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Statistical hypothesis testing has traditionally relied on point-null hypotheses, which posit that a parameter takes an exact numerical value (e.g., H 0 : μ = μ 0). Despite their foundational role in methods such as Fisherian significance testing and Neyman–Pearson hypothesis testing, point-null hypotheses have attracted significant criticism for their unrealistic and overly restrictive assumptions (Savage, The Foundations of Statistics. Wiley, Hoboken, 1954; Meehl, Philosophy Sci 34(2):103–115, 1967; Cohen, Am Psychol 45(12):1304–1312, 1990; Berger and Delampady, Stat Sci 2(3):317–335, 1987). Specifically, it has been argued that exact equality rarely, if ever, holds true in practical scientific investigations, making the strict formulation of a point-null hypothesis practically meaningless (Savage, J Am Stat Assoc 52(279):331–344, 1957; Nunnally, Educ Psychol Measure 20(4):641–650, 1960; Kadane, Stat Sci 2(3):347–348, 1987; Berger and Delampady, Stat Sci 2(3):317–335, 1987).

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Rao–Lovric Theorem and the Paradigm Shift in Hypothesis Testing

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  • 发表日期：

    2025年

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  • Miodrag Lovric

摘要

Statistical hypothesis testing has traditionally relied on point-null hypotheses, which posit that a parameter takes an exact numerical value (e.g., H 0 : μ = μ 0). Despite their foundational role in methods such as Fisherian significance testing and Neyman–Pearson hypothesis testing, point-null hypotheses have attracted significant criticism for their unrealistic and overly restrictive assumptions (Savage, The Foundations of Statistics. Wiley, Hoboken, 1954; Meehl, Philosophy Sci 34(2):103–115, 1967; Cohen, Am Psychol 45(12):1304–1312, 1990; Berger and Delampady, Stat Sci 2(3):317–335, 1987). Specifically, it has been argued that exact equality rarely, if ever, holds true in practical scientific investigations, making the strict formulation of a point-null hypothesis practically meaningless (Savage, J Am Stat Assoc 52(279):331–344, 1957; Nunnally, Educ Psychol Measure 20(4):641–650, 1960; Kadane, Stat Sci 2(3):347–348, 1987; Berger and Delampady, Stat Sci 2(3):317–335, 1987).