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 0.5 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 cells on the main diagonal 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

Name: McNemar Test Calculator
Availability: InStock
Author: Nham Vu

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

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.

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