McNemar Test

Test whether the marginal frequencies of a binary outcome change significantly between two related measurements.

The McNemar Test is the paired equivalent of the Chi-Square test for binary outcomes. It tests whether the proportion of people classified as 'positive' changes significantly from one time point to another (or between two related conditions). The test focuses only on the discordant pairs — cases that change from positive to negative or vice versa — because concordant pairs provide no information about change.

Common applications include testing whether a treatment changes the proportion of patients who are symptom-free (before vs. after), whether a training program changes the proportion of correct responses, or whether two raters classify the same cases differently.

McNemar's test compares two related proportions, for example the share of participants passing before and after a course. It uses only the discordant pairs — people who changed — and asks whether change in one direction (fail → pass) is more common than in the other (pass → fail). With few discordant pairs (under about 25), use the exact binomial version instead of the chi-square approximation.

When to use the McNemar Test

You have binary outcome data measured twice on the same participants (before/after, matched pairs)
You want to test whether a proportion changes significantly between two related conditions
You compare the proportion answering 'yes' before and after an intervention in the same sample
You compare two diagnostic tests applied to the same patients
You analyse matched case-control pairs with a binary exposure

When not to use it

Your outcome has more than two categories — use Stuart-Maxwell test (generalised McNemar) instead
Your two groups are independent (different participants) — use Chi-Square Test of Independence instead
You have three or more repeated binary measurements — use Cochran's Q test instead

Worked example

	Post: Positive	Post: Negative	Total
Pre: Positive	28	14	42
Pre: Negative	4	34	38
Total	32	48	80

How to report it (APA 7)

A McNemar test indicated a significant change in symptom-free status following treatment, χ²(1) = 8.45, p = .004. The proportion of symptom-free patients increased from 38% at baseline to 62% post-treatment.

Frequently asked questions

Is the McNemar test free on StatRyx?

Yes. You can run it without an account (3 free analyses), and a free account adds 10 more — a one-time allowance, no payment needed. Every result includes the APA 7 write-up. Paid plans (Student from $9/month) add more analyses and Word, PDF and Excel export.

Why does McNemar only use discordant pairs?

Concordant pairs (same response at both time points) provide no evidence about change. Only cases that switched from one category to the other contribute information about whether change occurred.

How do I report a McNemar test in APA 7?

Give the proportions at both time points, then χ²(1), N and p (or the exact p for small samples): "The proportion of symptom-free patients rose from 32% to 58%, χ²(1, N = 80) = 8.45, p = .004."

Can I use a chi-square test for before/after data?

No. A chi-square test of independence assumes the two measurements come from different people. Before/after data from the same people are paired, and McNemar's test accounts for that pairing.

What effect size goes with McNemar's test?

The odds ratio of the discordant pairs (b / c) is the usual effect size, alongside the difference between the two proportions with its confidence interval.

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