Fuzzy Statistical Inference for Managing Imprecision in Hypothesis Testing An Empirical Study of Medical Samples

Abstract

This study addresses the limitations of traditional statistical hypothesis testing, which relies on binary decision-making (accept/reject) and may not adequately represent the uncertainty inherent in real-world clinical data. To overcome these limitations, a fuzzy statistical framework is proposed by incorporating the concepts of possibility and necessity into the decision-making process. The proposed approach employs membership functions to replace rigid decision boundaries with necessary and possible acceptance/rejection regions, allowing more gradual and flexible statistical decisions. In addition, the study represents observations using hybrid numbers that integrate both randomness and imprecision, providing a more realistic representation of uncertain clinical phenomena.For empirical evaluation, real medical data collected from Mosul General Hospital were analyzed. The Z-test for two proportions and the one-sample t-test were implemented using both classical and fuzzy approaches, and their results were comparatively examined. The findings showed general consistency between the classical and fuzzy methods in cases characterized by clear statistical evidence. Moreover, the results demonstrated that the fuzzy expanstion coefficient η influences the width of the acceptance and rejection regions and consequently affects the associated fuzzy error measures, provided an improved balance between decision flexibility and statistical precision within the analyzed data. Overall, the proposed fuzzy approach offers a more flexible and interpretable framework for statistical inference and may provide practical advantages when dealing with uncertain medical datasets