Statistical Hypothesis Testing: A Comprehensive Review of Theory, Methods, and Applications

Statistical hypothesis testing is a foundational concept in inferential statistics, providing formal mechanisms for evaluating evidence and making decisions. This review article provides a comprehensive overview of the principles of hypothesis testing, including classical frameworks such as the Neyman–Pearson paradigm and Fisher’s significance testing, as well as modern perspectives including Bayesian approaches, robust testing, and high-dimensional inference. The article synthesizes key theoretical underpinnings, outlines commonly used statistical tests, and discusses methodological challenges and criticisms. Applications across various fields—ranging from medicine and economics to machine learning and psychology—are reviewed to demonstrate the versatility and evolving role of hypothesis testing in contemporary research. Finally, current debates and future research directions are highlighted, emphasizing the need for more robust, transparent, and reproducible statistical practices.