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The Levenson et al. (BOB) Method: Bound on Bias

The point of departure for a new method of consensus mean/uncertainty estimation, proposed by Levenson et al. at NIST [18], is to note that the intent of using multiple methods is to quantify systematic effects (biases) of individual methods by using the variation across the multiple methods results. However, if the number of methods is small--two to four, as is the case here--then the sample standard deviation of the method means will be a poor estimator of the uncertainty of the systematic effects. To overcome this, this method uses a Type B model [19] for the uncertainty of the systematic effects. In practice, a uniform distribution, bounded by the range of method results, has been found to be effective as a Type B model. Variants of the method make explicit use of intermethod bias (or bias squared), computed as the difference between the largest group mean and smallest group mean or between the largest and grand average of the group means [20], as a proxy for between-method variance. Here we explicitly combine in quadrature an estimate of within-method variation obtained by pooling the standard errors associated with each method with an estimate of between-method variation obtained by dividing half the max-mean minus the min-mean range by the square root of three to convert to a Uniform standard error.