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What is the McNemar Test?

The McNemar test is a non-parametric statistical test used to analyze paired binary data—situations where the same subjects are measured twice on a dichotomous outcome. Developed by Quinn McNemar in 1947, it determines whether the proportion of subjects who changed from one category to another is significantly different from what would be expected by chance. It is essentially a test of symmetry in a 2×2 contingency table for matched pairs.

When to Use the McNemar Test

Use the McNemar test when you have paired or matched binary data. Common scenarios include: comparing a diagnostic test result before and after treatment, evaluating whether a training program changes pass/fail rates, testing if an intervention changes behavior (yes/no), or comparing two diagnostic methods applied to the same patients. The test focuses exclusively on the discordant pairs—subjects who changed their response between the two measurements.

McNemar Test vs. Chi-Square vs. Cochran's Q

Assumptions of the McNemar Test

The McNemar test requires the following assumptions to be met:

Understanding the Continuity Correction

The standard McNemar test uses a chi-square statistic with one degree of freedom. Because the binomial distribution (which underlies the test) is discrete, a continuity correction of 1 is applied: χ² = (|b − c| − 1)² / (b + c). This correction makes the chi-square approximation more accurate for moderate sample sizes. For small samples (discordant pairs < 25), StatMate automatically uses the exact binomial test instead, which does not require any approximation.

How to Report McNemar Results in APA Format

Report the test statistic, degrees of freedom, and p-value. If the exact test was used, note this in the report:

Note: Use the exact test when the total number of discordant pairs (b + c) is less than 25. Report p-values to three decimal places, using p < .001 when below that threshold. Include descriptive statistics about the discordant pairs.

Common Mistakes to Avoid

• Using chi-square for paired data: The standard chi-square test assumes independent observations. When the same subjects are measured twice, McNemar's test must be used instead because the data are dependent.
• Ignoring small-sample requirements: When the total number of discordant pairs is less than 25, the chi-square approximation may be unreliable. Use the exact binomial test instead, which StatMate selects automatically.
• Misinterpreting the table layout: The rows represent the "before" condition and columns the "after" condition. The discordant cells (b and c) are what the test analyzes. Concordant cells (a and d) do not affect the test result.
• Applying to non-binary outcomes: McNemar's test is for binary outcomes only. For ordinal paired data, use the Wilcoxon signed-rank test. For three or more related binary measurements, use Cochran's Q test.
• Forgetting the continuity correction: The uncorrected McNemar statistic (b − c)² / (b + c) tends to overestimate significance. Always use the corrected version (|b − c| − 1)² / (b + c) for more accurate results.