The Fuzzy Approach to Assessment of ANOVA Results
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.
KeywordsAnalysis of variance ANOVA Alpha-cuts Fuzzy numbers Fuzzy statistics Materials science Bootstrap
- 9.Grzegorzewski, P.: Decision Support Under Uncertainty. Statistical Methods for Imprecise Data. EXIT, Warszawa (2006)Google Scholar
- 10.Pietraszek, J.: Fuzzy regression compared to classical experimental design in the case of flywheel assembly. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2012, Part I. LNCS, vol. 7267, pp. 310–317. Springer, Heidelberg (2012)CrossRefGoogle Scholar
- 12.Pietraszek, J.: The modified sequential-binary approach for fuzzy operations on correlated assessments. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2013, Part I. LNCS, vol. 7894, pp. 353–364. Springer, Heidelberg (2013)CrossRefGoogle Scholar