The modified sign test under indeterminacy with application to COVID-19 data

The sign test is a non-parametric method for assessing median differences in paired observations, especially when parametric assumptions (e.g., normality for paired t-tests) are violated. However, its conventional form is limited to exact categorical data (binary/ordinal) and cannot handle interval-valued data (measurements expressed as ranges), restricting its use in cases of imprecise, vague, or indeterminate observations. To address this gap, we propose a modified neutrosophic sign test that incorporates indeterminacy, enabling analysis of interval-valued data for both one-sample and two-sample hypothesis testing under uncertainty. We validate its efficacy through two real-world case studies: (1) assessing COVID-19 reproduction rates to evaluate transmission dynamics and (2) analyzing daily ICU occupancy trends for COVID-19-positive patients in Pakistan. These applications highlight its adaptability in public health scenarios with data variability. Results confirm that the neutrosophic sign test effectively resolves nonparametric decision-making problems involving interval data, providing robust statistical insights in fields like engineering, biological sciences, and public health—where indeterminate data are common. By accommodating imprecision, this approach enhances the traditional sign test's versatility, making it a practical tool for modern statistical analysis in complex, uncertain environments.