PONE-D-21-12542

The quantification of Simpson’s paradox and other contributions to contingency table theory

PLOS ONE

Dear Dr. Teuscher,

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Dear Author, we have reviewed your paper and found it well written and worthy to be published at PLOS ONE.

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Reviewers' comments:

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Comments to the Author

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Reviewer #1: Yes

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2. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

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Reviewer #1: Yes

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Reviewer #1: No

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5. Review Comments to the Author

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Reviewer #1: The study “The quantification of Simpson’s paradox and other contributions to contingency table theory” is interesting.

In this study, the authors claimed that, to date, there is no test available that determines whether the partial interactions of a certain variable agree or disagree, and the presented work closes this gap. This work reveals the relation of the multiplicative and the additive measure of a three-way interaction. Another contribution addresses the question of which cells in a contingency table are fixed when the first- and second-order marginal totals are given. The proposed procedure not only detects fixed zero counts but also fixed positive counts. This impacts the determination of the degrees of freedom. Furthermore, limitations of methods that simulate contingency tables with given pairwise associations are addressed.

The paper is well set, and the contents are clearly described. The authors almost achieved their objectives. However, the following suggestions should be incorporated before resubmitting the paper.

1. Lines 493, correct the equation 41. Some entries are doubled/missing.

2. Special attention must be given to the language as well.

3. A new section of the conclusion must be added to the paper which concludes the whole study.

4. To broaden the scope of the study the authors are needed to add some more recent references.

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Reviewer #1: No

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The quantification of Simpson’s paradox and other contributions to contingency table theory

PONE-D-21-12542R1

Dear Dr. Teuscher,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

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Kind regards,

Wei Zhu, Ph.D.

Academic Editor

PLOS ONE

Additional Editor Comments (optional):

Reviewers' comments: