McNemar's test compares two proportions from the same people, such as the share passing a test before and after training. It is the paired version of the chi-square test, the categorical counterpart of the paired t-test. Only the people who changed (the discordant pairs) carry information, which is why the write-up should mention them.
What you need before you write a single word
- The 2 × 2 table of paired outcomes (before by after).
- The proportion with the outcome at each time point.
- The number of discordant pairs: people who changed in each direction.
- McNemar's χ² (usually with a continuity correction) and its exact p, or the exact binomial p when discordant pairs are few.
The APA 7 format template
The proportion of [participants] who [outcome] [increased] from XX% before [event] to XX% after it. Of the [n] participants who changed, [n1] moved from [no] to [yes] and [n2] from [yes] to [no]. A McNemar test showed this change was significant, χ²(1, N = XXX) = X.XX, p = .XXX.
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Formatting rules reviewers actually check:
- McNemar's χ² always has 1 degree of freedom; give N, the number of pairs.
- Say whether you used the continuity correction or the exact version.
- Report the proportions at both time points so the direction is clear.
A worked example
Sixty trainee nurses sat a skills check before and after a simulation course.
| Before \ After | Pass | Fail |
|---|---|---|
| Pass | 25 | 4 |
| Fail | 15 | 16 |
Pass rates went from 29 of 60 (48%) to 40 of 60 (67%). Of the 19 who changed, 15 went from fail to pass and 4 from pass to fail. McNemar's test with continuity correction gives χ²(1, N = 60) = 5.26, p = .022; the exact test gives p = .019. Written up in APA 7:
The pass rate on the skills check rose from 48% before the simulation course to 67% after it. Of the 19 nurses whose result changed, 15 moved from fail to pass and 4 from pass to fail. A McNemar test with continuity correction showed that this change was significant, χ²(1, N = 60) = 5.26, p = .022.
Mistakes reviewers catch
- Using an ordinary chi-square test. The two measurements come from the same people, so they are not independent; use McNemar's test.
- Leaving out the discordant pairs. They are the whole basis of the test.
- Not saying which version you used. Corrected χ², uncorrected χ² and the exact test give different p values.
- χ² with few changes. When fewer than about 25 people changed, report the exact binomial p.
Let KyroStat do the write-up for you
KyroStat spots paired yes/no measurements, runs McNemar's test (exact when the discordant pairs are few) and writes the sentence with the proportions from your data.
Frequently asked questions
What about three or more paired measurements? Use Cochran's Q test, then pairwise McNemar tests with a correction.
Is there an effect size for McNemar's test? The odds ratio of the discordant pairs (here 15/4 = 3.75) or Cohen's g. See how to report effect sizes.
How is this different from the chi-square test of independence? The chi-square test of independence compares separate groups; McNemar compares the same people twice.