The Mann-Whitney Test for Interval-Valued Data

Przemysław Grzegorzewski, Martyna Śpiewak

2018 W: Advances in Fuzzy Logic and Technology 2017 : Proceedings of: EUSFLAT- 2017 – The 10th Conference of the European Society for Fuzzy Logic and Technology, September 11-15, 2017, Warsaw, Poland IWIFSGN’2017 – The Sixteenth International Workshop on Intuitionistic Fuzzy Sets and Generalized Nets, September 13-15, 2017, Warsaw, Poland, Volume 2 / Janusz Kacprzyk, Eulalia Szmidt, Sławomir Zadrożny, Krassimir T. Atanassov, Maciej Krawczak;Cham: Springer, s. 188-199

The Mann-Whitney test for the two-sample 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.