An Extended One-Way ANOVA Algorithm for Analyzing Interval-Valued Experiments

Single factor (one-way) analysis of variance (ANOVA) has been very broadly applied in analyzing experimental data with categorical treatments. Datasets to be analyzed with ANOVA have been point-valued mostly. Because data observed from experiments often contain interval uncertainty, researchers have studied ANOVA for interval-valued observations lately. The strategies include separately applying point-valued ANOVA to the lower bound, upper bound, midpoint, and radius of an interval-valued dataset; and then combine them with fuzzy numbers to make an inference. In contrast, we take a different approach in this work. With the notion of distance between two intervals, we extend one-way ANOVA from point-valued to interval-valued observations naturally. To clarify randomness, normality, and homogeneity of interval-valued data, we apply point-valued statistic and probabilistic measures for interval-valued observations. Our approach can be easily implemented with available software packages to carry out Fisher's test. Practitioners can apply it directly without previous knowledge on fuzzy logic and interval computing. Computational experiment presented in this paper demonstrates some advantages of this novel approach.