Optimal Statistical Analyses of Bell Experiments
Round 1
Reviewer 1 Report
This paper is very well-written and important. The author provides a careful analysis of Bell experiments. He shows that much better p-values could be obtained, with little extra computational effort, in all four Bell experiments performed at NIST, in Vienna, Innsbruck, and Munich. This is a very interesting result that may appeal to the journal readership. Overall, the paper is well-written and everything is clearly explained. I think the paper can be accepted in its current form.
I have only a minor suggestion: The author may want to improve the bibliography, directing the reader to papers discussing the very important physical motivation for Bell-type experiments. Although the paper, and the journal, are more mathematically oriented, this may help the general reader.
Author Response
Thanks for your positive recommendation. I have added a short section of a bit more than one page with a short history taking us from EPR (1935) to the loophole free experiments of 2015 and beyond to the 2022 Nobel prizes. This allowed me to add important references to the bibliography and I think it could help interested "outsiders" to this field to get a "big picture" of what and why, and hence access to relevant literature if they want to learn more. The section can easily be skipped either because the story is already known or because the reader wants to get as fast as possible into some applied mathematics.
Reviewer 2 Report
The article presents a method for computing smaller and more reliable p-values in Bell-type experiments. This is achieved by using statistical deviations from no-signalling equalities to reduce statistical noise in the estimation of Bell's S or Eberhard's J. Additionally, the study demonstrates that further improvements can be obtained by applying Wilks' likelihood ratio test.
The article is well written, and I did not find any methodological errors to highlight. However, I suggest that the author correctly cites the use of the R program.
Author Response
Thanks for your positive recommendation.
I have added a proper literature citation for the R statistical package.
