What is the difference between McNemar and chi-square?

The chi-square test of independence compares separate groups. McNemar's test is for the same people measured twice (or matched pairs) and only uses the people who changed.

Should I use the exact McNemar test?

Use the exact binomial version when the number of people who changed (b + c) is below about 25. With larger numbers, the chi-square version gives almost the same p value.

How do I report a McNemar test in APA style?

Write χ²(1, N = n) = X.XX, p = .XXX, give the before and after percentages, and say how many people changed in each direction.

MCNEMAR TEST CALCULATOR

McNemar test calculator for paired yes/no data.

Test whether a proportion changed between two related measurements, such as before and after training on the same people. Get McNemar's χ², the exact binomial p value, the continuity-corrected test, the odds ratio, and an APA sentence.

2 × 2 TABLE

Before (rows) × after (columns)

PAIRED

CATEGORY 1 NAMECATEGORY 2 NAME

Enter how many participants fall in each before → after combination. Each person is counted once.

a: Yes → Yesb: Yes → Noc: No → Yesd: No → No

Only the discordant cells b and c (people who changed) affect the test.

McNemar test formula, exact test, and APA reporting

When to use McNemar's test

Use it for a yes/no (dichotomous) outcome measured twice on the same people, or on matched pairs: for example, whether students passed before and after a workshop, or whether patients had a symptom before and after treatment. A regular chi-square test is wrong here because the two measurements are not independent.

Formula

χ² = (b − c)² ÷ (b + c), df = 1 (continuity-corrected: (|b − c| − 1)² ÷ (b + c))

b is the number who changed from category 1 to category 2 and c the number who changed the other way. The participants who did not change (a and d) carry no information about change, so they do not enter the statistic.

Exact binomial version

Under the null hypothesis, each of the b + c changers is equally likely to move in either direction, so b follows a binomial(b + c, 0.5) distribution. The exact two-sided p value is 2 × P(X ≤ min(b, c)). Use it when b + c is below about 25; SPSS reports this exact p automatically for small tables.

Effect size

The odds ratio b ÷ c tells you how much more likely change was in one direction than the other, with a 95% CI from SE(ln OR) = √(1/b + 1/c). Also report the two proportions (before and after) so readers see the size of the change.

How to report it (APA style)

“An exact McNemar test showed a significant change in the proportion of students who passed, from 45.0% before the workshop to 34.0% after, χ²(1, N = 100) = 6.37, p = .019. Fifteen students changed from pass to fail and four from fail to pass.”

References

McNemar, Q. (1947). Note on the sampling error of the difference between correlated proportions or percentages. Psychometrika, 12(2), 153–157.
Edwards, A. L. (1948). Note on the "correction for continuity" in testing the significance of the difference between correlated proportions. Psychometrika, 13(3), 185–187.
Fagerland, M. W., Lydersen, S., & Laake, P. (2013). The McNemar test for binary matched-pairs data: Mid-p and asymptotic are better than exact conditional. BMC Medical Research Methodology, 13, 91.
Agresti, A. (2013). Categorical data analysis (3rd ed.). Wiley.

McNemar Test Calculator

Test whether a proportion changed between two related measurements on the same people, with the exact test for small samples, the odds ratio, and a ready APA sentence.

Test a change in pass rates before and after training

Compare a yes/no survey answer at two time points

Analyse matched case-control pairs

KEY FUNCTIONS

McNemar χ² with and without continuity correctionExact binomial p value for small samplesOdds ratio with 95% CIBefore and after proportionsAPA 7 report sentence

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