Relating S-values to other measures of statistical information

[R_cubed]

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Very interesting and to me (from your table) it seems that we are just debating the change in level of evidence against the null from clearly unacceptable to clearly acceptable. So let us say we fix clearly unacceptable as a prior probability against the null in terms of odds

I actually used this type of reasoning to compare the data reported in a meta-analysis on ACL injury to the narrative section in this thread.

Using p-values, S-values, and the Bayesian Rejection Ratio to re-examine a meta-analysis on knee abduction kinematics and ACL injury risk

A colleague brought to my attention the following peer-reviewed meta-analysis of 12 prognostic studies that attempted to predict future ACL injury risk from knee kinematics. Title: Do knee abduction kinematics and kinetics predict future anterior cruciate ligament injury risk? A systematic review and meta-analysis of prospective studies The authors found 9 studies, using 3 different assessments, that attempt to detect excess angular motion as a predictor of future ACL injury. They reported …

It would be accurate to say that this table has compressed a number of independent papers that touch upon the issue of information and evidence.

Aside from Sander’s many writings on the topic that call for embedding statistical reasoning in information theoretical frameworks, I wanted to link that more directly to Bayesian and Fisher’s ideas, as described by Kulinskaya, Morganthaler, and Stadute in this book on meta-analysis:

Meta Analysis