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Combining Soft Computing and Statistical Methods in Data Analysis pp 475–482Cite as

Two-Way Analysis of Variance for Interval-Valued Data

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Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 77))

Abstract

We establish two-way analysis of variance (ANOVA) for interval-valued data. Each observation is assumed to be a compact convex interval, and the two-way ANOVA determines whether to reject null hypotheses about the effects of two factors on the observed intervals. The Minkowski support function is used to obtain a metric for intervals and to transform them to Hilbert-space-valued functions. We derive test statistics that are appropriate for testing the null hypotheses, and we develop a bootstrap scheme for approximating the p-values of the observed test statistics.

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Author information

Authors and Affiliations

  1. European Center for Soft Computing, Edificio Científico-Technológico, 33600, Mieres, Spain

    Takehiko Nakama

  2. Departamento de Estadística, I.O. y D.M., Universidad de Oviedo, 33007, Oviedo, Spain

    Ana Colubi & M. Asunción Lubiano

Authors
  1. Takehiko Nakama
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  2. Ana Colubi
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  3. M. Asunción Lubiano
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Editor information

Editors and Affiliations

  1. Research Unit on Intelligent Data Analysis and Graphical Models, European Centre for Soft Computing Edificio Científico-Tecnológico. 3a Planta, C/ Gonzalo Gutiérrez Quirós s/n, 33600, Mieres, Spain

    Christian Borgelt , Gil González-Rodríguez  & Wolfgang Trutschnig ,  & 

  2. Departamento de Estadística e I.O. y D.M., Universidad de Oviedo, Facultad de Ciencias, C/ Calvo Sotelo s/n, 33007, Oviedo, Spain

    María Asunción Lubiano

  3. Departamento de Estadística e I.O. yD.M., Universidad de Oviedo, Facultad de Ciencias, C/ Calvo Sotelo s/n, 33007, Oviedo, Spain

    María Ángeles Gil

  4. Systems Research Institute, Polish Academy of Sciences, Newelska 6, 01-447, Warsaw, Poland

    Przemysław Grzegorzewski

  5. Systems Research Institute, Polish Academy of Science, Newelska 6, 01-447, Warsaw, Poland

    Olgierd Hryniewicz

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Nakama, T., Colubi, A., Lubiano, M.A. (2010). Two-Way Analysis of Variance for Interval-Valued Data. In: Borgelt, C., et al. Combining Soft Computing and Statistical Methods in Data Analysis. Advances in Intelligent and Soft Computing, vol 77. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14746-3_59

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  • DOI: https://doi.org/10.1007/978-3-642-14746-3_59

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14745-6

  • Online ISBN: 978-3-642-14746-3

  • eBook Packages: EngineeringEngineering (R0)

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