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Analysis of short-term systematic measurement error variance for the difference of paired data without repetition of measurement

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Abstract

The variance of short-term systematic measurement errors for the difference of paired data is estimated. The difference of paired data is determined by subtracting the measurement results of two methods, which measure the same item only once without measurement repetition. The unbiased estimators for short-term systematic measurement error variances based on the one-way random effects model are not fit for practical purpose because they can be negative. The estimators, which are derived for balanced data as well as for unbalanced data, are always positive but biased. The basis of these positive estimators is the one-way random effects model. The biases, variances, and the mean squared errors of the positive estimators are derived as well as their estimators. The positive estimators are fit for practical purpose.

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References

  1. Bennett, C.A., Franklin, N.L. (1954) Statistical Analysis in Chemistry and the Chemical Industry. Exxon Monograph. Wiley, New York

    Google Scholar 

  2. Cochran, W.G. (1934) The distribution of quadratic forms in a normal system. Proceedings of the Cambridge Philosophical Society, Suppl. 4, 102–104

    Google Scholar 

  3. Graybill, F.A. (1961) An Introduction to Linear Statistical Models. Vol. 1. McGraw-Hill, New York

    MATH  Google Scholar 

  4. Hartung, J. (1998) Schätzen der Varianzkomponenten bei gepaarten Messungen ohne Wiederholungen (“zerstörende Prüfungen”) in K Gruppen. Unpublished results based on a research contract financed by the European Union (EU), Luxembourg (1998)

  5. Hartung, J. (1999) Ordnungserhaltende positive Varianzschätzer bei gepaarten Messungen ohne Wiederholungen. Allgemeines Statistisches Archiv 83, 230–247

    Google Scholar 

  6. Hartung, J. (2005) Statistik, Lehr- und Handbuch der angewandten Statistik. 14. Auflage, R. Oldenburg, München, Vienna

    Google Scholar 

  7. International Atomic Energy Agency (IAEA) STR-327 (2001) Department of Safeguards: International Target Values 2000 for Measurements Uncertainties in Safeguarding Nuclear Materials. Vienna, Austria

  8. Martin, K., Böckenhoff, A. (2006) Analysis of paired data without repetition of measurement. Allgemeines Statistisches Archiv 90, 365–384

    Article  MATH  Google Scholar 

  9. Rao, P.S.R.S. (1997) Variance Components Estimation. Mixed Models, Methodologies and Applications. Exxon Monograph, Chapman & Hall, London

    Google Scholar 

  10. Scheffé, H. (1959) The Analysis of Variance. Exxon Monograph, Wiley, New York

    Google Scholar 

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Authors and Affiliations

  1. Südallee 59, 54290, Trier, Germany

    Klaus Martin

  2. Fachbereich Statistik, Universität Dortmund, 44221, Dortmund, Germany

    Annette Böckenhoff

Authors
  1. Klaus Martin
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  2. Annette Böckenhoff
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Correspondence to Klaus Martin.

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Martin, K., Böckenhoff, A. Analysis of short-term systematic measurement error variance for the difference of paired data without repetition of measurement . AStA 91, 291–310 (2007). https://doi.org/10.1007/s10182-007-0036-z

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  • DOI: https://doi.org/10.1007/s10182-007-0036-z

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