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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.
Acknowledgements
The author thanks the referees for their constructive suggestions and comments, which improved the presentation of this work.
Disclosure statement
No potential conflict of interest was reported by the author.
Additional information
Notes on contributors
Gholamreza Hesamian
Gholamreza Hesamian was born in 1977 in Esfahan, Iran. He received his BSc (2001) and MSc (2004) both in statistics from Isfahan University and Isfahan University of Technology in Iran, respectively, and his PhD (2012) in statistics from Isfahan University of Technology in Iran. He is now a assistant professor in the Department of Statistics at Payame Noor University in Iran. His current interest includes fuzzy mathematics, especially on statistics and probability.