Neutrosophic Chi-Square Test for Analyzing Population Variances with Uncertain Data

• Published in: Journal of statistical theory and practice Vol. 19; no. 2
• Main Author: Aslam, Muhammad
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.06.2025
• Subjects: Mathematics and Statistics; Original Article; Probability Theory and Stochastic Processes; Statistical Theory and Methods; Statistics; Hypothesis testing; Power of the test; Incomplete data; Statistical analysis; Neutrosophic theory
• ISSN: 1559-8608; 1559-8616
• DOI: 10.1007/s42519-025-00436-4

The existing test for population variances under classical statistics assumes complete certainty and does not account for uncertainty. To address this limitation, we propose a novel statistical methodology for testing population variances in the presence of incomplete or uncertain data. Incorporating neutrosophic theory, which effectively addresses indeterminacy, this approach overcomes the limitations of traditional chi-square tests that rely solely on crisp data. By combining neutrosophic concepts with the chi-square statistic, the proposed method effectively handles uncertain data, offering a more realistic representation of uncertainty. This paper outlines the steps for implementing the neutrosophic chi-square test, including calculating the neutrosophic chi-square statistic and determining critical values for hypothesis testing. Power analysis reveals that as the degree of indeterminacy increases, the power of the test decreases. The method demonstrates clear advantages over traditional approaches, handling imprecise data and providing richer information. Empirical studies validate its effectiveness, highlighting its potential to enhance statistical analysis and hypothesis testing in uncertain contexts. The neutrosophic chi-square test offers significant benefits and potential applications in domains where uncertainty is prevalent.