McNemar’s Test in R: Compare Paired Proportions (Before/After)

Test whether a proportion changed between two paired measurements — the categorical paired test for before/after designs, with the exact version for small samples

Learn to run McNemar’s test in R — the test for comparing paired proportions, the categorical equivalent of the paired t-test for a before/after or matched design. Build the 2×2 paired table with base R, run rstatix mcnemar_test(), and use the exact binomial version when the discordant counts are small.

TipKey takeaways

• McNemar’s test compares paired proportions — the categorical equivalent of the paired t-test, for a before/after or matched 2×2 design where each subject is measured twice.
• It looks only at the discordant pairs (the off-diagonal cells — subjects who changed); the concordant pairs carry no information about change.
• Run it with rstatix::mcnemar_test() on the 2×2 paired table.
• For small numbers of discordant pairs (≲ 20), use the exact binomial version (binom_test() on the discordant counts).
• For three or more repeated measurements, use Cochran’s Q test.

Introduction

McNemar’s test compares two paired proportions — the same subjects measured twice, in a before/after design or a matched study. It is the categorical analogue of the paired t-test: instead of two independent groups (which would call for a chi-square test), the two measurements come from the same people.

The trick: only the subjects who changed (the discordant pairs — yes→no and no→yes) tell you whether the proportion shifted. The scenario here: did an anti-smoking intervention change the proportion of smokers, measured before and after? This lesson runs it with rstatix on the antismoking data.

Note

McNemar’s test hypotheses. Labelling the 2×2 paired table’s off-diagonal cells B and C (the two kinds of change), H₀: B = C (equal numbers changed each way → no net change). Hₐ: B ≠ C (the proportion changed).

The data: a paired before/after table

We use the antismoking dataset from datarium — 62 people whose smoking status was recorded before and after an intervention. Cross-tabulate into the paired 2×2 table with base R:

library(rstatix)

data("antismoking", package = "datarium")
xtab <- xtabs(~ before + after, data = antismoking)
xtab

            after
before       non.smoker smoker
  non.smoker         25      6
  smoker             21     10

The diagonal (25 stayed non-smokers, 10 stayed smokers) are the concordant pairs — no change. The off-diagonal are the discordant pairs: 6 went non-smoker → smoker, and 21 went smoker → non-smoker. McNemar’s test asks whether those two numbers (6 vs 21) differ.

Run McNemar’s test

library(rstatix)

data("antismoking", package = "datarium")
xtab <- xtabs(~ before + after, data = antismoking)

mcnemar_test(xtab)

# A tibble: 1 × 6
      n statistic    df       p p.signif method      
* <int>     <dbl> <dbl>   <dbl> <chr>    <chr>       
1    62      7.26     1 0.00705 **       McNemar test

There was a significant change in smoking status, χ²(1) = 7.26, p = 0.007 — far more people quit (21) than started (6), so the proportion of non-smokers rose after the intervention.

Small samples: the exact binomial version

McNemar’s chi-square is a large-sample approximation. When the total number of discordant pairs (B + C) is small (≲ 20), use the exact binomial test — under H₀, each discordant pair is equally likely to go either way, so the count tests against p = 0.5:

library(rstatix)

# B = 6 (non-smoker -> smoker), C = 21 (smoker -> non-smoker)
binom_test(x = 6, n = 6 + 21, p = 0.5)

# A tibble: 1 × 6
      n estimate conf.low conf.high       p p.signif
* <dbl>    <dbl>    <dbl>     <dbl>   <dbl> <chr>   
1    27    0.222   0.0862     0.423 0.00592 **      

The exact test agrees (p = 0.006). Here B + C = 27 so chi-square is fine, but for fewer discordant pairs the exact version is the safe choice.

Plot it

library(rstatix)
library(ggpubr)

data("antismoking", package = "datarium")
n <- nrow(antismoking)
long <- data.frame(
  time   = factor(rep(c("before", "after"), each = n), levels = c("before", "after")),
  status = c(as.character(antismoking$before), as.character(antismoking$after))
)
stat.test <- mcnemar_test(xtabs(~ before + after, data = antismoking))

ggbarplot(as.data.frame(table(long)), x = "time", y = "Freq", fill = "status",
          palette = "jco", ylab = "Count", xlab = NULL) +
  labs(subtitle = get_test_label(stat.test, detailed = TRUE))

Report

A McNemar’s test showed a statistically significant change in smoking status before vs after the intervention, χ²(1) = 7.26, p = 0.007: of the participants who changed, 21 quit smoking while only 6 took it up.

NoteThe math (optional)

McNemar’s statistic uses only the discordant counts B and C: \(\chi^2 = \dfrac{(B - C)^2}{B + C}\) (with a continuity correction, \(\dfrac{(|B - C| - 1)^2}{B + C}\)), compared to a chi-square distribution with 1 degree of freedom. The concordant cells (A and D) cancel out because they carry no information about change. Under H₀ the \(B + C\) changers split 50/50, which is exactly the exact-binomial formulation.

Try it live

Run McNemar’s test on your own paired 2×2 table — e.g. approval before vs after a campaign. Edit the counts and re-run; the sandbox boots on first Run.

🟢 With an AI agent

Ask Prova “I measured the same subjects before and after — test whether the proportion changed with McNemar’s test” — it answers with rstatix code you can run on your own paired table. The runtime is the judge. Ask Prova →

Common issues

You used a chi-square test on paired data. The ordinary chi-square test assumes the two groups are independent. For the same subjects measured twice (before/after, matched), use McNemar’s test — it accounts for the pairing by looking only at who changed.

You looked at the diagonal. McNemar ignores the concordant pairs (no change) — only the off-diagonal discordant counts matter. A table with huge diagonals but B ≈ C shows no significant change.

Few discordant pairs. When B + C is small (≲ 20), the chi-square approximation is shaky — report the exact binomial result instead.

Frequently asked questions

NoteWhat is McNemar’s test used for?

McNemar’s test compares two paired proportions — the same subjects measured twice (before/after) or matched pairs, on a yes/no outcome. It tests whether the proportion changed between the two measurements, making it the categorical equivalent of the paired t-test.

NoteWhat is the difference between McNemar’s test and the chi-square test?

The chi-square test of independence compares two independent groups; McNemar’s test compares the same subjects measured twice (paired data). McNemar uses only the discordant (changed) pairs, which is how it accounts for the pairing — using a chi-square test on paired data would be wrong.

NoteWhen should I use the exact (binomial) McNemar test?

When the total number of discordant pairs (B + C) is small — roughly 20 or fewer. The chi-square version is a large-sample approximation; below that, the exact binomial test (each discordant pair tested against p = 0.5) gives the correct p-value.

Test your understanding

ImportantPractice

1. Run it. In the live cell, run McNemar’s test on the paired 2×2 table. Fill the blank. Did the proportion change significantly?
2. Conceptual. Your paired table has 200 on the diagonal (no change) and B = 8, C = 9 off-diagonal. Will McNemar’s test be significant? Why?

NoteHint

Fill the blank with mcnemar_test. For question 2, recall that McNemar ignores the diagonal and depends on how different B and C are.

NoteSolution

mcnemar_test(tab)   #> chi-square(1) = 7.26, p = 0.007 — significant change.

For question 2: no — McNemar uses only the discordant pairs, and B = 8 vs C = 9 are almost equal, so there’s no evidence of net change regardless of the large concordant diagonal. The 200 unchanged subjects are irrelevant to the test.

TipWhich test when?

• Two paired proportions (before/after, 2 times) → McNemar’s test (this lesson).
• Three or more paired proportions → Cochran’s Q test.
• Two independent groups, categorical → chi-square test of independence.
• Two paired continuous measurements → the paired t-test / Wilcoxon.

Conclusion

You can now run McNemar’s test in R: cross-tabulate the paired before/after data into a 2×2 table, run mcnemar_test(), and read the discordant counts — it tests whether the proportion changed between two paired measurements. Use the exact binomial version when the number of changers is small, and step up to Cochran’s Q for three or more repeated measures.

Related lessons

• Cochran’s Q test in R — McNemar extended to three or more repeated measures. · Chi-square test of independence in R — the test for independent groups. · Proportion z-tests in R — comparing independent proportions.
• Go further: Categorical data analysis · Biostatistics

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