Introduction
The NIST Consensus Builder (NICOB) serves to combine measurement results obtained by different laboratories or by application of different measurement methods, into a consensus estimate of the value of a scalar measurand. The NICOB qualifies the consensus estimate with an evaluation of measurement uncertainty that captures not only the stated uncertainties associated with the individual measured values, but also any additional component of uncertainty that manifests itself only when these measured values are intercompared.
In addition, the NICOB can also report the differences between the individual measured values and the consensus value, and the differences between pairs of values measured by different laboratories or methods, in both cases qualifying these differences with evaluations of associated uncertainty. In the context of Key Comparisons, these differences and associated uncertainties are called (unilateral, and bilateral, respectively) Degrees of Equivalence (DoE) (Comité International des Poids et Mesures (CIPM), 1999).
When the reported measurement uncertainties associated with the individual measured values are qualified with the numbers of degrees of freedom that they are based on, these numbers are taken into account as well. In general, the numbers of degrees of freedom convey the reliability of the evaluations of measurement uncertainty, expressing the extent of the underlying evidentiary basis, be it the size of the experimental data or the strength of other information used when producing the evaluations.
For more information see the User's Manual.Quick Start
Enter Data

Labels designating the n participating laboratories (required — character strings comprised of letters or numbers, separated from one another by commas)

Measured values x_{1},..., x_{n} produced by n different laboratories or measurement methods, independently of one another (required — numbers separated by commas)

Measurement units to qualify the numerical values of the measured values which are used to label axes of plots (optional — character string)

Standard uncertainties u_{1},..., u_{n} associated with the measured values (required — positive numbers separated by commas)

Numbers of degrees of freedom ν_{1},..., ν_{n} that the standard uncertainties are based on (optional — positive numbers separated by commas)

Coverage probability (positive number between 0 and 1) desired for the coverage intervals (required, default: 0.95).

Indication, by means of a checkbox, of whether degrees of equivalence should be computed (default: Not computed).

Indication, by means of a radio button, of whether degrees of equivalence should be computed as defined in the MRA or based on leaveoneout estimates.

Number of bootstrap replicates for degrees of equivalence uncertainty calculation. This is only used for the DerSimonianLaird procedure (default: 10000); the Hierarchical Bayes and Linear Pool procedures use for this number the sample sizes of their method specific inputs.
If this box is checked, the following additional inputs appear:
Buttons at the bottom of the Enter data page allow the user to load and save configuration files with inputs for the NICOB. Clicking the button labeled Save Configuration File downloads a plain text file named consensus.ncb to the local machine, which specifies the current inputs for the NICOB. To use a previously saved configuration file, search for and select the file using the Browse button.
Alternatively, the NICOB also accepts configuration files with inputs specified as comma separated values and extensions .ncb, .csv, or .txt. Each row of the file designates data from a different laboratory or measurement method, and the file can have two, three, or four comma separated columns. For each row, data should by entered in the order: name (if available), measured value, standard uncertainty, and number of degrees of freedom (if available; missing or infinite degrees of freedom should be entered as Inf).
Choose a method for analysis
The three methods of data reduction implemented in the NICOB are not meant to be interchangeable, and the user should consider their characteristics, including advantages and disadvantages, to determine which may be best fit for the purpose that the results of the data reduction are intended to serve.
For more information see the User's Manual.
For the DerSimonianLaird procedure:
– If the KnappHartung adjustment is desired, check the corresponding box;
– To apply the parametric bootstrap for uncertainty evaluation, check the corresponding box. This reveals an input field for the desired number of bootstrap replicates (Suggested value: 10000).

For the hierarchical Bayesian procedure:
– Positive numbers in the corresponding boxes which are used as the medians of the prior distributions for the betweenlaboratory and for the withinlaboratory (or, betweenmethod and withinmethod) variance components (default: robust indications of spread of the measured values for the betweenlaboratory variability, and for the laboratoryspecific uncertainty)
– Total number of iterations for the Markov Chain Monte Carlo sampler (default: 250000).
– Length of burnin for the Markov chain, which is the number of values discarded from the beginning of the realization of the chain (default: 50000).
– Thinning rate for the Markov chain (default value is 25, meaning that only every 25th value generated in the chain should be kept).

For the Linear Pool:
– Weights (nonnegative numbers separated by commas) to be associated with the different measurement results (default: 1 for all).
– Size of sample drawn from the mixture distribution of the measurand (default: 100000).
Output

Consensus estimate, associated standard uncertainty, and coverage interval for the true value of the measurand;

If degrees of equivalence were requested, then estimates, standard uncertainties, and expanded uncertainties for differences between measured values and the consensus value, and between pairs of measured values are reported and depicted graphically.
List laboratory labels, measured values, standard uncertainties, and (if available) numbers of degrees of freedom, separated by commas.
Degrees of equivalence
Fit laboratory effects model using DerSimonianLaird procedure
DerSimonianLaird
The consensus estimate is:
The standard uncertainty is:
The dark uncertainty (tau) is:
Download plotParametric bootstrap for uncertainty evaluation
The standard uncertainty is:
The coverage interval ranges from:
Download bootstrap output
Unilateral degrees of equivalence
Download unilateral DoE plotBilateral degrees of equivalence
Yellow squares (with black asterisks in the center) indicate results that differ significantly from 0 at 95% coverage. Light blue squares indicate results that do not differ significantly at 95% coverage. Dark squares are spacefillers for results when compared to themselves. Download bilateral DoE plotFit using Bayesian method with weakly informative priors
Default is the median of the absolute values of the differences between the measured values and their median Default is the median of the labspecific standard uncertaintiesBayesian procedure
Assuming weakly informative prior distributions and allowing for uncertainty in standard uncertainties
The consensus estimate is:
The standard uncertainty is:
The credible interval ranges from:
The dark uncertainty (tau) is:
Download MCMC output Download plot
Unilateral degrees of equivalence
Download unilateral DoE plot
Bilateral degrees of equivalence
Yellow squares (with black asterisks in the center) indicate results that differ significantly from 0 at 95% coverage. Light blue squares indicate results that do not differ significantly at 95% coverage. Dark squares are spacefillers for results when compared to themselves. Download bilateral DoE plotLinear opinion pooling
Linear opinion pooling
The consensus estimate is:
The standard uncertainty is:
The coverage interval ranges from:
Download linear pool output Download plot