Bayesian Posterior Predictive p-value of Statistical Consistency in Interlaboratory Evaluations

Published

September 17, 2008

Author(s)

Raghu N. Kacker, Alistair Forbes, Ruediger Kessel, K D. Sommer

Abstract

Results from an interlaboratory evaluation are said to be statistically consistent if they fit a normal (Gaussian) consistency model which postulates that the results have the same unknown expected value and stated variances and covariances. We propose the use of Bayesian posterior predictive checking to check the fit of the normal consistency model to interlaboratory results. If the model fits, then the results may be regarded as consistent. We discuss a general measure of discrepancy for checking the consistency of interlaboratory results. We also discuss two sets of unilateral and bilateral measures of discrepancy. The degree of agreement is quantified by the Bayesian posterior predictive p-value of discrepancy measures. We suggest that the posterior predicative p-values may be used to define the degrees of equivalence in International Committee of Weights and Measures (CIPM) key comparisons.

Citation

Metrologia

Volume

45

Pub Type

Journals

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Keywords

Bayesian model checking, Interlaboratory comparisons

Citation

Kacker, R. , Forbes, A. , Kessel, R. and Sommer, K. (2008), Bayesian Posterior Predictive p-value of Statistical Consistency in Interlaboratory Evaluations, Metrologia, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=150672 (Accessed October 27, 2025)