How does McNemar's test differ from the regular chi-square test?

The standard chi-square test of independence is for independent samples. McNemar's test is for paired (matched) samples — the same subjects measured twice, or two matched groups. It only uses the discordant off-diagonal cells and ignores the concordant cells.

What is the null hypothesis?

The null hypothesis is that the two marginal proportions (row total vs column total) are equal — in other words, the probability of changing from Yes to No equals the probability of changing from No to Yes. A significant result means one direction of change is more frequent.

When should I apply the continuity correction?

The continuity (Edwards') correction — subtracting 1 from |b − c| before squaring — is recommended when the sum of discordant cells (b + c) is small (below about 25). It makes the test slightly more conservative and reduces type I error. For large discordant totals the correction barely matters.

If all subjects are concordant (both off-diagonal cells b and c are zero), the test statistic is undefined — there is no evidence of any change, so the test cannot be applied. The tool will display a warning in this case.

What is an exact McNemar test?

The standard McNemar test uses the chi-squared approximation. For very small discordant totals (b + c < 25), an exact binomial test is more accurate. This calculator implements the chi-squared version with optional continuity correction, which is appropriate for most practical sample sizes.

Can I use this for more than two categories?

No. McNemar's test applies only to binary (2-category) outcomes in a 2×2 table. For polytomous matched data, use the Stuart–Maxwell test instead.

McNemar Test Calculator

Enter the four cells of a 2×2 paired contingency table to compute McNemar's chi-squared statistic, p-value, and decide if marginal proportions differ.

2×2 Paired Contingency Table

Condition 1 label

Condition 2 label

	After: Yes	After: No
Before: Yes	a (Yes→Yes)	b (Yes→No)
Before: No	c (No→Yes)	d (No→No)

Significance level (α)

Apply Edwards' continuity correction

Table notation

aBoth measurements positive (concordant)

bPositive on Condition 1, negative on Condition 2 (discordant)

cNegative on Condition 1, positive on Condition 2 (discordant)

dBoth measurements negative (concordant)

Only cells b and c (the discordant pair) drive the test statistic.

Fill in the table and click Run Test to see results.

Summary

McNemar's test checks whether the marginal frequencies of two binary outcomes are equal in paired or matched samples — for example, before-and-after measurements on the same subjects. It focuses only on the discordant cells (the off-diagonal counts where the two measurements disagree) and asks whether one direction of change is significantly more common than the other. A small p-value (typically below 0.05) means the proportions have changed significantly between the two conditions.

How it works

Label your two conditions (e.g., Before / After or Test A / Test B).
Fill in the four cells: how many subjects went from Yes→Yes, Yes→No, No→Yes, and No→No.
Choose a significance level (default 0.05) and whether to apply the continuity correction.
Click "Run Test" — the tool reads the discordant cells b (Yes→No) and c (No→Yes).
McNemar's statistic χ² = (|b − c| − correction)² / (b + c), with 1 degree of freedom.
The p-value is read from the chi-squared distribution; the verdict tells you whether to reject the null hypothesis of equal marginals.

Use cases

Compare pass/fail rates on the same exam before and after a training intervention.
Test whether a medical treatment changes the proportion of positive diagnoses.
Evaluate whether two diagnostic tests disagree asymmetrically on the same patients.
Assess opinion change (agree/disagree) before and after an advertisement.
Measure whether a software UI change shifts task success rates for the same users.
Validate survey re-test consistency on binary yes/no questions.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu

McNemar Test Calculator

2×2 Paired Contingency Table

Table notation

Discordant Pair Summary

Marginal Proportions

Formula applied

Summary

How it works

Use cases

Frequently Asked Questions

McNemar Test Calculator

Use the McNemar Test Calculator

2×2 Paired Contingency Table

Table notation

Discordant Pair Summary

Marginal Proportions

Formula applied

Summary

How it works

Use cases

Frequently Asked Questions