Combining information from interlaboratory evaluations using a random effects model

This paper compares leading methods for combining information from interlaboratory evaluations of a common measurand through a random effects model of classical statistics. The leading methods are those of Cochran, Paule and Mandel, and DerSimonian and Laird. We show that all three methods are special cases of a unifying identity. The unifying identity suggests a new two-step method. This makes four methods for comparison. The comparison is based on six published data sets from three key comparisons. The method of Paule and Mandel is optimal in the sense of being conditionally restricted maximum likelihood under normality, the condition being that the estimated intralaboratory variances be treated as the true variances. The method of Paule and Mandel requires a simple iteration that can be easily done on a spreadsheet program. Therefore, it is the preferred method for combining results of interlaboratory evaluations through a random effects model. We compare the other three methods relative to the method of Paule and Mandel. The two-step method approximates the optimal method of Paule and Mandel better than the earlier methods of Cochran, and DerSimonian and Laird.