A note on data splitting with e-values: online appendix to my comment on Glenn Shafer's "Testing by betting"

Abstract

This note reanalyzes Cox's idealized example of testing with data splitting using e-values (Shafer's betting scores). Cox's exciting finding was that the method of data splitting, while allowing flexible data analysis, achieves quite high efficiencies, of about 80%. The most serious objection to the method was that it involves splitting data at random, and so different people analyzing the same data may get very different answers. Using e-values instead of p-values remedies this disadvantage.