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On Statistical Methods for Common Mean and Reference Confidence Intervals in Interlaboratory Comparisons for Temperature

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Abstract

We consider a problem of constructing the exact and/or approximate coverage intervals for the common mean of several independent distributions. In a metrological context, this problem is closely related to evaluation of the interlaboratory comparison experiments, and in particular, to determination of the reference value (estimate) of a measurand and its uncertainty, or alternatively, to determination of the coverage interval for a measurand at a given level of confidence, based on such comparison data. We present a brief overview of some specific statistical models, methods, and algorithms useful for determination of the common mean and its uncertainty, or alternatively, the proper interval estimator. We illustrate their applicability by a simple simulation study and also by example of interlaboratory comparisons for temperature. In particular, we shall consider methods based on (i) the heteroscedastic common mean fixed effect model, assuming negligible laboratory biases, (ii) the heteroscedastic common mean random effects model with common (unknown) distribution of the laboratory biases, and (iii) the heteroscedastic common mean random effects model with possibly different (known) distributions of the laboratory biases. Finally, we consider a method, recently suggested by Singh et al., for determination of the interval estimator for a common mean based on combining information from independent sources through confidence distributions.

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Acknowledgments

We would like to thank the editors and anonymous reviewers for their valuable suggestions which helped significantly to improve the quality of the presented material. The work was supported by the Slovak Research and Development Agency, Grant APVV-0096-10, and by the Scientific Grant Agency of the Ministry of Education of the Slovak Republic and the Slovak Academy of Sciences, Grants VEGA 2/0047/15 and VEGA 1/0604/15.

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Authors and Affiliations

  1. Institute of Measurement Science, Slovak Academy of Sciences, Dúbravská cesta 9, 841 04, Bratislava, Slovak Republic

    Viktor Witkovský

  2. Faculty of Natural Sciences, Matej Bel University, Tajovského 40, 947 01, Banská Bystrica, Slovak Republic

    Gejza Wimmer

  3. Mathematical Institute, Slovak Academy of Sciences, Bratislava, Slovak Republic

    Gejza Wimmer

  4. Faculty of Mechanical Engineering of the Slovak University of Technology, Námestie Slobody 17, 812 31, Bratislava, Slovak Republic

    Stanislav Ďuriš

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  1. Viktor Witkovský
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Correspondence to Viktor Witkovský.

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Witkovský, V., Wimmer, G. & Ďuriš, S. On Statistical Methods for Common Mean and Reference Confidence Intervals in Interlaboratory Comparisons for Temperature. Int J Thermophys 36, 2150–2171 (2015). https://doi.org/10.1007/s10765-015-1917-0

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