The line
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Some statisticians recommend interpreting *p*-values as measures of *evidence*. For example, Bland [-@bland_introduction_2015] teaches that *p*-values can be interpreted as a "rough and ready" guide for the strength of evidence, and that *p* \> 0.1 indicates 'little or no evidence', .05 \< *p* \< 0.1 indicates 'weak evidence', 0.01 \< *p* \< 0.05 indicates 'evidence', *p* \< 0.001 is 'very strong evidence'. This is incorrect [@johansson_hail_2011; @lakens_why_2022], as is clear from the previous discussions of Lindley's paradox and uniform *p*-value distributions. Researchers who claim *p* values are measures of evidence typically do not *define* the concept of evidence. In this textbook I follow the mathematical theory of evidence as developed by Shafer [-@shafer_mathematical_1976, p. 144], who writes "An adequate summary of the impact of the evidence on a particular proposition $A$ must include at least two items of information: a report on how well $A$ is supported and a report on how well its negation $\overline{A}$ is supported." According to Shafer, evidence is quantified through support functions, and when assessing statistical evidence, support is quantified by the likelihood function. If you want to quantify *evidence*, see the chapters on [likelihoods](#sec-likelihoods) or [Bayesian statistics](#sec-bayes). |
does not render correctly on my end. The glyph for
$\overline{A}$ is rendered exactly the same as
$A$.
[...] who writes "An adequate summary of the impact of the evidence on a particular proposition $A$ must include at least two items of information: a report on how well $A$ is supported and a report on how well its negation $\overline{A}$ is supported."[...]
