Two-way analysis of variance for interval-valued data

Abstract

We establish two-way analysis of variance (ANOVA) for interval-valued data. Each observation is assumed to be a compact convex interval, and the two-way ANOVA determines whether to reject null hypotheses about the effects of two factors on the observed intervals. The Minkowski support function is used to obtain a metric for intervals and to transform them to Hilbert-space-valued functions. We derive test statistics that are appropriate for testing the null hypotheses, and we develop a bootstrap scheme for approximating the p-values of the observed test statistics. © 2010 Springer-Verlag Berlin Heidelberg.