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Critical values of Mandel’s h and k, the Grubbs and the Cochran test statistic

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Abstract

According to ISO 5725-2 (1994), measurement results obtained in an interlaboratory experiment are inspected for consistency by plotting Mandel’s h and k statistics and for outliers by application of the Grubbs test and the Cochran test. Critical values of these statistics for significance levels α=5% and α=1% and for some numbers p of laboratories and n of repeated measurements in the laboratories are supplied in ISO 5725-2 without reference to methods for their calculation. In this paper, exact formulae for the critical values of Mandel’s h and k and approximate formulae for the critical values of the Single Grubbs test, the Double Grubbs test and the Cochran test are derived.

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References

  • Cochran, W.G.: The distribution of the largest of a set of estimated variances as a fraction of their total. Ann. Eugen. 11, 47–52 (1941)

    Article  MathSciNet  Google Scholar 

  • Eisenhart, Ch., Solomon, H.: Significance of the largest of a set of sample estimates of variance. In: Eisenhart, C., Hastay, M.W., Wallis, W.A. (eds.) Selected techniques of statistical analysis, pp. 390–391. McGraw-Hill, New York (1947)

    Google Scholar 

  • Grubbs, F.E.: Sample criteria for testing outlying observations. Ann. Math. Stat. 21, 27–58 (1950)

    Article  MathSciNet  MATH  Google Scholar 

  • Grubbs, F.E., Beck, G.: Extension of sample sizes and percentage points for significance tests of outlying observations. Technometrics 14, 847–854 (1972)

    Article  MathSciNet  Google Scholar 

  • Hawkins, D.M.: Identification of Outliers. Chapman and Hall, London (1980)

    MATH  Google Scholar 

  • ISO 5725-2: Accuracy (trueness and precision) of measurement methods and results—Part 2: Basic method for the determination of repeatability and reproducibility of a standard measurement method. International Organization for Standardization, Geneva (1994)

  • Mandel, J.: A new analysis of interlaboratory test results. In: ASQC Quality Congress Transaction—Baltimore, pp. 360–366 (1985)

    Google Scholar 

  • Mood, A.M., Graybill, F.A., Boes, D.C.: Introduction to the Theory of Statistics. McGraw-Hill, Tokyo (1974)

    MATH  Google Scholar 

  • Thompson, W.R.: On a criterion for the rejection of observations and the distribution of the ratio of the derivation to the sample standard deviation. Ann. Math. Stat. 6, 214–219 (1935)

    Article  Google Scholar 

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  1. Institut für Statistik und Ökonometrie, Freie Universität Berlin, Garystrasse 21, 14195, Berlin, Germany

    Peter-T. Wilrich

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  1. Peter-T. Wilrich
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Correspondence to Peter-T. Wilrich.

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Wilrich, PT. Critical values of Mandel’s h and k, the Grubbs and the Cochran test statistic. AStA Adv Stat Anal 97, 1–10 (2013). https://doi.org/10.1007/s10182-011-0185-y

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  • DOI: https://doi.org/10.1007/s10182-011-0185-y

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