Two-Sample Median Test for Interval-Valued Data

Przemysław Grzegorzewski, Martyna Śpiewak

2021 W.: Uncertainty and Imprecision in Decision Making and Decision Support: New Challenges, Solutions and Perspectives : Selected Papers from BOS-2018, held on September 24-26, 2018, and IWIFSGN-2018, held on September 27-28, 2018 in Warsaw, Poland / Krassimir T. Atanassov, Vassia Atanassova, Janusz Kacprzyk, Andrzej Kaluszko, Maciej Krawczak, Jan W. Owsinski, Sotir Sotirov, Evdokia Sotirova, Eulalia Szmidt, Slawomir Zadrozny. Cham : Springer, s. 113-128.

The median two-sample test for the location problem is considered. We adopt this nonparametric test to interval-valued data perceived from the epistemic perspective, where the available observations are just interval-valued perceptions of the unknown true outcomes of the experiment. Unlike typical generalizations of statistical procedures into the interval-valued framework, the proposed test entails very low computational costs. However, the presence of interval-valued data results in set-valued p-value which leads no longer to a definite binary decision (reject or not reject the null hypothesis) but may indicate the abstention from making a final decision if the information is too vague.