McNemar's Test Calculator

How it works

χ² = (|b − c| − 1)² ÷ (b + c) with 1 df; exact p = 2 · P(Binomial(b + c, ½) ≤ min(b, c))

McNemar's test is for the same subjects measured twice on a yes/no outcome — a symptom before and after treatment, two diagnostic tests on the same patients, two raters. Only the discordant pairs carry information: if the treatment did nothing, switches in each direction should be equally likely. The exact binomial version is preferred when fewer than about 25 pairs are discordant; the corrected chi-square matches it closely beyond that.

Worked example

6 switched yes→no and 16 switched no→yes: χ² = 3.68 (p = 0.055), exact p = 0.052 — borderline.

Frequently asked questions