Simultaneous Exact Tests for Contingency Tables

Definitions and mathematical statement

A contingency table with two rows and $c$ columns is an array $N=(N_{ij})_{1\leq i\leq 2,\,1\leq j\leq c}$ of nonnegative integer cell counts. The supplied question emphasizes $c=2$ and $c=3$, without restricting attention to those sizes. Simultaneous testing refers here to analyzing a collection of such tables and making multiple testing decisions; the record does not specify the collection, its sampling law, or the hypotheses to be tested.

The retained source question is: How can many contingency tables, especially $2$ by $2$ and $2$ by $3$ tables, be analyzed simultaneously using exact tests and suitable multiple-testing methods?

Unresolved formulation. This is a methodological question, not a recoverable mathematical conjecture. The supplied statement-verification note says that the phrase was extracted from a contribution title and abstract presenting methods and results, rather than a standalone open conjecture. The record marks the statement as unrecoverable and supplies no clean statement. In particular, it specifies neither a sampling model or conditioning scheme for an exact test, nor null and alternative hypotheses, dependence assumptions among tables, a multiplicity error criterion, a significance level, or a desired mathematical conclusion. Consequently, no quantified existence claim, performance guarantee, or open theorem can be stated from this evidence without adding unsupported assumptions.

Short English statement

The record asks how to combine exact tests for many contingency tables, particularly $2\times2$ and $2\times3$ tables, with multiple-testing methods. Its supplied curation identifies this as a description of methods rather than a definite open conjecture. The testing model and intended guarantee remain unspecified.

Sources

• Local UnsolvedMath registry: supplied record with permanent ID $30001923$, title Simultaneous Exact Tests for Contingency Tables, and exact source problem code catalogue entry; collection: Oberwolfach Reports Open Problems. No individual proposer is supplied. The proposed year is recorded as 2011.
• Supplied report citation: Very High Dimensional Semiparametric Models (2012), Oberwolfach Reports, pp. 2745--2779, DOI 10.4171/owr/2011/48. Source URL: https://doi.org/10.4171/owr/2011/48. The supplied background describes Oberwolfach Reports as documenting mathematical workshops and their open-problem discussions.
• Supplied literature source, labeled "original OWR report": https://doi.org/10.4171/owr/2011/48.
• Literature assessment dated 2026-08-21: the supplied status is "open," but the assessment says this is a talk title followed by a description of multiple-testing methods and that no definite open claim is extracted. This is supplied dated curation derived from the OWR record, not an independently verified literature assessment. The supplied background calls for independent verification of time-sensitive status and cited claims.
• The supplied statement-verification note retains the original public record for provenance and promotes no separate clean statement. The report citation is supplied provenance; no precise contribution author, contribution page, or authoritative citation to a standalone conjecture is supplied.