A Neutrosophic Framework for Resolving Statistical Paradoxes and Hypothesis Ambiguities in University Music Programs Teaching Quality Evaluation

Abstract

Traditional statistical methods often fail to capture contradictions and 
uncertainties inherent in real-world educational data. In the context of university teaching 
evaluation, it is common to encounter paradoxes  such as differing student ratings across 
time slots or class sections  that invalidate simple statistical conclusions. This paper 
proposes a novel framework based on Neutrosophic Probability and Logic to 
systematically detect and resolve such contradictions. We introduce the Neutrosophic 
Statistical Paradox Resolution Model (NSPRM) and the Neutrosophic Hypothesis 
Resolution Framework (NHRF), which respectively quantify inconsistency in descriptive 
statistics and uncertainty in hypothesis testing outcomes. Each statistical statement is 
redefined using a neutrosophic triplet: the degree of truth, indeterminacy, and falsity, 
allowing the formulation of a Triple-State Hypothesis Evaluation method that replaces 
binary decisions with a more nuanced spectrum. The framework is applied to real-world
inspired data from student evaluations of university music instructors, highlighting how 
traditional significance tests can fail under data fragmentation and contradiction. A series 
of detailed equations, mathematical proofs, and numeric examples is presented to validate 
the proposed methodology. The results demonstrate the capacity of the neutrosophic 
approach to provide robust, contradiction-aware insights in educational quality analysis.

DOI: 10.5281/zenodo.16754559