There are natural scores: Full comment on Shafer,"Testing by betting: A strategy for statistical and scientific communication"

By Sander Greenland. 2021

171 citations recorded by the source corpus.

Shafer (2021) offers a betting perspective on statistical testing which may be useful for foundational debates, given that disputes over such testing continue to be intense. To be helpful for researchers, however, this perspective will need more elaboration using real examples in which (a) the betting score has a justification and interpretation in terms of study goals that distinguishes it from the uncountable mathematical possibilities, and (b) the assumptions in the sampling model are uncertain. On justification, Shafer says 'No one has made a convincing case for any particular choice' of a score derived from a P-value and then states that 'the choice is fundamentally arbitrary'. Yet some (but not most) scores can be motivated by study goals (e.g., information measurement; decision making). The one I have seen repeatedly in information statistics and data mining is the surprisal, logworth or S-value s = -log(p), where the log base determines the scale. The present comment explains the rationale for this choice.

Subfields: Artificial Intelligence, Economics and Econometrics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/7ee435d516ba33753c461e7763b31ea5d2d6afad

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Citations in the corpus

Safe Testing (2019, background): “One option is to pick a certain target growth L (essentially the logarithm of Shafer (2021)’s notion of “implied target”) and determine the sample size at which we expect to gain L .”
Time-uniform central limit theory and asymptotic confidence sequences (2021, unknown): “Furthermore, e-values have received considerable attention for philosophical reasons including how they relate testing to betting [39] and connect frequentist and Bayesian notions of uncertainty [12, 60].”