Abstract

A novel parametric hypothesis test of equality of two mean intervals for p-dimensional interval-valued datasets is proposed. An orthogonal transformation is applied to obtain an equivalent hypothesis test of p-dimensional mean intervals for two interval-valued datasets in terms of normal p-dimensional vector of mid-points and log-normal p-dimensional vector of ranges. The variance-covariance matrices of the vector of mid-points and the vector of ranges are not calculated from the mid-points and mid-ranges, but from the orthogonally transformed vectors. Our proposed method for the hypothesis testing of two mean intervals for p-dimensional interval-valued datasets is comprised of an exact test (normal data: using Hotelling’s T-squared distribution) and a generalized pivotal test (log-normal data: using a Monte Carlo simulation) that works for small interval-valued datasets. Robustness of our method is shown through simulation study. The performance of the proposed test is illustrated with two real-life examples.