McNemar test calculator

It computes the McNemar test statistic and p-values from a 2x2 contingency framework for paired binary data. Users supply two counts: b and c, the numbers of discordant outcomes in opposite directions. The tool returns both approximate results based on the chi-square distribution and exact p-values, supporting robust inference and clear reporting for small or large samples.

Conceptually, the test compares changes between two correlated measurements within subjects. Only the discordant counts drive the statistic; identical outcomes cancel out. The standard asymptotic form uses a chi-square distribution with 1 degree of freedom: chi2 = (b - c)^2 / (b + c) when b+c > 0. A Yates continuity correction can be applied to reduce error in small samples, with chi2_cc = (|b - c| - 1)^2 / (b + c).

Outputs include the test statistic, p-values, and the total number of discordant pairs. The tool offers two modes: asymptotic calculation with or without continuity correction and an exact p-value based on a binomial model with n = b + c. The exact method produces p-values that are valid for small samples, while the asymptotic method is faster for large counts. This combination supports robust decision making and method validation.

Intended users are researchers conducting before-after studies, clinicians evaluating paired diagnostic outcomes, and data scientists validating matched-pairs analyses. The tool provides a minimal, transparent workflow focused on core counts and results, enabling quick checks during study design, analysis, and reporting. It is designed for statistical accuracy, reproducibility, and straightforward interpretation, avoiding unnecessary complexity while offering optional exact calculations for edge cases.