Correctly Rounded or Refused — preprint v0.2

Publication status

Version 0.2 on Zenodo is the current public manuscript.

What the paper studies

Most statistical software returns p-values and confidence limits as numbers, but does not say whether the final digits are reliable. This paper tests a stricter rule for the paired Student-t test. Software must either return the nearest binary64 number and prove it is correctly rounded, return a narrow interval containing the answer, or refuse to return a result.

Binary64 is the standard number format used for most scientific computing. The study covers paired and one-sample Student-t tests with integer degrees of freedom up to 30. It compares widely used software with an independent high-precision reference and tests whether each result can be certified.

Evidence and limits

The manuscript, version history, and persistent identifier are available in theZenodo record.

The reported results have not completed peer review. They do not show that the conclusions of any study using a Student-t test are scientifically valid, or that calculations outside the tests and number ranges studied here are correct.

Relation to nomue Protocol

This paper does not define or change nomue Protocol. It may inform future work, but its scope differs from the planned Release 1: the paper studies paired and one-sample tests, while Release 1 plans to support the Welch two-sample test. Using these findings in a future protocol version would require its own specification update and verification tests.