A Bootstrap Factorial ANOVA for Random Intervals

An ANOVA problem for interval-valued experimental data is considered. When a random variable is observed on several populations, the ANOVA technique focuses on testing whether the variable behaves significantly different on those groups. The theoretical formalization of the three-way ANOVA problem when the random element takes on interval values is shown. Since no distribution assumptions for interval-valued variables are established, a bootstrap technique for the statistical resolution of the inferential study is developed and implemented. The theoretical validity of the procedure is guaranteed from previous results, and its empirical behaviour is shown with a case study.

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