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The Fuzzy Approach to Assessment of ANOVA Results

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Computational Collective Intelligence (ICCCI 2016)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9875))

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Abstract

Typically, the analysis of variance (ANOVA) is used to compare means in the subsets obtained through the division of a large numerical dataset by assigning a categorical variable labels to dataset’s values. The test criterion for the decision on ‘all equal’ vs. ‘not all equal’ is a comparison of the significance level described by a well-known p-value and the a priori assigned critical significance level, α, usually 0.05. This comparison is treated very strictly basing on the crisp value; however, it should not be so, especially if p-value is near α, because the certainty of the decision varies rather smoothly from ‘strongly not’ to ‘no opinion’ to ‘strongly yes’. It is very interesting to analyze such results on the basis of the fuzzy arithmetic theory, using the modified Buckley’s fuzzy approach to the statistics combined with the bootstrap approach, because it may be adopted to the cases where subjective assessments are introduced as quasi-measurements.

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Authors and Affiliations

  1. Department of Software Engineering and Applied Statistics, Cracow University of Technology, Al. Jana Pawla II 37, 31-864, Kraków, Poland

    Jacek Pietraszek, Maciej Kołomycki & Renata Dwornicka

  2. Institute of Materials Science, Faculty of Materials Science and Metallurgy, Silesian University of Technology, ul. Krasinskiego 8, 40-019, Katowice, Poland

    Agnieszka Szczotok

Authors
  1. Jacek Pietraszek
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  2. Maciej Kołomycki
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  3. Agnieszka Szczotok
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  4. Renata Dwornicka
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Corresponding author

Correspondence to Jacek Pietraszek .

Editor information

Editors and Affiliations

  1. Wrocław University of Technology, Wrocław, Poland

    Ngoc-Thanh Nguyen

  2. Aristotle University of Thessaloniki, Thessaloniki, Greece

    Lazaros Iliadis

  3. Department of Forestry and Management, Democritus University of Thrace, Orestiada, Thrace, Greece

    Yannis Manolopoulos

  4. Wrocław University of Technology, Wrocław, Poland

    Bogdan Trawiński

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Pietraszek, J., Kołomycki, M., Szczotok, A., Dwornicka, R. (2016). The Fuzzy Approach to Assessment of ANOVA Results. In: Nguyen, NT., Iliadis, L., Manolopoulos, Y., Trawiński, B. (eds) Computational Collective Intelligence. ICCCI 2016. Lecture Notes in Computer Science(), vol 9875. Springer, Cham. https://doi.org/10.1007/978-3-319-45243-2_24

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  • DOI: https://doi.org/10.1007/978-3-319-45243-2_24

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-45242-5

  • Online ISBN: 978-3-319-45243-2

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