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Robust Statistics

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  • Gather, Ursula
  • Davies, P. Laurie

Abstract

The first example involves the real data given in Table 1 which are the results of an interlaboratory test. The boxplots are shown in Fig. 1 where the dotted line denotes the mean of the observations and the solid line the median. We note that only the results of the Laboratories 1 and 3 lie below the mean whereas all the remaining laboratories return larger values. In the case of the median, 7 of the readings coincide with the median, 24 readings are smaller and 24 are larger. A glance at Fig. 1 suggests that in the absence of further information the Laboratories 1 and 3 should be treated as outliers. This is the course which we recommend although the issues involved require careful thought. For the moment we note simply that the median is a robust statistic whereas the mean is not.

Suggested Citation

  • Gather, Ursula & Davies, P. Laurie, 2004. "Robust Statistics," Papers 2004,20, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    • Handle: RePEc:zbw:caseps:200420
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    References listed on IDEAS

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    6. Barme-Delcroix, Marie-Francoise & Gather, Ursula, 2000. "An isobar-surfaces approach to multidimensional outlier-proneness," Technical Reports 2000,20, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
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    Cited by:

    1. Sonja Kuhnt, 2010. "Breakdown concepts for contingency tables," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 71(3), pages 281-294, May.

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