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The Fuzzy Approach to Assessment of ANOVA Results

  • Jacek PietraszekEmail author
  • Maciej Kołomycki
  • Agnieszka Szczotok
  • Renata Dwornicka
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9875)

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.

Keywords

Analysis of variance ANOVA Alpha-cuts Fuzzy numbers Fuzzy statistics Materials science Bootstrap 

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Jacek Pietraszek
    • 1
    Email author
  • Maciej Kołomycki
    • 1
  • Agnieszka Szczotok
    • 2
  • Renata Dwornicka
    • 1
  1. 1.Department of Software Engineering and Applied StatisticsCracow University of TechnologyKrakówPoland
  2. 2.Institute of Materials Science, Faculty of Materials Science and MetallurgySilesian University of TechnologyKatowicePoland

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