Confusion Over Measures of Evidence (p's) Versus Errors (α's) in Classical Statistical Testing

By R. Hubbard, Maria J. Bayarri, Thomas F. Sheehan, Scott Armstrong, James O. Berger, S. Goodman, Rahul Parsa. 2003

278 citations recorded by the source corpus.

Subfields: Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/67fd52280af7d0b42f79f5564a3bb9247b509eaf

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Citations in the corpus

The need for Bayesian hypothesis testing in psychological science (2017, background): “For details on the confusion between the two paradigms see Berger (2003), Christensen (2005), Hubbard and Bayarri (2003).”
Bayesian hypothesis testing for psychologists: a tutorial on the Savage-Dickey method. (2010, unknown): “An indepth discussion on the advantages of Bayesian inference, especially when compared to p-value 1 For more information about the difference between the three statistical paradigms, see for instance Christensen (2005), Hubbard and Bayarri (2003) and Royall (1997).”
Why P Values Are Not a Useful Measure of Evidence in Statistical Significance Testing (2008, background): “See Hubbard and Bayarri (2003a) for further discussion of this.”
Testing Fisher, Neyman, Pearson, and Bayes (2005, background): “To handle more general testing situations, NP theory has developed a variety of concepts such as unbiased tests, invariant tests, and α similar tests; see Lehmann (1997). For example, the two-sided t test is not a uniformly most powerful test but it is a uniformly most powerful unbiased test.”
A New Strategy for Testing Structural Equation Models (2016, background): “From the preceding it becomes clear that the α error is close to meaningless if considered in isolation, because a reasonable decision between null and alternative hypotheses (H1) requires both error probabilities α and β to be small (Cohen, 1988; Hubbard & Bayarri, 2003).”
Statistical challenges in null model analysis (2012, methodology): “Following standard statistical procedure, we equate the calculated P -value (Fisher ’ s evidential P -value ( P (data|H 0 ))) with α (but see Hubbard and Bayari 2003).”
Strengthening statistical usage in marine ecology (2012, background): “Statisticians have decried this reasoning for decades (Cohen, 1994; Fisher, 1959; Gelman and Stern, 2006; Gigerenzer, 2004; Gigerenzer et al., 2004; Hubbard and Bayarri, 2003; Stephens et al., 2005; and the numerous references cited in these works).”
A practical solution to the pervasive problems ofp values (2007, methodology): “In the Fisherian framework of statistical hypothesis testing, a p value is meant to indicate “the strength of the evidence against the hypothesis” (Fisher, 1958, p. 80); the lower the p value, the stronger the evidence against the null hypothesis (see also Hubbard & Bayarri, 2003).”
Design Science Methodology for Information Systems and Software Engineering (2014, background): “More about them can be found in the relevant literature [3, 13, 19, 20, 30, 31].”
Introduction to Applied Bayesian Statistics and Estimation for Social Scientists (2007, background): “…one involving Fisherian maximum likelihood estimation and the other involving Fisherian and Neyman and Pearsonian hypothesis testing and confidence interval construction (DeGroot 1986; Edwards 1992; see Hubbard and Bayarri 2003 for a discussion of the confusion regarding the two approaches).”
Final Collapse of the Neyman-Pearson Decision Theoretic Framework and Rise of the neoFisherian (2009, background): “Pollard and Richardson (1987), Goodman (1999a) and Hubbard and Bayari (2003) give good clarifications of the α-P distinction also.”
P-Values are Random Variables (2008, methodology): “Schervish (1996) pointed out that logically they do not measure support for H0 on an absolute scale; Hubbard and Bayarri (2003) pointed out the inconsistency between p-values and fixed Neyman–Pearson α levels. Sackrowitz and Samuel-Cahn (1999) emphasized the stochastic nature of p-values, and recomm”
Valid P-Values Behave Exactly as They Should: Some Misleading Criticisms of P-Values and Their Resolution With S-Values (2019, background): “The latter interpretation is just a mistake (Goodman 1999; Sellke et al. 2001; Hubbard and Bayarri 2003; see also Greenland et al. 2016, item 9): The theory of α-level hypothesis tests requires an α 2 In parallel, P is conservatively valid if the rule “reject H when p ≤ α” will reject H with…”
REASONING ABOUT INFORMAL STATISTICAL INFERENCE: ONE STATISTICIAN’S VIEW (2008, background): “In his discussion of this article, Carlton (2003) argues that students “can handle both approaches” and suggests that α levels be introduced as prespecified thresholds for determining whether a p-value is small enough to constitute convincing evidence against the null model.”