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One-way ANOVA based on interval information

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  • Gholamreza Hesamian

Abstract

This paper deals with extending the one-way analysis of variance (ANOVA) to the case where the observed data are represented by closed intervals rather than real numbers. In this approach, first a notion of interval random variable is introduced. Especially, a normal distribution with interval parameters is introduced to investigate hypotheses about the equality of interval means or test the homogeneity of interval variances assumption. Moreover, the least significant difference (LSD method) for investigating multiple comparison of interval means is developed when the null hypothesis about the equality of means is rejected. Then, at a given interval significance level, an index is applied to compare the interval test statistic and the related interval critical value as a criterion to accept or reject the null interval hypothesis of interest. Finally, the method of decision-making leads to some degrees to accept or reject the interval hypotheses. An applied example will be used to show the performance of this method.

Suggested Citation

  • Gholamreza Hesamian, 2016. "One-way ANOVA based on interval information," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(11), pages 2682-2690, August.
    • Handle: RePEc:taf:tsysxx:v:47:y:2016:i:11:p:2682-2690
    DOI: 10.1080/00207721.2015.1014449
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    References listed on IDEAS

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    1. Gil, Maria Angeles & Montenegro, Manuel & Gonzalez-Rodriguez, Gil & Colubi, Ana & Rosa Casals, Maria, 2006. "Bootstrap approach to the multi-sample test of means with imprecise data," Computational Statistics & Data Analysis, Elsevier, vol. 51(1), pages 148-162, November.
    2. González-Rodríguez, Gil & Colubi, Ana & Gil, María Ángeles, 2012. "Fuzzy data treated as functional data: A one-way ANOVA test approach," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 943-955.
    3. M. Nourbakhsh & M. Mashinchi & A. Parchami, 2013. "Analysis of variance based on fuzzy observations," International Journal of Systems Science, Taylor & Francis Journals, vol. 44(4), pages 714-726.
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