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. 1982 Sep-Oct;87(5):377-385.
doi: 10.6028/jres.087.022.

Consensus Values and Weighting Factors

Robert C Paule  1 , John Mandel  1
Affiliations

Consensus Values and Weighting Factors

Robert C Paule et al. J Res Natl Bur Stand (1977). 1982 Sep-Oct.

Abstract

A method is presented for the statistical analysis of sets of data which are assembled from multiple experiments. The analysis recognizes the existence of both within group and between group variabilities, and calculates appropriate weighting factors based on the observed variability for each group. The weighting factors are used to calculate a "best" consensus value from the overall experiment. The technique for obtaining the consensus value is applicable to either the determination of the weighted average value, or to the parameters associated with a weighted least squares regression problem. The calculations are made by using an iterative technique with a truncated Taylor series expansion. The calculations are straightforward, and are easily programmed on a desktop computer. An examination of the observed variabilities, both within groups and between groups, leads to considerable insight into the overall experiment and greatly aids in the design of future experiments.

Keywords: ANOVA (within-between); components of variance; consensus values; design of experiments; pooling of variance; weighted average; weighted least squares regression.

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References

    1. Birge R. T., The Calculation of Errors by the Method of Least Squares, Phys. Rev., 40, 207–227 (1932).
    1. Mandel J. and Paule R. C., Interlaboratory Evaluation of a Material with Unequal Numbers of Replicates, Anal. Chem., 42, 1194–7 (1970), and Correction, Anal. Chem., 43, 1287 (1971).
    1. Cochran W. G., The Combination of Estimates from Different Experiments, Biometrics, 10,101–29 (1954).
    1. Youden W. J., Enduring Values, Technometrics, 14, 1–11 (1972).
    1. Paule R. C. and Mandel J., Analysis of Interlaboratory Measurements on the Vapor Pressure of Cadmium and Silver, NBS Special Publication; 260–21 (1971).

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