23 0.24

37 176.33 7.51 -106.69 -0.41 0.10

38 1248.00 314.45 964.98 3.73 4.01

39 154.33 17.04 -128.69 -0.50 0.22

40 460.00 20.00 176.98 0.68 0.26

41 235.00 39.59 -48.02 -0.19 0.50

Average of cell averages = 283.01961 

Standard Deviation of cell averages = 258.61948 

Repeatability Standard Deviation = 78.42894 

Reproducibility Standard Deviation = 266.42966 

Ca

Initial Preparation of Test Result Data for Material: 5 (Cereal E)

Laboratory

Number

Cell

Mean

Cell

SD d h k

1 279.67 4.51 -2.25 -0.01 0.04

2 196.67 5.03 -85.25 -0.45 0.05

9 206.67 5.77 -75.25 -0.39 0.05

10 232.67 43.02 -49.25 -0.26 0.39

11 198.67 7.57 -83.25 -0.44 0.07

15 238.33 9.87 -43.59 -0.23 0.09

20 161.33 5.51 -120.59 -0.63 0.05

22 146.33 2.08 -135.59 -0.71 0.02

29 229.67 35.92 -52.25 -0.27 0.33

31 213.33 23.09 -68.59 -0.36 0.21

33 216.67 5.77 -65.25 -0.34 0.05

34 216.67 12.66 -65.25 -0.34 0.12

37 170.67 2.52 -111.25 -0.58 0.02

38 960.67 435.18 678.75 3.56 3.95

39 390.00 91.33 108.08 0.57 0.83

40 440.00 10.00 158.08 0.83 0.09

41 294.67 62.95 12.75 0.07 0.57

Average of cell averages = 281.92157 

Standard Deviation of cell averages = 190.88215 

Repeatability Standard Deviation = 110.06041 

Reproducibility Standard Deviation = 210.97754 

Ca

Initial Preparation of Test Result Data for Material: 6 (Cereal F)

Laboratory

Number

Cell

Mean

Cell

SD d h k

1 21131.00 920.23 2847.37 1.04 0.53

2 18259.33 170.39 -24.29 -0.01 0.10

9 16700.00 1212.44 -1583.63 -0.58 0.70

10 16296.67 346.46 -1986.96 -0.73 0.20

11 17700.00 600.00 -583.63 -0.21 0.35

15 13128.33 1103.07 -5155.29 -1.89 0.64

20 16120.33 538.26 -2163.29 -0.79 0.31

22 17254.67 303.90 -1028.96 -0.38 0.18

29 18416.67 1500.28 133.04 0.05 0.87

31 18013.33 1213.44 -270.29 -0.10 0.70

33 16400.00 2805.35 -1883.63 -0.69 1.63

34 20666.67 1305.12 2383.04 0.87 0.76

37 17364.00 227.53 -919.63 -0.34 0.13

39
38 19438.67 1759.52 1155.04 0.42 1.02

39 19733.33 1436.43 1449.71 0.53 0.83

40 18266.67 152.75 -16.96 -0.01 0.09

41 25932.00 5254.32 7648.37 2.80 3.05

Average of cell averages = 18283.62745 

Standard Deviation of cell averages = 2730.81197 

Repeatability Standard Deviation = 1724.62449 

Reproducibility Standard Deviation = 3072.49417 

Ca-h

Material

Laboratory 1 2 3

1 0.00 -0.01 1.04

2 -0.34 -0.45 -0.01

9 -0.33 -0.39 -0.58

10 -0.34 -0.26 -0.73

11 -0.34 -0.44 -0.21

15 -0.19 -0.23 -1.89

20 -0.43 -0.63 -0.79

22 -0.53 -0.71 -0.38

29 -0.32 -0.27 0.05

31 -0.08 -0.36 -0.10

33 -0.19 -0.34 -0.69

34 -0.23 -0.34 0.87

37 -0.41 -0.58 -0.34

38 3.73 3.56 0.42

39 -0.50 0.57 0.53

40 0.68 0.83 -0.01

41 -0.19 0.07 2.80

Critical Value = 2.51000 

Ca-k

Material

Laboratory 1 2 3

1 0.13 0.04 0.53

2 0.01 0.05 0.10

9 0.15 0.05 0.70

10 0.10 0.39 0.20

11 0.08 0.07 0.35

15 0.03 0.09 0.64

20 0.04 0.05 0.31

22 0.04 0.02 0.18

29 0.57 0.33 0.87

31 0.29 0.21 0.70

33 0.15 0.05 1.63

34 0.24 0.12 0.76

37 0.10 0.02 0.13

38 4.01 3.95 1.02

39 0.22 0.83 0.83

40 0.26 0.09 0.09

41 0.50 0.57 3.05

Critical Value = 2.19000 

Ca-Precision Statistics

Material Xbar sx sr sR r R

4 283.02 258.62 78.43 266.43 219.60 746.00

5 281.92 190.88 110.06 210.98 308.17 590.74

6 18283.63 2730.81 1724.62 3072.49 4828.95 8602.98

40
41
Fe

Initial Preparation of Test Result Data for Material: 4 (Cereal D)

Laboratory

Number

Cell

Mean

Cell

SD d h k

1 524.00 15.72 24.24 0.66 0.63

2 489.40 10.78 -10.36 -0.28 0.43

9 453.33 5.77 -46.43 -1.26 0.23

10 459.50 24.55 -40.26 -1.09 0.98

11 516.33 12.42 16.57 0.45 0.50

15 472.33 13.05 -27.43 -0.75 0.52

20 572.00 11.53 72.24 1.96 0.46

22 492.33 7.57 -7.43 -0.20 0.30

26 506.67 7.23 6.91 0.19 0.29

30 461.00 41.90 -38.76 -1.05 1.67

31 513.33 20.82 13.57 0.37 0.83

33 460.00 10.00 -39.76 -1.08 0.40

34 539.67 16.92 39.91 1.09 0.67

37 517.00 8.89 17.24 0.47 0.35

38 440.47 54.12 -59.29 -1.61 2.16

39 513.33 62.27 13.57 0.37 2.48

40 556.67 11.55 56.91 1.55 0.46

41 508.33 13.05 8.57 0.23 0.52

Average of cell averages = 499.76111 

Standard Deviation of cell averages = 36.77321 

Repeatability Standard Deviation = 25.08917 

Reproducibility Standard Deviation = 42.09410 

Fe

Initial Preparation of Test Result Data for Material: 5 (Cereal E)

Laboratory

Number

Cell

Mean

Cell

SD d h k

1 533.67 17.21 43.49 0.71 0.69

2 494.17 9.92 3.99 0.06 0.40

9 426.67 30.55 -63.51 -1.04 1.22

10 384.07 32.58 -106.11 -1.73 1.30

11 506.00 8.00 15.82 0.26 0.32

15 487.00 35.00 -3.18 -0.05 1.40

20 577.00 15.52 86.82 1.42 0.62

22 490.33 10.97 0.15 0.00 0.44

26 501.33 4.73 11.15 0.18 0.19

30 331.67 30.83 -158.51 -2.58 1.23

31 500.00 60.83 9.82 0.16 2.43

33 466.67 11.55 -23.51 -0.38 0.46

34 536.67 18.77 46.49 0.76 0.75

37 513.33 4.93 23.15 0.38 0.20

38 459.37 26.21 -30.81 -0.50 1.05

39 570.67 34.78 80.49 1.31 1.39

40 543.33 5.77 53.15 0.87 0.23

41 501.33 11.59 11.15 0.18 0.46

Average of cell averages = 490.18148 

Standard Deviation of cell averages = 61.34454 

Repeatability Standard Deviation = 25.04024 

Reproducibility Standard Deviation = 64.66190 

Fe

Initial Preparation of Test Result Data for Material: 6 (Cereal F)

Laboratory

Number

Cell

Mean

Cell

SD d h k

1 738.33 10.07 105.31 1.06 0.38

2 610.33 14.26 -22.69 -0.23 0.54

9 603.33 15.28 -29.69 -0.30 0.57

10 499.77 24.54 -133.26 -1.35 0.92

11 654.00 22.00 20.98 0.21 0.83

15 622.67 9.71 -10.36 -0.10 0.37

20 703.00 9.17 69.98 0.71 0.34

22 652.67 5.86 19.64 0.20 0.22

26 667.00 6.24 33.98 0.34 0.23

30 346.67 69.04 -286.36 -2.89 2.59

31 706.67 35.12 73.64 0.74 1.32

33 583.33 32.15 -49.69 -0.50 1.21

34 730.00 25.51 96.98 0.98 0.96

42
37 627.33 16.92 -5.69 -0.06 0.64

38 523.67 49.25 -109.36 -1.10 1.85

39 733.67 13.50 100.64 1.02 0.51

40 706.67 15.28 73.64 0.74 0.57

41 685.33 7.37 52.31 0.53 0.28

Average of cell averages = 633.02407 

Standard Deviation of cell averages = 99.05590 

Repeatability Standard Deviation = 26.60641 

Reproducibility Standard Deviation = 101.41009 

Fe-h

Material

Laboratory 1 2 3

1 0.66 0.71 1.06

2 -0.28 0.06 -0.23

9 -1.26 -1.04 -0.30

10 -1.09 -1.73 -1.35

11 0.45 0.26 0.21

15 -0.75 -0.05 -0.10

20 1.96 1.42 0.71

22 -0.20 0.00 0.20

26 0.19 0.18 0.34

30 -1.05 -2.58 -2.89

31 0.37 0.16 0.74

33 -1.08 -0.38 -0.50

34 1.09 0.76 0.98

37 0.47 0.38 -0.06

38 -1.61 -0.50 -1.10

39 0.37 1.31 1.02

40 1.55 0.87 0.74

41 0.23 0.18 0.53

Critical Value = 2.53000 

Fe-k

Material

Laboratory 1 2 3

1 0.63 0.69 0.38

2 0.43 0.40 0.54

9 0.23 1.22 0.57

10 0.98 1.30 0.92

11 0.50 0.32 0.83

15 0.52 1.40 0.37

20 0.46 0.62 0.34

22 0.30 0.44 0.22

26 0.29 0.19 0.23

30 1.67 1.23 2.59

31 0.83 2.43 1.32

33 0.40 0.46 1.21

34 0.67 0.75 0.96

37 0.35 0.20 0.64

38 2.16 1.05 1.85

39 2.48 1.39 0.51

40 0.46 0.23 0.57

41 0.52 0.46 0.28

Critical Value = 2.20000 

Fe-Precision Statistics

Material Xbar sx sr sR r R

4 499.76 36.77 25.09 42.09 70.25 117.86

5 490.18 61.34 25.04 64.66 70.11 181.05

6 633.02 99.06 26.61 101.41 74.50 283.95

43
44
Zn

Initial Preparation of Test Result Data for Material: 4 (Cereal D)

Laboratory

Number

Cell

Mean

Cell

SD d h k

1 21.10 1.31 0.97 0.16 0.98

2 23.57 0.12 3.44 0.56 0.09

9 19.33 0.58 -0.80 -0.13 0.43

10 20.47 0.70 0.34 0.05 0.53

11 20.20 0.62 0.07 0.01 0.47

13 18.33 0.58 -1.80 -0.29 0.43

20 7.97 0.95 -12.16 -1.98 0.71

26 20.57 0.15 0.44 0.07 0.11

29 13.50 3.32 -6.63 -1.08 2.49

30 23.33 2.66 3.20 0.52 2.00

34 16.90 0.85 -3.23 -0.53 0.64

37 20.20 0.26 0.07 0.01 0.20

38 20.63 0.71 0.50 0.08 0.53

39 19.00 1.44 -1.13 -0.18 1.08

40 38.33 1.53 18.20 2.97 1.15

41 18.67 0.58 -1.46 -0.24 0.43

Average of cell averages = 20.13125 

Standard Deviation of cell averages = 6.13492 

Repeatability Standard Deviation = 1.32979 

Reproducibility Standard Deviation = 6.23026 

Zn

Initial Preparation of Test Result Data for Material: 5 (Cereal E)

Laboratory

Number

Cell

Mean

Cell

SD d h k

1 21.47 0.57 0.83 0.13 0.37

2 23.67 0.06 3.03 0.46 0.04

9 19.33 0.58 -1.30 -0.20 0.38

10 17.67 1.88 -2.97 -0.45 1.23

11 20.23 0.55 -0.40 -0.06 0.36

13 18.33 0.58 -2.30 -0.35 0.38

20 7.20 0.92 -13.44 -2.04 0.60

26 20.20 0.26 -0.44 -0.07 0.17

29 19.00 0.10 -1.64 -0.25 0.07

30 20.83 1.21 0.20 0.03 0.79

34 16.67 0.58 -3.97 -0.60 0.38

37 20.03 0.32 -0.60 -0.09 0.21

38 20.43 1.27 -0.20 -0.03 0.83

39 25.13 1.33 4.50 0.68 0.87

40 40.67 4.93 20.03 3.05 3.21

41 19.33 1.53 -1.30 -0.20 1.00

Average of cell averages = 20.63750 

Standard Deviation of cell averages = 6.57569 

Repeatability Standard Deviation = 1.53508 

Reproducibility Standard Deviation = 6.69408 

Zn

Initial Preparation of Test Result Data for Material: 6 (Cereal F)

Laboratory

Number

Cell

Mean

Cell

SD d h k

1 448.33 18.72 91.17 1.96 1.04

2 396.67 2.99 39.50 0.85 0.17

9 313.33 15.28 -43.83 -0.94 0.85

10 284.17 7.12 -73.00 -1.57 0.40

11 357.33 4.73 0.17 0.00 0.26

13 320.00 17.32 -37.16 -0.80 0.96

20 316.67 12.50 -40.50 -0.87 0.69

26 342.67 2.89 -14.50 -0.31 0.16

29 366.33 23.63 9.17 0.20 1.31

30 318.80 6.70 -38.36 -0.83 0.37

34 358.00 31.05 0.84 0.02 1.72

37 310.00 11.79 -47.16 -1.02 0.65

38 391.67 33.68 34.50 0.74 1.87

39 416.33 34.20 59.17 1.27 1.90

40 416.67 5.77 59.50 1.28 0.32

41 357.67 4.73 0.50 0.01 0.26

45
Average of cell averages = 357.16458 

Standard Deviation of cell averages = 46.45193 

Repeatability Standard Deviation = 18.02046 

Reproducibility Standard Deviation = 48.72651 

Zn-h

Material

Laboratory 1 2 3

1 0.16 0.13 1.96

2 0.56 0.46 0.85

9 -0.13 -0.20 -0.94

10 0.05 -0.45 -1.57

11 0.01 -0.06 0.00

13 -0.29 -0.35 -0.80

20 -1.98 -2.04 -0.87

26 0.07 -0.07 -0.31

29 -1.08 -0.25 0.20

30 0.52 0.03 -0.83

34 -0.53 -0.60 0.02

37 0.01 -0.09 -1.02

38 0.08 -0.03 0.74

39 -0.18 0.68 1.27

40 2.97 3.05 1.28

41 -0.24 -0.20 0.01

Critical Value = 2.49000 

Zn-k

Material

Laboratory 1 2 3

1 0.98 0.37 1.04

2 0.09 0.04 0.17

9 0.43 0.38 0.85

10 0.53 1.23 0.40

11 0.47 0.36 0.26

13 0.43 0.38 0.96

20 0.71 0.60 0.69

26 0.11 0.17 0.16

29 2.49 0.07 1.31

30 2.00 0.79 0.37

34 0.64 0.38 1.72

37 0.20 0.21 0.65

38 0.53 0.83 1.87

39 1.08 0.87 1.90

40 1.15 3.21 0.32

41 0.43 1.00 0.26

Critical Value = 2.18000 

Zn-Precision Statistics

Material Xbar sx sr sR r R

4 20.13 6.13 1.33 6.23 3.72 17.44

5 20.64 6.58 1.54 6.69 4.30 18.74

6 357.16 46.45 18.02 48.73 50.46 136.43

46
APPENDIX D Consensus Plots

The following 18 plots represent the consensus results for Ca, Fe and Zn (mg/kg) in the six materials (Cereals A-F). The 

DerSimonian-Laird (DSL) consensus means are represented by the dark solid lines with ± 1, 2, 3, 4, 5, 6 Horn-Horn-Duncan (HHD) 

standard uncertainty lines. The median value for the triplicate data are represented as circles (•) with the corresponding vertical lines 

representing the range of the values (min to max) for each individual laboratory. 

47
Ca in Cereal A: Wheat Ground (SRM 3233)

48
Ca in Cereal B: Wheat Ground

49
Ca in Cereal C: Wheat Flake

50
Ca in Cereal D: Rice Ground

51
Ca in Cereal E: Rice Flake

52
Ca in Cereal F: Wheat/Rice Crushed

53
Fe in Cereal A: Wheat Ground (SRM 3233)

54
Fe in Cereal B: Wheat Ground

55
Fe in Cereal C: Wheat Flake

56
Fe in Cereal D: Rice Ground

57
Fe in Cereal E: Rice Flake

58
Fe in Cereal F: Wheat/Rice Crushed

59
Zn in Cereal A: Wheat Ground (SRM 3233)

60
Zn in Cereal B: Wheat Ground

61
Zn in Cereal C: Wheat Flake

62
Zn in Cereal D: Rice Ground

63
Zn in Cereal E: Rice Flake

64
Zn in Cereal F: Wheat/Rice Crushed

65
APPENDIX E Individualized Laboratory Reports

Appendix E contains an individualized summary of each of the 20 participating laboratories’ 

performance in the interlaboratory exercise. Each laboratory was provided this 2-page laboratoryspecific report that delivered a table of each laboratory’s summarized data and a summary 

consensus plot that graphically displays the laboratory’s results in comparison to the exercise 

consensus results together with explanatory details and data interpretation. 

66
Part II. Your Individual Laboratory Results (Lab Code: E543 - NIST)

Your laboratory’s data is summarized in Table Z. The mean (average) ± 1 standard deviation were 

determined from the reported triplicate (n=3) values for each of the 18 measurements (Fe, Ca and 

Zn within the six study materials, Cereals A-F) in Exercise E. 

Your laboratory’s summary consensus plot for Fe, Ca and Zn in the six cereal study materials is 

provided in Figure Z. The data have been normalized relative to consensus means and Horn-HornDuncan (HHD) uncertainties so that the consensus value is equal to zero. The thick blue line in this

plot represents the consensus values for each of the 18 measurements (Fe, Ca and Zn within the six 

study materials, Cereals A-F). The thin blue lines represent ± 3 HHD standard uncertainty intervals 

about the consensus values. The figure is scaled so that the top and bottom of the Y-axis represent 

± 6 HHD intervals. Your laboratory’s results for each of the 18 measurements are illustrated by the 

black bars. The ends of bars that are entirely within the ± 6 HHD intervals are marked with an open 

circle (); red circles () indicate that some or all of the bar is outside the ± 6 HHD interval. 

The length of each bar indicates how well your measurements agree with themselves. The distance 

from the center of the bars to the consensus line indicates how well your measurements agree with 

those of the other participants in this study. (An example consensus plot with explanations is also 

included to aid in the interpretation your results.) As a general rule, we consider results that fall 

within ± 3 HHD standard uncertainty lines to be within consensus (approximate 99% confidence 

limit) and results that have a black bar length ≈ 3 HHD units are considered as acceptable precision. 

If values are consistently very high or low for a particular element, then a calibration problem may 

exist. In such cases, it is important to make sure your calibration standards are from a reliable 

source, the quality is confirmed, and that your calibration solutions are correctly prepared and 

stored. In addition, calibration points must be linear in the expected measurement range and closely 

surround expected values. 

The means of your laboratory’s measurement results for the wheat cereal (materials B & C) and the 

rice cereal (D & E) pairs agree well for all three elements, indicating a consistent sample 

preparation process. However, your results for Ca differ markedly between the wheat-based cereals 

(A, B & C) and rice-based cereals (D & E) which suggests that your Ca measurement process may 

have a matrix-specific bias. Your results for Ca and Zn are precise (bar lengths of 1 to 2 HHD 

units), your results for Fe are somewhat less precise. Your results for all three elements in Cereal F 

are relatively high compared to those in the other materials. As discussed in Part I of the report, this 

hand-crushed material was noticeably less homogeneous than the other five materials.

Table Z. Summary of Fe, Ca and Zn values within the six study materials, Cereals A-F

 Code: E543 Mean Results ± 1 SD (n = 3)

Cereal A

Wheat

Ground

(SRM 3233)

Cereal B

Wheat

Ground

Cereal C

Wheat

Flake

Cereal D

Rice

Ground

Cereal E

Rice

Flake

Cereal F

Wheat/Rice

Crushed

Fe (μg/g) 785 ± 10 845 ± 21 839 ± 7 524 ± 16 534 ± 17 738 ± 10

Ca (μg/g) 37 250 ± 340 34 620 ± 160 34 500 ± 500 282 ± 11 279 ± 5 21 130 ± 920

Zn (μg/g) 626 ± 2 694 ± 5 696 ± 6 21 ± 1 21 ± 1 448 ± 19

67
Figure Z. A consensus plot summarizing your individual results: (Lab Code: E543 - NIST)

How to interpret your consensus summary plot:

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

•moderate precision

•agrees with consensus 

(-3 < ranking < 3)

•wide range = relatively poor precision

•biased high, relative to consensus

red symbols represent 

consensus difference ≥ 6 (or ≤ -6)

symbols without range bars represent nearly equivalent values 

(i.e., very good precision) for the triplicate measurements

•narrow range = better precision

•biased low, relative to consensus

solitary red symbols signify an entire

consensus difference ≥ 6 (or ≤ -6)

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

•moderate precision

•agrees with consensus 

(-3 < ranking < 3)

•wide range = relatively poor precision

•biased high, relative to consensus

red symbols represent 

consensus difference ≥ 6 (or ≤ -6)

symbols without range bars represent nearly equivalent values 

(i.e., very good precision) for the triplicate measurements

•narrow range = better precision

•biased low, relative to consensus

solitary red symbols signify an entire

consensus difference ≥ 6 (or ≤ -6)

68
Part II. Your Individual Laboratory Results (Lab Code: E502)

Your laboratory’s data is summarized in Table Z. The mean (average) ± 1 standard deviation were 

determined from the reported triplicate (n=3) values for each of the 18 measurements (Fe, Ca and 

Zn within the six study materials, Cereals A-F) in Exercise E. 

Your laboratory’s summary consensus plot for Fe, Ca and Zn in the six cereal study materials is 

provided in Figure Z. The data have been normalized relative to consensus means and Horn-HornDuncan (HHD) uncertainties so that the consensus value is equal to zero. The thick blue line in this

plot represents the consensus values for each of the 18 measurements (Fe, Ca and Zn within the six 

study materials, Cereals A-F). The thin blue lines represent ± 3 HHD standard uncertainty intervals 

about the consensus values. The figure is scaled so that the top and bottom of the Y-axis represent 

± 6 HHD intervals. Your laboratory’s results for each of the 18 measurements are illustrated by the 

black bars. The ends of bars that are entirely within the ± 6 HHD intervals are marked with an open 

circle (); red circles () indicate that some or all of the bar is outside the ± 6 HHD interval. 

The length of each bar indicates how well your measurements agree with themselves. The distance 

from the center of the bars to the consensus line indicates how well your measurements agree with 

those of the other participants in this study. (An example consensus plot with explanations is also 

included to aid in the interpretation your results.) As a general rule, we consider results that fall 

within ± 3 HHD standard uncertainty lines to be within consensus (approximate 99% confidence 

limit) and results that have a black bar length ≈ 3 HHD units are considered as acceptable precision. 

If values are consistently very high or low for a particular element, then a calibration problem may 

exist. In such cases, it is important to make sure your calibration standards are from a reliable 

source, the quality is confirmed and that your calibration solutions are correctly prepared and 

stored. In addition, calibration points must be linear in the expected measurement range and closely 

surround expected values. 

Your laboratory’s measurement results for Ca agree well with the consensus values; your Zn values 

are consistently somewhat greater than consensus and those for Fe are a bit lower. You may want 

to check the calibration materials you use for Fe and Zn. The means of your results for the wheatbased cereal (B & C) and the rice-based cereal (D & E) pairs agree well for Ca and Zn, indicating a 

consistent sample preparation process. Your results for Ca and Zn are precise (bar length of about 1 

HHD units), your results for Fe are somewhat less so. The very low result for Fe in material B

stands out suggesting possible problems with the linearity of your calibration curve. Based on the 

information given to the DSQAP Team, the range of your calibration curve extends quite high 

which would cause possible saturation at the upper points of the curve leading to unreliable results. 

Table Z. Summary of Fe, Ca and Zn values within the six study materials, Cereals A-F

Lab Code: E502 Mean Results ± 1 SD (n = 3)

Cereal A

Wheat

Ground

(SRM 3233)

Cereal B

Wheat

Ground

Cereal C

Wheat

Flake

Cereal D

Rice

Ground

Cereal E

Rice

Flake

Cereal F

Wheat/Rice

Crushed

Fe (μg/g) 700 ± 8 704 ± 34 771 ± 21 489 ± 11 494 ± 10 610 ± 14

Ca (μg/g) 37 330 ± 200 35 760 ± 260 35 630 ± 410 196 ± 1 197 ± 5 18 260 ± 170

Zn (μg/g) 631 ± 1 716 ± 6 716 ± 5 24 ± 0.1 24 ± 0.1 397 ± 3

69
Figure Z. A consensus plot summarizing your individual results (Lab Code: E502)

How to interpret your consensus summary plot:

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

•moderate precision

•agrees with consensus 

(-3 < ranking < 3)

•wide range = relatively poor precision

•biased high, relative to consensus

red symbols represent 

consensus difference ≥ 6 (or ≤ -6)

symbols without range bars represent nearly equivalent values 

(i.e., very good precision) for the triplicate measurements

•narrow range = better precision

•biased low, relative to consensus

solitary red symbols signify an entire

consensus difference ≥ 6 (or ≤ -6)

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

•moderate precision

•agrees with consensus 

(-3 < ranking < 3)

•wide range = relatively poor precision

•biased high, relative to consensus

red symbols represent 

consensus difference ≥ 6 (or ≤ -6)

symbols without range bars represent nearly equivalent values 

(i.e., very good precision) for the triplicate measurements

•narrow range = better precision

•biased low, relative to consensus

solitary red symbols signify an entire

consensus difference ≥ 6 (or ≤ -6)

70
Part II. Your Individual Laboratory Results (Lab Code: E509)

Your laboratory’s data is summarized in Table Z. The mean (average) ± 1 standard deviation were 

determined from the reported triplicate (n=3) values for each of the 18 measurements (Fe, Ca and 

Zn within the six study materials, Cereals A-F) in Exercise E. 

Your laboratory’s summary consensus plot for Fe, Ca and Zn in the six cereal study materials is 

provided in Figure Z. The data have been normalized relative to consensus means and Horn-HornDuncan (HHD) uncertainties so that the consensus value is equal to zero. The thick blue line in this

plot represents the consensus values for each of the 18 measurements (Fe, Ca and Zn within the six 

study materials, Cereals A-F). The thin blue lines represent ± 3 HHD standard uncertainty intervals 

about the consensus values. The figure is scaled so that the top and bottom of the Y-axis represent 

± 6 HHD intervals. Your laboratory’s results for each of the 18 measurements are illustrated by the 

black bars. The ends of bars that are entirely within the ± 6 HHD intervals are marked with an open 

circle (); red circles () indicate that some or all of the bar is outside the ± 6 HHD interval. 

The length of each bar indicates how well your measurements agree with themselves. The distance 

from the center of the bars to the consensus line indicates how well your measurements agree with 

those of the other participants in this study. (An example consensus plot with explanations is also 

included to aid in the interpretation your results.) As a general rule, we consider results that fall 

within ± 3 HHD standard uncertainty lines to be within consensus (approximate 99% confidence 

limit) and results that have a black bar length ≈ 3 HHD units are considered as acceptable precision. 

If values are consistently very high or low for a particular element, then a calibration problem may 

exist. In such cases, it is important to make sure your calibration standards are from a reliable 

source, the quality is confirmed and that your calibration solutions are correctly prepared and 

stored. In addition, calibration points must be linear in the expected measurement range and closely 

surround expected values. 

The means of your laboratory’s measurement results for Ca and Zn in the rice ground and flake 

cereal pairs (D & E) and Fe in the wheat cereals (B & C) agree well with each other and with the 

consensus means, indicating a consistent sample preparation process. The values for Zn in B & C 

do not agree well; the relatively high value for Zn in wheat flake cereal C may result from 

contamination of cereal C, either during packaging or during sample processing. This could also be 

due to a calculation error which was applied to all three values for Zn in cereal C. The precision of 

your measurement results is fairly variable, ranging from quite good (bars of 1 to 2 HHD units in 

length) to marginal (bars longer than 3 HHD units). In combination with the generally low results 

relative to consensus, this may suggest that your sample digestion process is somewhat inconsistent.

Table Z. Summary of Fe, Ca and Zn values within the six study materials, Cereals A-F

Lab Code: E509 Mean Results ± 1 SD (n = 3)

Cereal A

Wheat

Ground

(SRM 3233)

Cereal B

Wheat

Ground

Cereal C

Wheat

Flake

Cereal D

Rice

Ground

Cereal E

Rice

Flake

Cereal F

Wheat/Rice

Crushed

Fe (μg/g) 720 ± 26 787 ± 25 820 ± 20 453 ± 6 427 ± 31 603 ± 15

Ca (μg/g) 35 100 ± 850 34 000 ± 0 33 800 ± 720 197 ± 12 207 ± 6 16 700 ± 1210

Zn (μg/g) 547 ± 12 610 ± 10 820 ± 20 19 ± 1 19 ± 1 313 ± 15

71
Figure Z. A consensus plot summarizing your individual results (Lab Code: E509)

How to interpret your consensus summary plot:

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

•moderate precision

•agrees with consensus 

(-3 < ranking < 3)

•wide range = relatively poor precision

•biased high, relative to consensus

red symbols represent 

consensus difference ≥ 6 (or ≤ -6)

symbols without range bars represent nearly equivalent values 

(i.e., very good precision) for the triplicate measurements

•narrow range = better precision

•biased low, relative to consensus

solitary red symbols signify an entire

consensus difference ≥ 6 (or ≤ -6)

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

•moderate precision

•agrees with consensus 

(-3 < ranking < 3)

•wide range = relatively poor precision

•biased high, relative to consensus

red symbols represent 

consensus difference ≥ 6 (or ≤ -6)

symbols without range bars represent nearly equivalent values 

(i.e., very good precision) for the triplicate measurements

•narrow range = better precision

•biased low, relative to consensus

solitary red symbols signify an entire

consensus difference ≥ 6 (or ≤ -6)

72
Part II. Your Individual Laboratory Results (Lab Code: E510)

Your laboratory’s data is summarized in Table Z. The mean (average) ± 1 standard deviation were 

determined from the reported triplicate (n=3) values for each of the 18 measurements (Fe, Ca and Zn 

within the six study materials, Cereals A-F) in Exercise E. 

Your laboratory’s summary consensus plot for Fe, Ca and Zn in the six cereal study materials is 

provided in Figure Z. The data have been normalized relative to consensus means and Horn-HornDuncan (HHD) uncertainties so that the consensus value is equal to zero. The thick blue line in this

plot represents the consensus values for each of the 18 measurements (Fe, Ca and Zn within the six 

study materials, Cereals A-F). The thin blue lines represent ± 3 HHD standard uncertainty intervals 

about the consensus values. The figure is scaled so that the top and bottom of the Y-axis represent ±

6 HHD intervals. Your laboratory’s results for each of the 18 measurements are illustrated by the 

black bars. The ends of bars that are entirely within the ± 6 HHD intervals are marked with an open 

circle (); red circles () indicate that some or all of the bar is outside the ± 6 HHD interval. 

The length of each bar indicates how well your measurements agree with themselves. The distance 

from the center of the bars to the consensus line indicates how well your measurements agree with 

those of the other participants in this study. (An example consensus plot with explanations is also 

included to aid in the interpretation your results.) As a general rule, we consider results that fall 

within ± 3 HHD standard uncertainty lines to be within consensus (approximate 99% confidence 

limit) and results that have a black bar length ≈ 3 HHD units are considered as acceptable precision. 

If values are consistently very high or low for a particular element, then a calibration problem may 

exist. In such cases, it is important to make sure your calibration standards are from a reliable source, 

the quality is confirmed and that your calibration solutions are correctly prepared and stored. In 

addition, calibration points must be linear in the expected measurement range and closely surround 

expected values. 

Your laboratory’s measurement results are pretty consistently below the consensus means; many 

values are below the 6 HHD limits of the graph. These very low values suggest that your samples 

were incompletely digested. Your laboratory was the only participant that took sample replicates 

from both sets of bottles or packages. This may contribute to the relatively large variability of all 

elements in Cereals C and E as homogeneity within the package may be an issue with these flake 

materials.

Table Z. Summary of Fe, Ca and Zn values within the six study materials, Cereals A-F

Lab Code: E510 Mean Results ± 1 SD (n = 3)

Cereal A

Wheat

Ground

(SRM 3233)

Cereal B

Wheat

Ground

Cereal C

Wheat

Flake

Cereal D

Rice

Ground

Cereal E

Rice

Flake

Cereal F

Wheat/Rice

Crushed

Fe (μg/g) 683 ± 9 732 ± 14 667 ± 96 460 ± 25 384 ± 33 500 ± 25

Ca (μg/g) 32 850 ± 650 32 010 ± 330 30 740 ± 790 195 ± 7 233 ± 43 16 300 ± 350

Zn (μg/g) 536 ± 30 587 ± 38 522 ± 66 20 ± 1 18 ± 2 284 ± 7

73
Figure Z. A consensus plot summarizing your individual results (Lab Code: E510)

How to interpret your consensus summary plot:

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

•moderate precision

•agrees with consensus 

(-3 < ranking < 3)

•wide range = relatively poor precision

•biased high, relative to consensus

red symbols represent 

consensus difference ≥ 6 (or ≤ -6)

symbols without range bars represent nearly equivalent values 

(i.e., very good precision) for the triplicate measurements

•narrow range = better precision

•biased low, relative to consensus

solitary red symbols signify an entire

consensus difference ≥ 6 (or ≤ -6)

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

•moderate precision

•agrees with consensus 

(-3 < ranking < 3)

•wide range = relatively poor precision

•biased high, relative to consensus

red symbols represent 

consensus difference ≥ 6 (or ≤ -6)

symbols without range bars represent nearly equivalent values 

(i.e., very good precision) for the triplicate measurements

•narrow range = better precision

•biased low, relative to consensus

solitary red symbols signify an entire

consensus difference ≥ 6 (or ≤ -6)

74
Part II. Your Individual Laboratory Results (Lab Code: E511)

Your laboratory’s data is summarized in Table Z. The mean (average) ± 1 standard deviation were 

determined from the reported triplicate (n=3) values for each of the 18 measurements (Fe, Ca and Zn 

within the six study materials, Cereals A-F) in Exercise E. 

Your laboratory’s summary consensus plot for Fe, Ca and Zn in the six cereal study materials is 

provided in Figure Z. The data have been normalized relative to consensus means and Horn-HornDuncan (HHD) uncertainties so that the consensus value is equal to zero. The thick blue line in this

plot represents the consensus values for each of the 18 measurements (Fe, Ca and Zn within the six 

study materials, Cereals A-F). The thin blue lines represent ± 3 HHD standard uncertainty intervals 

about the consensus values. The figure is scaled so that the top and bottom of the Y-axis represent ±

6 HHD intervals. Your laboratory’s results for each of the 18 measurements are illustrated by the 

black bars. The ends of bars that are entirely within the ± 6 HHD intervals are marked with an open 

circle (); red circles () indicate that some or all of the bar is outside the ± 6 HHD interval. 

The length of each bar indicates how well your measurements agree with themselves. The distance 

from the center of the bars to the consensus line indicates how well your measurements agree with 

those of the other participants in this study. (An example consensus plot with explanations is also 

included to aid in the interpretation your results.) As a general rule, we consider results that fall 

within ± 3 HHD standard uncertainty lines to be within consensus (approximate 99% confidence 

limit) and results that have a black bar length ≈ 3 HHD units are considered as acceptable precision. 

If values are consistently very high or low for a particular element, then a calibration problem may 

exist. In such cases, it is important to make sure your calibration standards are from a reliable source, 

the quality is confirmed and that your calibration solutions are correctly prepared and stored. In 

addition, calibration points must be linear in the expected measurement range and closely surround 

expected values. 

Your laboratory’s measurement results generally agree well with the consensus means indicating 

good calibration. The mean values for Fe, Ca and Zn in the wheat ground and flake cereal pairs (B & 

C) and the rice ground and flake cereal pairs (D & E) pairs agree quite well, indicating a quite 

consistent sample preparation process. Your laboratory’s values for the three elements in all 

materials are mostly moderately precise (many bar lengths of 2 to 3 HHD units). The somewhat less 

precise (slightly longer bars) values in Cereal A relative to the other materials is counter to our 

expectation, given the established homogeneity of Cereal A.

Table Z. Summary of Fe, Ca and Zn values within the six study materials, Cereals A-F

Lab Code: E511 Mean Results ± 1 SD (n = 3)

Cereal A

Wheat

Ground

(SRM 3233)

Cereal B

Wheat

Ground

Cereal C

Wheat

Flake

Cereal D

Rice

Ground

Cereal E

Rice

Flake

Cereal F

Wheat/Rice

Crushed

Fe (μg/g) 747 ± 25 806 ± 23 818 ± 29 516 ± 12 506 ± 8 654 ± 22

Ca (μg/g) 36 630 ± 1120 34 430 ± 920 34 830 ± 1010 196 ± 6 199 ± 8 17700 ± 600

Zn (μg/g) 609 ± 19 675 ± 17 688 ± 22 20 ± 1 20 ± 1 357 ± 5

75
Figure Z. A consensus plot summarizing your individual results (Lab Code: E511)

How to interpret your consensus summary plot:

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

•moderate precision

•agrees with consensus 

(-3 < ranking < 3)

•wide range = relatively poor precision

•biased high, relative to consensus

red symbols represent 

consensus difference ≥ 6 (or ≤ -6)

symbols without range bars represent nearly equivalent values 

(i.e., very good precision) for the triplicate measurements

•narrow range = better precision

•biased low, relative to consensus

solitary red symbols signify an entire

consensus difference ≥ 6 (or ≤ -6)

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

•moderate precision

•agrees with consensus 

(-3 < ranking < 3)

•wide range = relatively poor precision

•biased high, relative to consensus

red symbols represent 

consensus difference ≥ 6 (or ≤ -6)

symbols without range bars represent nearly equivalent values 

(i.e., very good precision) for the triplicate measurements

•narrow range = better precision

•biased low, relative to consensus

solitary red symbols signify an entire

consensus difference ≥ 6 (or ≤ -6)

76
Part II. Your Individual Laboratory Results (Lab Code: E513)

Your laboratory’s data is summarized in Table Z. The mean (average) ± 1 standard deviation were 

determined from the reported triplicate (n=3) values for each of the 18 measurements (Fe, Ca and Zn 

within the six study materials, Cereals A-F) in Exercise E. 

Your laboratory’s summary consensus plot for Fe, Ca and Zn in the six cereal study materials is 

provided in Figure Z. The data have been normalized relative to consensus means and Horn-HornDuncan (HHD) uncertainties so that the consensus value is equal to zero. The thick blue line in this

plot represents the consensus values for each of the 18 measurements (Fe, Ca and Zn within the six 

study materials, Cereals A-F). The thin blue lines represent ± 3 HHD standard uncertainty intervals 

about the consensus values. The figure is scaled so that the top and bottom of the Y-axis represent 

± 6 HHD intervals. Your laboratory’s results for each of the 18 measurements are illustrated by the 

black bars. The ends of bars that are entirely within the ± 6 HHD intervals are marked with an open 

circle (); red circles () indicate that some or all of the bar is outside the ± 6 HHD interval. 

The length of each bar indicates how well your measurements agree with themselves. The distance 

from the center of the bars to the consensus line indicates how well your measurements agree with 

those of the other participants in this study. (An example consensus plot with explanations is also 

included to aid in the interpretation your results.) As a general rule, we consider results that fall 

within ± 3 HHD standard uncertainty lines to be within consensus (approximate 99% confidence 

limit) and results that have a black bar length ≈ 3 HHD units are considered as acceptable precision. 

If values are consistently very high or low for a particular element, then a calibration problem may 

exist. In such cases, it is important to make sure your calibration standards are from a reliable source, 

the quality is confirmed and that your calibration solutions are correctly prepared and stored. In 

addition, calibration points must be linear in the expected measurement range and closely surround 

expected values. 

Your laboratory’s measurement results for Fe mostly agree well with the consensus results. Many of 

your results for Ca and Zn are lower than consensus; you may want to check your Ca and Zn 

calibration standards. The mean values for all three elements in the ground and flake rice cereal pairs 

(D & E) agree well, as do those for Ca and Zn in the ground and flake wheat cereal pairs (B & C); 

this suggests that your sample preparation process was fairly consistent. Your results are mostly 

quite precise (bar lengths of less than 2 HHD units), except for Ca in the wheat-based cereals (A, B & 

C). This relatively poor precision in these high Ca materials suggests that the mass fraction of Ca in 

the samples analyzed may have been above the linear region of your calibration curve. It is important 

when preparing samples to have appropriate concentration levels and to use enough calibration points 

to adequately cover the expected concentration range to ensure linearity.

Table Z. Summary of Fe, Ca and Zn values within the six study materials, Cereals A-F

Lab Code: E513 Mean Results ± 1 SD (n = 3)

Cereal A

Wheat

Ground

(SRM 3233)

Cereal B

Wheat

Ground

Cereal C

Wheat

Flake

Cereal D

Rice

Ground

Cereal E

Rice

Flake

Cereal F

Wheat/Rice

Crushed

Fe (μg/g) 743 ± 6 773 ± 6 800 ± 10 513 ± 12 500 ± 0 660 ± 10

Ca (μg/g) 37 000 ± 1000 34 000 ± 1000 34 670 ± 1,160 180 ± 0 180 ± 0 16 670 ± 580

Zn (μg/g) 533 ± 6 573 ± 6 587 ± 6 18 ± 1 18 ± 1 320 ± 17

77
Figure Z. A consensus plot summarizing your individual results (Lab Code: E513)

How to interpret your consensus summary plot:

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

•moderate precision

•agrees with consensus 

(-3 < ranking < 3)

•wide range = relatively poor precision

•biased high, relative to consensus

red symbols represent 

consensus difference ≥ 6 (or ≤ -6)

symbols without range bars represent nearly equivalent values 

(i.e., very good precision) for the triplicate measurements

•narrow range = better precision

•biased low, relative to consensus

solitary red symbols signify an entire

consensus difference ≥ 6 (or ≤ -6)

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

•moderate precision

•agrees with consensus 

(-3 < ranking < 3)

•wide range = relatively poor precision

•biased high, relative to consensus

red symbols represent 

consensus difference ≥ 6 (or ≤ -6)

symbols without range bars represent nearly equivalent values 

(i.e., very good precision) for the triplicate measurements

•narrow range = better precision

•biased low, relative to consensus

solitary red symbols signify an entire

consensus difference ≥ 6 (or ≤ -6)

78
Part II. Your Individual Laboratory Results (Lab Code: E515)

Your laboratory’s data is summarized in Table Z. The mean (average) ± 1 standard deviation were 

determined from the reported triplicate (n=3) values for each of the 18 measurements (Fe, Ca and 

Zn within the six study materials, Cereals A-F) in Exercise E. 

Your laboratory’s summary consensus plot for Fe, Ca and Zn in the six cereal study materials is

provided in Figure Z. The data have been normalized relative to consensus means and Horn-HornDuncan (HHD) uncertainties so that the consensus value is equal to zero. The thick blue line in this

plot represents the consensus values for each of the 18 measurements (Fe, Ca and Zn within the six 

study materials, Cereals A-F). The thin blue lines represent ± 3 HHD standard uncertainty intervals 

about the consensus values. The figure is scaled so that the top and bottom of the Y-axis represent 

± 6 HHD intervals. Your laboratory’s results for each of the 18 measurements are illustrated by the 

black bars. The ends of bars that are entirely within the ± 6 HHD intervals are marked with an open 

circle (); red circles () indicate that some or all of the bar is outside the ± 6 HHD interval. 

The length of each bar indicates how well your measurements agree with themselves. The distance 

from the center of the bars to the consensus line indicates how well your measurements agree with 

those of the other participants in this study. (An example consensus plot with explanations is also 

included to aid in the interpretation your results.) As a general rule, we consider results that fall 

within ± 3 HHD standard uncertainty lines to be within consensus (approximate 99% confidence 

limit) and results that have a black bar length ≈ 3 HHD units are considered as acceptable precision. 

If values are consistently very high or low for a particular element, then a calibration problem may 

exist. In such cases, it is important to make sure your calibration standards are from a reliable 

source, the quality is confirmed and that your calibration solutions are correctly prepared and 

stored. In addition, calibration points must be linear in the expected measurement range and closely 

surround expected values. 

Your laboratory’s measurement results for the ground and flake wheat cereal pairs (B & C) and 

ground and flake rice cereal pairs (D & E) agree fairly well, indicating that your sample preparation 

process is fairly consistent. However, many of your laboratory’s measurement results are 

inconsistently above or below the consensus means. The precision of your measurements likewise 

is rather inconsistent, ranging from quite good (bars less that 1 HHD unit long) to moderately poor

(bars longer than 3 HHD units). These results suggest inconsistent sample digestion and/or sample 

dilution.

Table Z. Summary of Fe, Ca and Zn values within the six study materials, Cereals A-F

Lab Code: E515 Mean Results ± 1 SD (n = 3)

Cereal A

Wheat

Ground

(SRM 3233)

Cereal B

Wheat

Ground

Cereal C

Wheat

Flake

Cereal D

Rice

Ground

Cereal E

Rice

Flake

Cereal F

Wheat/Rice

Crushed

Fe (μg/g) 805 ± 14 899 ± 12 908 ± 15 472 ± 13 487 ± 35 623 ± 10

Ca (μg/g) 35 320 ± 310 33 270 ± 390 34 160 ± 700 233 ± 2 238 ± 10 13 130 ± 1100

Zn (μg/g) 648 ± 3 723 ± 21 756 ± 13 26 ± 0 25 ± 1 299 ± 26

79
Figure Z. A consensus plot summarizing your individual results (Lab Code: E515)

How to interpret your consensus summary plot:

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

•moderate precision

•agrees with consensus 

(-3 < ranking < 3)

•wide range = relatively poor precision

•biased high, relative to consensus

red symbols represent 

consensus difference ≥ 6 (or ≤ -6)

symbols without range bars represent nearly equivalent values 

(i.e., very good precision) for the triplicate measurements

•narrow range = better precision

•biased low, relative to consensus

solitary red symbols signify an entire

consensus difference ≥ 6 (or ≤ -6)

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

•moderate precision

•agrees with consensus 

(-3 < ranking < 3)

•wide range = relatively poor precision

•biased high, relative to consensus

red symbols represent 

consensus difference ≥ 6 (or ≤ -6)

symbols without range bars represent nearly equivalent values 

(i.e., very good precision) for the triplicate measurements

•narrow range = better precision

•biased low, relative to consensus

solitary red symbols signify an entire

consensus difference ≥ 6 (or ≤ -6)

80
Part II. Your Individual Laboratory Results (Lab Code: E520)

Your laboratory’s data is summarized in Table Z. The mean (average) ± 1 standard deviation were 

determined from the reported triplicate (n=3) values for each of the 18 measurements (Fe, Ca and 

Zn within the six study materials, Cereals A-F) in Exercise E. 

Your laboratory’s summary consensus plot for Fe, Ca and Zn in the six cereal study materials is 

provided in Figure Z. The data have been normalized relative to consensus means and Horn-HornDuncan (HHD) uncertainties so that the consensus value is equal to zero. The thick blue line in this

plot represents the consensus values for each of the 18 measurements (Fe, Ca and Zn within the six 

study materials, Cereals A-F). The thin blue lines represent ± 3 HHD standard uncertainty intervals 

about the consensus values. The figure is scaled so that the top and bottom of the Y-axis represent 

± 6 HHD intervals. Your laboratory’s results for each of the 18 measurements are illustrated by the 

black bars. The ends of bars that are entirely within the ± 6 HHD intervals are marked with an open 

circle (); red circles () indicate that some or all of the bar is outside the ± 6 HHD interval. 

The length of each bar indicates how well your measurements agree with themselves. The distance 

from the center of the bars to the consensus line indicates how well your measurements agree with 

those of the other participants in this study. (An example consensus plot with explanations is also 

included to aid in the interpretation your results.) As a general rule, we consider results that fall 

within ± 3 HHD standard uncertainty lines to be within consensus (approximate 99% confidence 

limit) and results that have a black bar length ≈ 3 HHD units are considered as acceptable precision. 

If values are consistently very high or low for a particular element, then a calibration problem may 

exist. In such cases, it is important to make sure your calibration standards are from a reliable 

source, the quality is confirmed and that your calibration solutions are correctly prepared and 

stored. In addition, calibration points must be linear in the expected measurement range and closely 

surround expected values. 

Your laboratory’s measurement results for all three elements in the rice cereal (D & E) pair agree 

well with each other, indicating a consistent sample preparation process for this material. Your 

results are in general quite precise (bar lengths of 1 to 2 HHD units) for all elements and all 

materials. However, with the exception of Ca and Zn in the rice-based cereals (D, E and F), your 

measurement values are consistently higher than the consensus values. Given that Ca and Zn 

require very different dilution schemes for the wheat-based and rice-based materials, this unusual 

pattern suggests problems with calibration and/or sample preparation steps. It is important to 

prepare samples that will have appropriate concentration levels and to use calibration points to 

adequately cover the expected concentration range.

Table Z. Summary of Fe, Ca and Zn values within the six study materials, Cereals A-F

Lab Code: E520 Mean Results ± 1 SD (n = 3)

Cereal A

Wheat

Ground

(SRM 3233)

Cereal B

Wheat

Ground

Cereal C

Wheat

Flake

Cereal D

Rice

Ground

Cereal E

Rice

Flake

Cereal F

Wheat/Rice

Crushed

Fe (μg/g) 861 ± 21 912 ± 7 938 ± 13 572 ± 12 577 ± 16 703 ± 9

Ca (μg/g) 41 730 ± 560 38 720 ± 220 38 890 ± 650 171 ± 4 161 ± 6 16 120 ± 540

Zn (μg/g) 675 ± 7 730 ± 5 743 ± 10 8 ± 1 7 ± 1 317 ± 13

81
Figure Z. A consensus plot summarizing your individual results (Lab Code: E520)

How to interpret your consensus summary plot:

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

•moderate precision

•agrees with consensus 

(-3 < ranking < 3)

•wide range = relatively poor precision

•biased high, relative to consensus

red symbols represent 

consensus difference ≥ 6 (or ≤ -6)

symbols without range bars represent nearly equivalent values 

(i.e., very good precision) for the triplicate measurements

•narrow range = better precision

•biased low, relative to consensus

solitary red symbols signify an entire

consensus difference ≥ 6 (or ≤ -6)

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

•moderate precision

•agrees with consensus 

(-3 < ranking < 3)

•wide range = relatively poor precision

•biased high, relative to consensus

red symbols represent 

consensus difference ≥ 6 (or ≤ -6)

symbols without range bars represent nearly equivalent values 

(i.e., very good precision) for the triplicate measurements

•narrow range = better precision

•biased low, relative to consensus

solitary red symbols signify an entire

consensus difference ≥ 6 (or ≤ -6)

82
Part II. Your Individual Laboratory Results (Lab Code: E522)

Your laboratory’s data is summarized in Table Z. The mean (average) ± 1 standard deviation were 

determined from the reported triplicate (n=3) values for each of the 18 measurements (Fe, Ca and 

Zn within the six study materials, Cereals A-F) in Exercise E. 

Your laboratory’s summary consensus plot for Fe, Ca and Zn in the six cereal study materials is 

provided in Figure Z. The data have been normalized relative to consensus means and Horn-HornDuncan (HHD) uncertainties so that the consensus value is equal to zero. The thick blue line in this

plot represents the consensus values for each of the 18 measurements (Fe, Ca and Zn within the six 

study materials, Cereals A-F). The thin blue lines represent ± 3 HHD standard uncertainty intervals 

about the consensus values. The figure is scaled so that the top and bottom of the Y-axis represent 

± 6 HHD intervals. Your laboratory’s results for each of the 18 measurements are illustrated by the 

black bars. The ends of bars that are entirely within the ± 6 HHD intervals are marked with an open 

circle (); red circles () indicate that some or all of the bar is outside the ± 6 HHD interval. 

The length of each bar indicates how well your measurements agree with themselves. The distance 

from the center of the bars to the consensus line indicates how well your measurements agree with 

those of the other participants in this study. (An example consensus plot with explanations is also 

included to aid in the interpretation your results.) As a general rule, we consider results that fall 

within ± 3 HHD standard uncertainty lines to be within consensus (approximate 99% confidence 

limit) and results that have a black bar length ≈ 3 HHD units are considered as acceptable precision. 

If values are consistently very high or low for a particular element, then a calibration problem may 

exist. In such cases, it is important to make sure your calibration standards are from a reliable 

source, the quality is confirmed and that your calibration solutions are correctly prepared and 

stored. In addition, calibration points must be linear in the expected measurement range and closely 

surround expected values. 

Your laboratory’s measurement results generally agree quite well with the consensus means, with 

the exception of the Ca values in the two rice-based cereals, D & E. Given the relatively low 

amount of Ca in these rice materials, these low results suggest that the solutions analyzed may not 

have been in the linear region of your calibration curve. It is important to prepare samples to have 

appropriate mass fraction levels and to use enough calibration points to adequately cover the 

expected mass fraction range. Your results for all three elements in the wheat cereal (B & C) and 

rice cereal (D & E) pairs agree fairly well with each other, indicating a consistent sample 

preparation process. The precision of your measurement is quite good (bar lengths of 1 to 2 HHD 

units), with the exception of Fe in the ground wheat-based cereal B. This exception may possibly 

be due to a single contaminate sample or other unexplained outlier among two close values.

Table Z. Summary of Fe, Ca and Zn values within the six study materials, Cereals A-F

Lab Code: E522 Mean Results ± 1 SD (n = 3)

Cereal A

Wheat

Ground

(SRM 3233)

Cereal B

Wheat

Ground

Cereal C

Wheat

Flake

Cereal D

Rice

Ground

Cereal E

Rice

Flake

Cereal F

Wheat/Rice

Crushed

Fe (μg/g) 744 ± 11 787 ± 43 845 ± 21 492 ± 8 490 ± 11 653 ± 6

Ca (μg/g) 37 250 ± 340 35 070 ± 300 34 860 ± 460 145 ± 4 146 ± 2 17 260 ± 300

Zn (μg/g) 620 ± 7 688 ± 6 699 ± 11 19 ± 0 20 ± 0.1 358 ± 4

83
Figure Z. A consensus plot summarizing your individual results (Lab Code: E522)

How to interpret your consensus summary plot:

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

•moderate precision

•agrees with consensus 

(-3 < ranking < 3)

•wide range = relatively poor precision

•biased high, relative to consensus

red symbols represent 

consensus difference ≥ 6 (or ≤ -6)

symbols without range bars represent nearly equivalent values 

(i.e., very good precision) for the triplicate measurements

•narrow range = better precision

•biased low, relative to consensus

solitary red symbols signify an entire

consensus difference ≥ 6 (or ≤ -6)

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

•moderate precision

•agrees with consensus 

(-3 < ranking < 3)

•wide range = relatively poor precision

•biased high, relative to consensus

red symbols represent 

consensus difference ≥ 6 (or ≤ -6)

symbols without range bars represent nearly equivalent values 

(i.e., very good precision) for the triplicate measurements

•narrow range = better precision

•biased low, relative to consensus

solitary red symbols signify an entire

consensus difference ≥ 6 (or ≤ -6)

84
Part II. Your Individual Laboratory Results (Lab Code: E526)

Your laboratory’s data is summarized in Table Z. The mean (average) ± 1 standard deviation were 

determined from the reported triplicate (n=3) values for each of the 18 measurements (Fe, Ca and Zn 

within the six study materials, Cereals A-F) in Exercise E. 

Your laboratory’s summary consensus plot for Fe, Ca and Zn in the six cereal study materials is 

provided in Figure Z. The data have been normalized relative to consensus means and Horn-HornDuncan (HHD) uncertainties so that the consensus value is equal to zero. The thick blue line in this

plot represents the consensus values for each of the 18 measurements (Fe, Ca and Zn within the six 

study materials, Cereals A-F). The thin blue lines represent ± 3 HHD standard uncertainty intervals 

about the consensus values. The figure is scaled so that the top and bottom of the Y-axis represent ± 6 

HHD intervals. Your laboratory’s results for each of the 18 measurements are illustrated by the black 

bars. The ends of bars that are entirely within the ± 6 HHD intervals are marked with an open circle 

(); red circles () indicate that some or all of the bar is outside the ± 6 HHD interval. 

The length of each bar indicates how well your measurements agree with themselves. The distance 

from the center of the bars to the consensus line indicates how well your measurements agree with 

those of the other participants in this study. (An example consensus plot with explanations is also 

included to aid in the interpretation your results.) As a general rule, we consider results that fall within 

± 3 HHD standard uncertainty lines to be within consensus (approximate 99% confidence limit) and 

results that have a black bar length ≈ 3 HHD units are considered as acceptable precision. If values are 

consistently very high or low for a particular element, then a calibration problem may exist. In such 

cases, it is important to make sure your calibration standards are from a reliable source, the quality is 

confirmed and that your calibration solutions are correctly prepared and stored. In addition, calibration 

points must be linear in the expected measurement range and closely surround expected values. 

Your laboratory’s measurement results for Fe and Zn in all six materials agree well with the consensus 

means. The Ca values are consistently slightly low, suggesting that you should check your Ca 

calibration standard. Your results for all three elements in the wheat cereal (B & C) and rice cereal (D 

& E) pairs agree fairly well with each other, indicating a consistent sample preparation process. The 

precision of your measurements is quite good (bar lengths mostly of 1 to 2 HHD units).

Table Z. Summary of Fe, Ca and Zn values within the six study materials, Cereals A-F

Lab Code: E526 Mean Results ± 1 SD (n = 3)

Cereal A

Wheat

Ground

(SRM 3233)

Cereal B

Wheat

Ground

Cereal C

Wheat

Flake

Cereal D

Rice

Ground

Cereal E

Rice

Flake

Cereal F

Wheat/Rice

Crushed

Fe (μg/g) 747 ± 6 826 ± 2 848 ± 43 507 ± 7 501 ± 5 667 ± 6

Ca (μg/g) 36 180 ± 60 34 420 ± 130 34 780 ± 80 183 ± 6 190 ± 0 16 430 ± 180

Zn (μg/g) 608 ± 11 679 ± 4 709 ± 7 21 ± 0.2 20 ± 0.3 343 ± 3

85
Figure Z. A consensus plot summarizing your individual results (Lab Code: E526)

How to interpret your consensus summary plot:

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

•moderate precision

•agrees with consensus 

(-3 < ranking < 3)

•wide range = relatively poor precision

•biased high, relative to consensus

red symbols represent 

consensus difference ≥ 6 (or ≤ -6)

symbols without range bars represent nearly equivalent values 

(i.e., very good precision) for the triplicate measurements

•narrow range = better precision

•biased low, relative to consensus

solitary red symbols signify an entire

consensus difference ≥ 6 (or ≤ -6)

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

•moderate precision

•agrees with consensus 

(-3 < ranking < 3)

•wide range = relatively poor precision

•biased high, relative to consensus

red symbols represent 

consensus difference ≥ 6 (or ≤ -6)

symbols without range bars represent nearly equivalent values 

(i.e., very good precision) for the triplicate measurements

•narrow range = better precision

•biased low, relative to consensus

solitary red symbols signify an entire

consensus difference ≥ 6 (or ≤ -6)

86
Part II. Your Individual Laboratory Results (Lab Code: E529)

Your laboratory’s data is summarized in Table Z. The mean (average) ± 1 standard deviation were 

determined from the reported triplicate (n=3) values for each of the 18 measurements (Fe, Ca and Zn 

within the six study materials, Cereals A-F) in Exercise E. 

Your laboratory’s summary consensus plot for Fe, Ca and Zn in the six cereal study materials is 

provided in Figure Z. The data have been normalized relative to consensus means and Horn-HornDuncan (HHD) uncertainties so that the consensus value is equal to zero. The thick blue line in this

plot represents the consensus values for each of the 18 measurements (Fe, Ca and Zn within the six 

study materials, Cereals A-F). The thin blue lines represent ± 3 HHD standard uncertainty intervals 

about the consensus values. The figure is scaled so that the top and bottom of the Y-axis represent ± 6 

HHD intervals. Your laboratory’s results for each of the 18 measurements are illustrated by the black 

bars. The ends of bars that are entirely within the ± 6 HHD intervals are marked with an open circle 

(); red circles () indicate that some or all of the bar is outside the ± 6 HHD interval. 

The length of each bar indicates how well your measurements agree with themselves. The distance 

from the center of the bars to the consensus line indicates how well your measurements agree with 

those of the other participants in this study. (An example consensus plot with explanations is also 

included to aid in the interpretation your results.) As a general rule, we consider results that fall within 

± 3 HHD standard uncertainty lines to be within consensus (approximate 99% confidence limit) and 

results that have a black bar length ≈ 3 HHD units are considered as acceptable precision. If values are 

consistently very high or low for a particular element, then a calibration problem may exist. In such 

cases, it is important to make sure your calibration standards are from a reliable source, the quality is 

confirmed and that your calibration solutions are correctly prepared and stored. In addition, calibration 

points must be linear in the expected measurement range and closely surround expected values. 

Your laboratory’s measurement results for Ca and Zn (you did not report results for Fe) generally 

agree with the consensus means, indicating that your measurement processes are well calibrated. 

While your average results for Zn in the wheat-based cereal pair (B & C) and for Ca in the rice-based 

pair (D & E) agree well, the results for Zn in D & E and Ca in B & C do not agree well. The precision 

of your results is also somewhat variable, being rather good for the wheat-based materials (bar lengths 

of 1 to 2 HHD units for materials A, B & C) but less good for the rice-based materials (some bars 

greater than 3 HDD units) and fairly poor for the mixed-source material F. These observations suggest 

that your sample preparation processes may not have sufficiently homogenized some of the sample 

materials or that sample digestions were incomplete.

Table Z. Summary of Ca and Zn values within the six study materials, Cereals A-F

Lab Code: E529 Mean Results ± 1 SD (n = 3)

Cereal A

Wheat

Ground

(SRM 3233)

Cereal B

Wheat

Ground

Cereal C

Wheat

Flake

Cereal D

Rice

Ground

Cereal E

Rice

Flake

Cereal F

Wheat/Rice

Crushed

Ca (μg/g) 38 820 ± 270 34 710 ± 350 37 050 ± 260 201 ± 45 230 ± 36 18 420 ± 1500

Zn (μg/g) 588 ± 6 686 ± 7 682 ± 7 14 ± 3 19 ± 0.1 366 ± 24

87
Figure Z. A consensus plot summarizing your individual results (Lab Code: E529)

How to interpret your consensus summary plot:

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

•moderate precision

•agrees with consensus 

(-3 < ranking < 3)

•wide range = relatively poor precision

•biased high, relative to consensus

red symbols represent 

consensus difference ≥ 6 (or ≤ -6)

symbols without range bars represent nearly equivalent values 

(i.e., very good precision) for the triplicate measurements

•narrow range = better precision

•biased low, relative to consensus

solitary red symbols signify an entire

consensus difference ≥ 6 (or ≤ -6)

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

•moderate precision

•agrees with consensus 

(-3 < ranking < 3)

•wide range = relatively poor precision

•biased high, relative to consensus

red symbols represent 

consensus difference ≥ 6 (or ≤ -6)

symbols without range bars represent nearly equivalent values 

(i.e., very good precision) for the triplicate measurements

•narrow range = better precision

•biased low, relative to consensus

solitary red symbols signify an entire

consensus difference ≥ 6 (or ≤ -6)

88
Part II. Your Individual Laboratory Results (Lab Code: E530)

Your laboratory’s data is summarized in Table Z. The mean (average) ± 1 standard deviation were 

determined from the reported triplicate (n=3) values for each of the 18 measurements (Fe, Ca and Zn 

within the six study materials, Cereals A-F) in Exercise E. 

Your laboratory’s summary consensus plot for Fe, Ca and Zn in the six cereal study materials is 

provided in Figure Z. The data have been normalized relative to consensus means and Horn-HornDuncan (HHD) uncertainties so that the consensus value is equal to zero. The thick blue line in this

plot represents the consensus values for each of the 18 measurements (Fe, Ca and Zn within the six 

study materials, Cereals A-F). The thin blue lines represent ± 3 HHD standard uncertainty intervals 

about the consensus values. The figure is scaled so that the top and bottom of the Y-axis represent ± 6 

HHD intervals. Your laboratory’s results for each of the 18 measurements are illustrated by the black 

bars. The ends of bars that are entirely within the ± 6 HHD intervals are marked with an open circle 

(); red circles () indicate that some or all of the bar is outside the ± 6 HHD interval. 

The length of each bar indicates how well your measurements agree with themselves. The distance 

from the center of the bars to the consensus line indicates how well your measurements agree with 

those of the other participants in this study. (An example consensus plot with explanations is also 

included to aid in the interpretation your results.) As a general rule, we consider results that fall within 

± 3 HHD standard uncertainty lines to be within consensus (approximate 99% confidence limit) and 

results that have a black bar length ≈ 3 HHD units are considered as acceptable precision. If values are 

consistently very high or low for a particular element, then a calibration problem may exist. In such 

cases, it is important to make sure your calibration standards are from a reliable source, the quality is 

confirmed and that your calibration solutions are correctly prepared and stored. In addition, calibration 

points must be linear in the expected measurement range and closely surround expected values. 

Your laboratory’s measurement results for Zn generally agree with the consensus means, indicating 

that your measurement process for this element is well calibrated. Your results for Fe fall consistently 

below the consensus values, with many less than -6 HHD. Iron is relatively easy to digest indicating a 

possible calibration problem and suggests that you should check your Fe calibration standards or a 

possible loss of Fe. You did not report results for Ca. The results for Fe in the wheat-based cereal pair 

(B & C) and the rice-based pair (D & E) and Zn in the wheat-based cereal pair (B & C) are not in good 

agreement, suggesting that your sample preparation process may not be consistently providing 

representative subsamples.

Table Z. Summary of Fe and Zn values within the six study materials, Cereals A-F

Lab Code: E530 Mean Results ± 1 SD (n = 3)

Cereal A

Wheat

Ground

(SRM 3233)

Cereal B

Wheat

Ground

Cereal C

Wheat

Flake

Cereal D

Rice

Ground

Cereal E

Rice

Flake

Cereal F

Wheat/Rice

Crushed

Fe (μg/g) 375 ± 35 697 ± 65 439 ± 50 461 ± 42 332 ± 31 347 ± 69

Zn (μg/g) 590 ± 5 674 ± 3 647 ± 25 23 ± 3 21 ± 1 319 ± 7

89
Figure Z. A consensus plot summarizing your individual results (Lab Code: E530)

How to interpret your consensus summary plot:

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

•moderate precision

•agrees with consensus 

(-3 < ranking < 3)

•wide range = relatively poor precision

•biased high, relative to consensus

red symbols represent 

consensus difference ≥ 6 (or ≤ -6)

symbols without range bars represent nearly equivalent values 

(i.e., very good precision) for the triplicate measurements

•narrow range = better precision

•biased low, relative to consensus

solitary red symbols signify an entire

consensus difference ≥ 6 (or ≤ -6)

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

•moderate precision

•agrees with consensus 

(-3 < ranking < 3)

•wide range = relatively poor precision

•biased high, relative to consensus

red symbols represent 

consensus difference ≥ 6 (or ≤ -6)

symbols without range bars represent nearly equivalent values 

(i.e., very good precision) for the triplicate measurements

•narrow range = better precision

•biased low, relative to consensus

solitary red symbols signify an entire

consensus difference ≥ 6 (or ≤ -6)

90
Part II. Your Individual Laboratory Results (Lab Code: E531)

Your laboratory’s data is summarized in Table Z. The mean (average) ± 1 standard deviation were 

determined from the reported triplicate (n=3) values for each of the 18 measurements (Fe, Ca and Zn 

within the six study materials, Cereals A-F) in Exercise E. 

Your laboratory’s summary consensus plot for Fe, Ca and Zn in the six cereal study materials is 

provided in Figure Z. The data have been normalized relative to consensus means and Horn-HornDuncan (HHD) uncertainties so that the consensus value is equal to zero. The thick blue line in this

plot represents the consensus values for each of the 18 measurements (Fe, Ca and Zn within the six 

study materials, Cereals A-F). The thin blue lines represent ± 3 HHD standard uncertainty intervals 

about the consensus values. The figure is scaled so that the top and bottom of the Y-axis represent ± 6 

HHD intervals. Your laboratory’s results for each of the 18 measurements are illustrated by the black 

bars. The ends of bars that are entirely within the ± 6 HHD intervals are marked with an open circle 

(); red circles () indicate that some or all of the bar is outside the ± 6 HHD interval. 

The length of each bar indicates how well your measurements agree with themselves. The distance 

from the center of the bars to the consensus line indicates how well your measurements agree with 

those of the other participants in this study. (An example consensus plot with explanations is also 

included to aid in the interpretation your results.) As a general rule, we consider results that fall within 

± 3 HHD standard uncertainty lines to be within consensus (approximate 99% confidence limit) and 

results that have a black bar length ≈ 3 HHD units are considered as acceptable precision. If values are 

consistently very high or low for a particular element, then a calibration problem may exist. In such 

cases, it is important to make sure your calibration standards are from a reliable source, the quality is 

confirmed and that your calibration solutions are correctly prepared and stored. In addition, calibration 

points must be linear in the expected measurement range and closely surround expected values. 

Many of your laboratory’s measurement results are rather imprecise (bar lengths of more than 3 HHD 

units). This imprecision may in part be related to your processing the materials after subsampling. 

You may want to investigate the use of subsampling and processing procedures that can more 

uniformly capture the bulk characteristics of the sampled materials (i.e. process entire sample before 

subsampling for analysis). Such imprecision for both ground and flake materials however may also 

suggest an incomplete digestion of samples.

Table Z. Summary of Fe, Ca and Zn values within the six study materials, Cereals A-F

Lab Code: E531 Mean Results ± 1 SD (n = 3)

Cereal A

Wheat

Ground

(SRM 3233)

Cereal B

Wheat

Ground

Cereal C

Wheat

Flake

Cereal D

Rice

Ground

Cereal E

Rice

Flake

Cereal F

Wheat/Rice

Crushed

Fe (μg/g) 773 ± 29 823 ± 87 817 ± 12 513 ± 21 500 ± 61 707 ± 35

Ca (μg/g) 38 910 ± 3290 37 240 ± 2620 37 870 ± 2140 263 ± 23 213 ± 23 18 010 ± 1210

Zn (μg/g) 677 ± 42 793 ± 40 683 ± 55 20 ± 0 20 ± 0 427 ± 21

91
Figure Z. A consensus plot summarizing your individual results (Lab Code: E531)

How to interpret your consensus summary plot:

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

•moderate precision

•agrees with consensus 

(-3 < ranking < 3)

•wide range = relatively poor precision

•biased high, relative to consensus

red symbols represent 

consensus difference ≥ 6 (or ≤ -6)

symbols without range bars represent nearly equivalent values 

(i.e., very good precision) for the triplicate measurements

•narrow range = better precision

•biased low, relative to consensus

solitary red symbols signify an entire

consensus difference ≥ 6 (or ≤ -6)

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

•moderate precision

•agrees with consensus 

(-3 < ranking < 3)

•wide range = relatively poor precision

•biased high, relative to consensus

red symbols represent 

consensus difference ≥ 6 (or ≤ -6)

symbols without range bars represent nearly equivalent values 

(i.e., very good precision) for the triplicate measurements

•narrow range = better precision

•biased low, relative to consensus

solitary red symbols signify an entire

consensus difference ≥ 6 (or ≤ -6)

92
Part II. Your Individual Laboratory Results (Lab Code: E533)

Your laboratory’s data is summarized in Table Z. The mean (average) ± 1 standard deviation were 

determined from the reported triplicate (n=3) values for each of the 18 measurements (Fe, Ca and Zn 

within the six study materials, Cereals A-F) in Exercise E. 

Your laboratory’s summary consensus plot for Fe, Ca and Zn in the six cereal study materials is 

provided in Figure Z. The data have been normalized relative to consensus means and Horn-HornDuncan (HHD) uncertainties so that the consensus value is equal to zero. The thick blue line in this

plot represents the consensus values for each of the 18 measurements (Fe, Ca and Zn within the six 

study materials, Cereals A-F). The thin blue lines represent ± 3 HHD standard uncertainty intervals 

about the consensus values. The figure is scaled so that the top and bottom of the Y-axis represent ± 6 

HHD intervals. Your laboratory’s results for each of the 18 measurements are illustrated by the black 

bars. The ends of bars that are entirely within the ± 6 HHD intervals are marked with an open circle 

(); red circles () indicate that some or all of the bar is outside the ± 6 HHD interval. 

The length of each bar indicates how well your measurements agree with themselves. The distance 

from the center of the bars to the consensus line indicates how well your measurements agree with 

those of the other participants in this study. (An example consensus plot with explanations is also 

included to aid in the interpretation your results.) As a general rule, we consider results that fall within 

± 3 HHD standard uncertainty lines to be within consensus (approximate 99% confidence limit) and 

results that have a black bar length ≈ 3 HHD units are considered as acceptable precision. If values are 

consistently very high or low for a particular element, then a calibration problem may exist. In such 

cases, it is important to make sure your calibration standards are from a reliable source, the quality is 

confirmed and that your calibration solutions are correctly prepared and stored. In addition, calibration 

points must be linear in the expected measurement range and closely surround expected values. 

Many of your laboratory’s measurement results agree reasonably well with the consensus means, 

indicating that your measurement processes are adequately calibrated. However, the precision of your 

measurement processes is quite variable – ranging from quite good (bar lengths of 1 HHD unit) to 

quite poor (bars longer than 6 HHD units). In combination with somewhat inconsistent results for the 

flake/crush wheat (B & C) and rice (D & E) pairs, this suggests that your sample processing methods 

may not be consistently providing representative subsamples and/or that your sample digestion is not 

exhaustive.

Table Z. Summary of Fe, Ca and Zn values within the six study materials, Cereals A-F

Lab Code: E531 Mean Results ± 1 SD (n = 3)

Cereal A

Wheat

Ground

(SRM 3233)

Cereal B

Wheat

Ground

Cereal C

Wheat

Flake

Cereal D

Rice

Ground

Cereal E

Rice

Flake

Cereal F

Wheat/Rice

Crushed

Fe (μg/g) 690 ± 20 753 ± 29 793 ± 6 460 ± 10 467 ± 12 583 ± 32

Ca (μg/g) 37 530 ± 250 35 100 ± 170 35 430 ± 720 233 ± 12 217 ± 6 16 400 ± 2800

Zn (μg/g) 573 ± 6 650 ± 36 707 ± 21 30 ± 0 30 ± 0 327 ± 50

93
Figure Z. A consensus plot summarizing your individual results (Lab Code: E533)

How to interpret your consensus summary plot:

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

•moderate precision

•agrees with consensus 

(-3 < ranking < 3)

•wide range = relatively poor precision

•biased high, relative to consensus

red symbols represent 

consensus difference ≥ 6 (or ≤ -6)

symbols without range bars represent nearly equivalent values 

(i.e., very good precision) for the triplicate measurements

•narrow range = better precision

•biased low, relative to consensus

solitary red symbols signify an entire

consensus difference ≥ 6 (or ≤ -6)

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

•moderate precision

•agrees with consensus 

(-3 < ranking < 3)

•wide range = relatively poor precision

•biased high, relative to consensus

red symbols represent 

consensus difference ≥ 6 (or ≤ -6)

symbols without range bars represent nearly equivalent values 

(i.e., very good precision) for the triplicate measurements

•narrow range = better precision

•biased low, relative to consensus

solitary red symbols signify an entire

consensus difference ≥ 6 (or ≤ -6)

94
Part II. Your Individual Laboratory Results (Lab Code: E534)

Your laboratory’s data is summarized in Table Z. The mean (average) ± 1 standard deviation were 

determined from the reported triplicate (n=3) values for each of the 18 measurements (Fe, Ca and Zn 

within the six study materials, Cereals A-F) in Exercise E. 

Your laboratory’s summary consensus plot for Fe, Ca and Zn in the six cereal study materials is 

provided in Figure Z. The data have been normalized relative to consensus means and Horn-HornDuncan (HHD) uncertainties so that the consensus value is equal to zero. The thick blue line in this

plot represents the consensus values for each of the 18 measurements (Fe, Ca and Zn within the six 

study materials, Cereals A-F). The thin blue lines represent ± 3 HHD standard uncertainty intervals 

about the consensus values. The figure is scaled so that the top and bottom of the Y-axis represent ± 6 

HHD intervals. Your laboratory’s results for each of the 18 measurements are illustrated by the black 

bars. The ends of bars that are entirely within the ± 6 HHD intervals are marked with an open circle 

(); red circles () indicate that some or all of the bar is outside the ± 6 HHD interval. 

The length of each bar indicates how well your measurements agree with themselves. The distance 

from the center of the bars to the consensus line indicates how well your measurements agree with 

those of the other participants in this study. (An example consensus plot with explanations is also 

included to aid in the interpretation your results.) As a general rule, we consider results that fall within 

± 3 HHD standard uncertainty lines to be within consensus (approximate 99% confidence limit) and 

results that have a black bar length ≈ 3 HHD units are considered as acceptable precision. If values are 

consistently very high or low for a particular element, then a calibration problem may exist. In such 

cases, it is important to make sure your calibration standards are from a reliable source, the quality is 

confirmed and that your calibration solutions are correctly prepared and stored. In addition, calibration 

points must be linear in the expected measurement range and closely surround expected values. 

Your laboratory’s mean measurement values for Fe, Ca and Zn in the ground and flake wheat (B & C) 

and rice (D & E) cereal pairs agree fairly well and many of your measurement processes are adequately 

precise (bar lengths less than 3 HHD units), indicating a fairly consistent sample preparation process. 

Your results for Fe are consistently higher than the consensus means and the majority of Zn results are 

somewhat low; you may want to check your calibration standards for these elements. While your 

results for the relatively low-Ca content rice materials (D & E) agree well with the consensus values, 

your results for the relatively high-Ca wheat materials (A, B & C) are a bit high. These results suggest 

that you may not be adequately matching sample mass fractions to the linear range of the calibration 

curve. It is important to prepare samples dilutions to have appropriate concentration levels and to use 

enough calibration points to adequately cover the expected concentration range.

Table Z. Summary of Fe, Ca and Zn values within the six study materials, Cereals A-F

Lab Code: E534 Mean Results ± 1 SD (n = 3)

Cereal A

Wheat

Ground

(SRM 3233)

Cereal B

Wheat

Ground

Cereal C

Wheat

Flake

Cereal D

Rice

Ground

Cereal E

Rice

Flake

Cereal F

Wheat/Rice

Crushed

Fe (μg/g) 849 ± 32 880 ± 30 900 ± 11 540 ± 17 537 ± 19 730 ± 26

Ca (μg/g) 39 700 ± 530 37 000 ± 1310 37 370 ± 970 224 ± 19 217 ± 13 20670 ± 1300

Zn (μg/g) 582 ± 4 622 ± 16 601 ± 16 17 ± 1 17 ± 1 358 ± 31

95
Figure Z. A consensus plot summarizing your individual results (Lab Code: E534)

How to interpret your consensus summary plot:

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

•moderate precision

•agrees with consensus 

(-3 < ranking < 3)

•wide range = relatively poor precision

•biased high, relative to consensus

red symbols represent 

consensus difference ≥ 6 (or ≤ -6)

symbols without range bars represent nearly equivalent values 

(i.e., very good precision) for the triplicate measurements

•narrow range = better precision

•biased low, relative to consensus

solitary red symbols signify an entire

consensus difference ≥ 6 (or ≤ -6)

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

•moderate precision

•agrees with consensus 

(-3 < ranking < 3)

•wide range = relatively poor precision

•biased high, relative to consensus

red symbols represent 

consensus difference ≥ 6 (or ≤ -6)

symbols without range bars represent nearly equivalent values 

(i.e., very good precision) for the triplicate measurements

•narrow range = better precision

•biased low, relative to consensus

solitary red symbols signify an entire

consensus difference ≥ 6 (or ≤ -6)

96
Part II. Your Individual Laboratory Results (Lab Code: E537)

Your laboratory’s data is summarized in Table Z. The mean (average) ± 1 standard deviation were 

determined from the reported triplicate (n=3) values for each of the 18 measurements (Fe, Ca and Zn 

within the six study materials, Cereals A-F) in Exercise E. 

Your laboratory’s summary consensus plot for Fe, Ca and Zn in the six cereal study materials is 

provided in Figure Z. The data have been normalized relative to consensus means and Horn-HornDuncan (HHD) uncertainties so that the consensus value is equal to zero. The thick blue line in this

plot represents the consensus values for each of the 18 measurements (Fe, Ca and Zn within the six 

study materials, Cereals A-F). The thin blue lines represent ± 3 HHD standard uncertainty intervals 

about the consensus values. The figure is scaled so that the top and bottom of the Y-axis represent ± 6 

HHD intervals. Your laboratory’s results for each of the 18 measurements are illustrated by the black 

bars. The ends of bars that are entirely within the ± 6 HHD intervals are marked with an open circle 

(); red circles () indicate that some or all of the bar is outside the ± 6 HHD interval. 

The length of each bar indicates how well your measurements agree with themselves. The distance 

from the center of the bars to the consensus line indicates how well your measurements agree with 

those of the other participants in this study. (An example consensus plot with explanations is also 

included to aid in the interpretation your results.) As a general rule, we consider results that fall within 

± 3 HHD standard uncertainty lines to be within consensus (approximate 99% confidence limit) and 

results that have a black bar length ≈ 3 HHD units are considered as acceptable precision. If values are 

consistently very high or low for a particular element, then a calibration problem may exist. In such 

cases, it is important to make sure your calibration standards are from a reliable source, the quality is 

confirmed and that your calibration solutions are correctly prepared and stored. In addition, calibration 

points must be linear in the expected measurement range and closely surround expected values. 

Your laboratory’s measurement results agree modestly well with the consensus values and are 

relatively precise (many of the bars are less than 2 HHD units long), indicating that your measurement 

processes are adequately calibrated and fairly consistent within each material. However, while your 

mean results for all three elements for the rice ground and flake cereal pair (D & E) are quite similar, 

your results for Ca in the wheat ground and flake pair (B & C) are significantly different. Given the 

Ca measurement precision in the high-Ca wheat materials (A, B & C) is much poorer than in the rice 

materials (D & E), this may indicate that you are not adequately matching sample mass fractions to the 

linear range of the calibration curve. It is important to prepare samples to have appropriate 

concentration levels and to use enough calibration points to adequately cover the expected 

concentration range.

Table Z. Summary of Fe, Ca and Zn values within the six study materials, Cereals A-F

Lab Code: E537 Mean Results ± 1 SD (n = 3)

Cereal A

Wheat

Ground

(SRM 3233)

Cereal B

Wheat

Ground

Cereal C

Wheat

Flake

Cereal D

Rice

Ground

Cereal E

Rice

Flake

Cereal F

Wheat/Rice

Crushed

Fe (μg/g) 716 ± 8 783 ± 19 746 ± 14 517 ± 9 513 ± 5 627 ± 17

Ca (μg/g) 40 620 ± 970 34 170 ± 780 37 850 ± 760 176 ± 8 171 ± 3 17 360 ± 230

Zn (μg/g) 619 ± 3 660 ± 8 653 ± 11 20 ± 0.3 20 ± 0.3 310 ± 12

97
Figure Z. A consensus plot summarizing your individual results (Lab Code: E537)

How to interpret your consensus summary plot:

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

•moderate precision

•agrees with consensus 

(-3 < ranking < 3)

•wide range = relatively poor precision

•biased high, relative to consensus

red symbols represent 

consensus difference ≥ 6 (or ≤ -6)

symbols without range bars represent nearly equivalent values 

(i.e., very good precision) for the triplicate measurements

•narrow range = better precision

•biased low, relative to consensus

solitary red symbols signify an entire

consensus difference ≥ 6 (or ≤ -6)

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

•moderate precision

•agrees with consensus 

(-3 < ranking < 3)

•wide range = relatively poor precision

•biased high, relative to consensus

red symbols represent 

consensus difference ≥ 6 (or ≤ -6)

symbols without range bars represent nearly equivalent values 

(i.e., very good precision) for the triplicate measurements

•narrow range = better precision

•biased low, relative to consensus

solitary red symbols signify an entire

consensus difference ≥ 6 (or ≤ -6)

98
Part II. Your Individual Laboratory Results (Lab Code: E538)

Your laboratory’s data is summarized in Table Z. The mean (average) ± 1 standard deviation were 

determined from the reported triplicate (n=3) values for each of the 18 measurements (Fe, Ca and Zn 

within the six study materials, Cereals A-F) in Exercise E. 

Your laboratory’s summary consensus plot for Fe, Ca and Zn in the six cereal study materials is 

provided in Figure Z. The data have been normalized relative to consensus means and Horn-HornDuncan (HHD) uncertainties so that the consensus value is equal to zero. The thick blue line in this

plot represents the consensus values for each of the 18 measurements (Fe, Ca and Zn within the six 

study materials, Cereals A-F). The thin blue lines represent ± 3 HHD standard uncertainty intervals 

about the consensus values. The figure is scaled so that the top and bottom of the Y-axis represent ±

6 HHD intervals. Your laboratory’s results for each of the 18 measurements are illustrated by the 

black bars. The ends of bars that are entirely within the ± 6 HHD intervals are marked with an open 

circle (); red circles () indicate that some or all of the bar is outside the ± 6 HHD interval. 

The length of each bar indicates how well your measurements agree with themselves. The distance 

from the center of the bars to the consensus line indicates how well your measurements agree with 

those of the other participants in this study. (An example consensus plot with explanations is also 

included to aid in the interpretation your results.) As a general rule, we consider results that fall 

within ± 3 HHD standard uncertainty lines to be within consensus (approximate 99% confidence

limit) and results that have a black bar length ≈ 3 HHD units are considered as acceptable precision. 

If values are consistently very high or low for a particular element, then a calibration problem may 

exist. In such cases, it is important to make sure your calibration standards are from a reliable source, 

the quality is confirmed and that your calibration solutions are correctly prepared and stored. In 

addition, calibration points must be linear in the expected measurement range and closely surround 

expected values. 

Your laboratory’s measurement values for Zn are on average consistent with the consensus results; 

however your Fe results are consistently rather low. The precision of your measurement processes 

for all three elements is quite variable, ranging from good (bar lengths of 2 HHD units or less) to 

quite poor (bar lengths greater than 4 HHD units). This suggests that your sample preparation 

processes are inconsistent and your sample digestion process may not always be complete. You may 

want to investigate preparing samples from a larger subsample mass: the 1 g you reported using is 

small relative to that of other participants.

Table Z. Summary of Fe, Ca and Zn values within the six study materials, Cereals A-F

Lab Code: E538 Mean Results ± 1 SD (n = 3)

Cereal A

Wheat

Ground

(SRM 3233)

Cereal B

Wheat

Ground

Cereal C

Wheat

Flake

Cereal D

Rice

Ground

Cereal E

Rice

Flake

Cereal F

Wheat/Rice

Crushed

Fe (μg/g) 477 ± 79 556 ± 107 561 ± 110 440 ± 54 459 ± 26 524 ± 49

Ca (μg/g) 36 602 ± 1530 34 320 ± 1440 34 970 ± 1480 1248 ± 314 960 ± 435 19 440 ± 1760

Zn (μg/g) 577 ± 23 620 ± 17 627 ± 28 21 ± 1 20 ± 1 392 ± 34

99
Figure Z. A consensus plot summarizing your individual results (Lab Code: E538)

How to interpret your consensus summary plot:

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

•moderate precision

•agrees with consensus 

(-3 < ranking < 3)

•wide range = relatively poor precision

•biased high, relative to consensus

red symbols represent 

consensus difference ≥ 6 (or ≤ -6)

symbols without range bars represent nearly equivalent values 

(i.e., very good precision) for the triplicate measurements

•narrow range = better precision

•biased low, relative to consensus

solitary red symbols signify an entire

consensus difference ≥ 6 (or ≤ -6)

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

•moderate precision

•agrees with consensus 

(-3 < ranking < 3)

•wide range = relatively poor precision

•biased high, relative to consensus

red symbols represent 

consensus difference ≥ 6 (or ≤ -6)

symbols without range bars represent nearly equivalent values 

(i.e., very good precision) for the triplicate measurements

•narrow range = better precision

•biased low, relative to consensus

solitary red symbols signify an entire

consensus difference ≥ 6 (or ≤ -6)

100
Part II. Your Individual Laboratory Results (Lab Code: E539)

Your laboratory’s data is summarized in Table Z. The mean (average) ± 1 standard deviation were 

determined from the reported triplicate (n=3) values for each of the 18 measurements (Fe, Ca and Zn 

within the six study materials, Cereals A-F) in Exercise E. 

Your laboratory’s summary consensus plot for Fe, Ca and Zn in the six cereal study materials is 

provided in Figure Z. The data have been normalized relative to consensus means and Horn-HornDuncan (HHD) uncertainties so that the consensus value is equal to zero. The thick blue line in this

plot represents the consensus values for each of the 18 measurements (Fe, Ca and Zn within the six 

study materials, Cereals A-F). The thin blue lines represent ± 3 HHD standard uncertainty intervals 

about the consensus values. The figure is scaled so that the top and bottom of the Y-axis represent ±

6 HHD intervals. Your laboratory’s results for each of the 18 measurements are illustrated by the 

black bars. The ends of bars that are entirely within the ± 6 HHD intervals are marked with an open 

circle (); red circles () indicate that some or all of the bar is outside the ± 6 HHD interval. 

The length of each bar indicates how well your measurements agree with themselves. The distance 

from the center of the bars to the consensus line indicates how well your measurements agree with 

those of the other participants in this study. (An example consensus plot with explanations is also 

included to aid in the interpretation your results.) As a general rule, we consider results that fall 

within ± 3 HHD standard uncertainty lines to be within consensus (approximate 99% confidence 

limit) and results that have a black bar length ≈ 3 HHD units are considered as acceptable precision. 

If values are consistently very high or low for a particular element, then a calibration problem may 

exist. In such cases, it is important to make sure your calibration standards are from a reliable source, 

the quality is confirmed and that your calibration solutions are correctly prepared and stored. In 

addition, calibration points must be linear in the expected measurement range and closely surround 

expected values. 

Your laboratory’s measurement results agree modestly well with the consensus values and are 

relatively precise (many of the bars are less than 2 HHD units long), indicating that your 

measurement processes are adequately calibrated and fairly consistently applied within each material. 

However, the extremely long bar for Fe in material D reflects an unusually large difference among 

the replicates and suggests that the consistency of your processes could be improved. Your results 

for the low-Ca rice ground and flake pair (D & E) differ significantly for Ca and somewhat for Zn. 

This suggests that you may not be adequately matching the sample mass fractions to the linear range 

of the calibration curve. It is important to prepare samples to have appropriate concentration levels 

and to use calibration points that cover the expected concentration range.

Table Z. Summary of Fe, Ca and Zn values within the six study materials, Cereals A-F

Lab Code: E539 Mean Results ± 1 SD (n = 3)

Cereal A

Wheat

Ground

(SRM 3233)

Cereal B

Wheat

Ground

Cereal C

Wheat

Flake

Cereal D

Rice

Ground

Cereal E

Rice

Flake

Cereal F

Wheat/Rice

Crushed

Fe (μg/g) 782 ± 11 855 ± 15 850 ± 40 513 ± 62 571 ± 35 734 ± 14

Ca (μg/g) 36 700 ± 460 34 930 ± 990 35 500 ± 610 154 ± 17 390 ± 91 19 730 ± 1440

Zn (μg/g) 613 ± 1 684 ± 7 702 ± 27 19 ± 1 25 ± 1 416 ± 34

101
Figure Z. A consensus plot summarizing your individual results (Lab Code: E539)

How to interpret your consensus summary plot:

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

•moderate precision

•agrees with consensus 

(-3 < ranking < 3)

•wide range = relatively poor precision

•biased high, relative to consensus

red symbols represent 

consensus difference ≥ 6 (or ≤ -6)

symbols without range bars represent nearly equivalent values 

(i.e., very good precision) for the triplicate measurements

•narrow range = better precision

•biased low, relative to consensus

solitary red symbols signify an entire

consensus difference ≥ 6 (or ≤ -6)

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

•moderate precision

•agrees with consensus 

(-3 < ranking < 3)

•wide range = relatively poor precision

•biased high, relative to consensus

red symbols represent 

consensus difference ≥ 6 (or ≤ -6)

symbols without range bars represent nearly equivalent values 

(i.e., very good precision) for the triplicate measurements

•narrow range = better precision

•biased low, relative to consensus

solitary red symbols signify an entire

consensus difference ≥ 6 (or ≤ -6)

102
Part II. Your Individual Laboratory Results (Lab Code: E540)

Your laboratory’s data is summarized in Table Z. The mean (average) ± 1 standard deviation were 

determined from the reported triplicate (n=3) values for each of the 18 measurements (Fe, Ca and Zn 

within the six study materials, Cereals A-F) in Exercise E. 

Your laboratory’s summary consensus plot for Fe, Ca and Zn in the six cereal study materials is 

provided in Figure Z. The data have been normalized relative to consensus means and Horn-HornDuncan (HHD) uncertainties so that the consensus value is equal to zero. The thick blue line in this

plot represents the consensus values for each of the 18 measurements (Fe, Ca and Zn within the six 

study materials, Cereals A-F). The thin blue lines represent ± 3 HHD standard uncertainty intervals 

about the consensus values. The figure is scaled so that the top and bottom of the Y-axis represent ± 6 

HHD intervals. Your laboratory’s results for each of the 18 measurements are illustrated by the black 

bars. The ends of bars that are entirely within the ± 6 HHD intervals are marked with an open circle 

(); red circles () indicate that some or all of the bar is outside the ± 6 HHD interval. 

The length of each bar indicates how well your measurements agree with themselves. The distance 

from the center of the bars to the consensus line indicates how well your measurements agree with 

those of the other participants in this study. (An example consensus plot with explanations is also 

included to aid in the interpretation your results.) As a general rule, we consider results that fall within 

± 3 HHD standard uncertainty lines to be within consensus (approximate 99% confidence limit) and 

results that have a black bar length ≈ 3 HHD units are considered as acceptable precision. If values are 

consistently very high or low for a particular element, then a calibration problem may exist. In such 

cases, it is important to make sure your calibration standards are from a reliable source, the quality is 

confirmed and that your calibration solutions are correctly prepared and stored. In addition, calibration 

points must be linear in the expected measurement range and closely surround expected values. 

Your laboratory’s measurement results for Fe in all materials and Ca and Zn in the wheat-based 

materials (A, B &C) agree fairly well the consensus means. However, your results for both Ca and Zn 

in the rice-based cereal pair (D & E) are a factor of two higher than the consensus values. Such 

significant differences may indicate a sample dilution, calibration, data evaluation, or transcription 

error. The mean values for all elements in both the ground and flake wheat (B & C) and rice (D & E) 

cereal pairs agree well and the precision of all your measurement processes is quite good (bar lengths 

of 2 HHD units are less), both indicating that your sample preparation and analysis are quite consistent.

Table Z. Summary of Fe, Ca and Zn values within the six study materials, Cereals A-F

Lab Code: E540 Mean Results ± 1 SD (n = 3)

Cereal A

Wheat

Ground

(SRM 3233)

Cereal B

Wheat

Ground

Cereal C

Wheat

Flake

Cereal D

Rice

Ground

Cereal E

Rice

Flake

Cereal F

Wheat/Rice

Crushed

Fe (μg/g) 790 ± 26 847 ± 15 857 ± 12 557 ± 12 543 ± 6 707 ± 15

Ca (μg/g) 37 130 ± 380 34 230 ± 250 34 800 ± 350 460 ± 20 440 ± 10 18 270 ± 150

Zn (μg/g) 653 ± 12 707 ± 6 713 ± 6 38 ± 2 41 ± 5 417 ± 6

103
Figure Z. A consensus plot summarizing your individual results (Lab Code: E540)

How to interpret your consensus summary plot:

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

•moderate precision

•agrees with consensus 

(-3 < ranking < 3)

•wide range = relatively poor precision

•biased high, relative to consensus

red symbols represent 

consensus difference ≥ 6 (or ≤ -6)

symbols without range bars represent nearly equivalent values 

(i.e., very good precision) for the triplicate measurements

•narrow range = better precision

•biased low, relative to consensus

solitary red symbols signify an entire

consensus difference ≥ 6 (or ≤ -6)

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

•moderate precision

•agrees with consensus 

(-3 < ranking < 3)

•wide range = relatively poor precision

•biased high, relative to consensus

red symbols represent 

consensus difference ≥ 6 (or ≤ -6)

symbols without range bars represent nearly equivalent values 

(i.e., very good precision) for the triplicate measurements

•narrow range = better precision

•biased low, relative to consensus

solitary red symbols signify an entire

consensus difference ≥ 6 (or ≤ -6)

104
Part II. Your Individual Laboratory Results (Lab Code: E541)

Your laboratory’s data is summarized in Table Z. The mean (average) ± 1 standard deviation were 

determined from the reported triplicate (n=3) values for each of the 18 measurements (Fe, Ca and Zn 

within the six study materials, Cereals A-F) in Exercise E. 

Your laboratory’s summary consensus plot for Fe, Ca and Zn in the six cereal study materials is 

provided in Figure Z. The data have been normalized relative to consensus means and Horn-HornDuncan (HHD) uncertainties so that the consensus value is equal to zero. The thick blue line in this

plot represents the consensus values for each of the 18 measurements (Fe, Ca and Zn within the six 

study materials, Cereals A-F). The thin blue lines represent ± 3 HHD standard uncertainty intervals 

about the consensus values. The figure is scaled so that the top and bottom of the Y-axis represent ± 6 

HHD intervals. Your laboratory’s results for each of the 18 measurements are illustrated by the black 

bars. The ends of bars that are entirely within the ± 6 HHD intervals are marked with an open circle 

(); red circles () indicate that some or all of the bar is outside the ± 6 HHD interval. 

The length of each bar indicates how well your measurements agree with themselves. The distance 

from the center of the bars to the consensus line indicates how well your measurements agree with 

those of the other participants in this study. (An example consensus plot with explanations is also 

included to aid in the interpretation your results.) As a general rule, we consider results that fall within 

± 3 HHD standard uncertainty lines to be within consensus (approximate 99% confidence limit) and 

results that have a black bar length ≈ 3 HHD units are considered as acceptable precision. If values are 

consistently very high or low for a particular element, then a calibration problem may exist. In such 

cases, it is important to make sure your calibration standards are from a reliable source, the quality is 

confirmed and that your calibration solutions are correctly prepared and stored. In addition, calibration 

points must be linear in the expected measurement range and closely surround expected values. 

Your laboratory’s measurement results for Fe agree well with the consensus means and are quite 

precise (bars are mostly less than 2 HHD units long). Your Zn results are also precise in all materials, 

however the values for the relatively high-Zn wheat-based materials (A, B & C) are somewhat low. 

Your Ca results show the opposite effect, where your results for the high-Ca content wheat-based 

materials are somewhat high. These results suggest that you may not be adequately matching of 

sample mass fractions to the linear range of the calibration curve. The points on your calibration curve 

extend quite high which would cause possible saturation or a flattening of the linear regression line at 

the upper points of the curve leading to unreliable results. It is important to prepare samples and 

calibration points to have appropriate concentration levels and to have enough calibration points to 

adequately cover the expected concentration range.

Table Z. Summary of Fe, Ca and Zn values within the six study materials, Cereals A-F

Lab Code: E540 Mean Results ± 1 SD (n = 3)

Cereal A

Wheat

Ground

(SRM 3233)

Cereal B

Wheat

Ground

Cereal C

Wheat

Flake

Cereal D

Rice

Ground

Cereal E

Rice

Flake

Cereal F

Wheat/Rice

Crushed

Fe (μg/g) 706 ± 7 779 ± 8 800 ± 2 508 ± 13 501 ± 12 685 ± 7

Ca (μg/g) 40 240 ± 940 37 810 ± 300 39 920 ± 530 235 ± 40 295 ± 63 25 930 ± 5250

Zn (μg/g) 553 ± 2 610 ± 1 624 ± 2 19 ± 1 19 ± 2 358 ± 5

105
Figure Z. A consensus plot summarizing your individual results (Lab Code: E541)

How to interpret your consensus summary plot:

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

•moderate precision

•agrees with consensus 

(-3 < ranking < 3)

•wide range = relatively poor precision

•biased high, relative to consensus

red symbols represent 

consensus difference ≥ 6 (or ≤ -6)

symbols without range bars represent nearly equivalent values 

(i.e., very good precision) for the triplicate measurements

•narrow range = better precision

•biased low, relative to consensus

solitary red symbols signify an entire

consensus difference ≥ 6 (or ≤ -6)

A B C D E F A B C D E F A B C D E F

Fe Ca Zn

-6

-3

0

3

6

Difference from Consensus

Cereal:

Element:

•moderate precision

•agrees with consensus 

(-3 < ranking < 3)

•wide range = relatively poor precision

•biased high, relative to consensus

red symbols represent 

consensus difference ≥ 6 (or ≤ -6)

symbols without range bars represent nearly equivalent values 

(i.e., very good precision) for the triplicate measurements

•narrow range = better precision

•biased low, relative to consensus

solitary red symbols signify an entire

consensus difference ≥ 6 (or ≤ -6)

106