How to Report McNemar's Test in APA 7

You measure the same binary variable twice in the same people — met caseness or did not, relapsed or did not, passed or failed — and you end up with a 2 × 2 table that looks like it is begging for an ordinary chi-square. It is not. Pearson's chi-square assumes the two columns come from different people, and here they come from the same people. What you need is McNemar's test, which is written almost identically and means something quite different. If your two columns really are independent groups, the place to go is how to report a chi-square test in APA 7.

Which numbers go in

Four things: the chi-square with its degrees of freedom and the N inside the parentheses, the p value, an effect size, and the frequencies of the two cells that changed. The full template is χ²(1, N = 140) = 11.52, p < .001, OR = 2.32, 95% CI [1.41, 3.82].

The degrees of freedom are always 1, and that is not a detail you can wave through. The test compares two cells and only two, so there is exactly one degree of freedom to be had. If your output says df = 2 or df = 3, you did not run McNemar. Either you ran a Pearson chi-square on the crosstabulation, or you ran the McNemar-Bowker extension, which handles variables with more than two categories and does carry more degrees of freedom.

The N in the parentheses is the number of pairs: 140 clients measured twice are N = 140, never 280. McNemar behaves differently from other paired tests here. In a Wilcoxon signed-rank test, ties drop out and the n shrinks; in McNemar, the people who did not change still count toward the N you declare, even though they never touch the statistic. That is why the number of discordant pairs belongs in the same sentence — it is a different, smaller number.

Italics: the χ stays upright, because Greek letters are not italicized, and the 2 is a superscript rather than a digit typed afterwards. Italicize N, n and p; OR and CI are abbreviations and stay upright. Chi-square can exceed 1, so keep the leading zero when it has one (χ² = 0.87) and give it two decimals. A p value cannot exceed 1, so it loses the leading zero: p = .011, and below .001 you write p < .001.

Only the people who changed count

Your table has four cells and the test looks at two of them. Put numbers on it: 140 clients in a talking therapies service, screened for anxiety caseness on the GAD-7 at intake and again at discharge. Forty-two met caseness at both time points, 51 met it at intake but not at discharge, 22 met it at discharge without meeting it at intake, and 25 never met it at all.

The statistic is χ² = (51 − 22)² / (51 + 22) = 841 / 73 = 11.52. The 42 who stayed and the 25 who never met caseness appear nowhere in that arithmetic: of 140 pairs, only 73 feed the number. This has a consequence that surprises people the first time they meet it — two studies with very different sample sizes produce identical chi-squares whenever their discordant cells match. McNemar does not tell you how many people changed. It tells you how lopsided the changes were.

So write both frequencies out in words rather than burying them in a table that may end up in the supplement. A reviewer who reads χ²(1, N = 140) = 11.52 and nothing else cannot reconstruct anything, and cannot check your effect size either, because the effect size is calculated from exactly those two cells.

Give the marginal percentages too, since that is what a reader actually wants: caseness fell from 66.4% (93 of 140) at intake to 45.7% (64 of 140) at discharge. Notice that the 20.7-point drop is precisely (51 − 22) / 140. The marginals and the discordant cells tell one story along two routes, and showing both is what makes it convincing.

McNemar or Pearson's chi-square: the difference that settles it

The question is not which test has more power. It is where the two columns of your table came from. Pearson's chi-square assumes every observation is independent of every other, and in a pre-post design they are not: a person's discharge score is tied to their own intake score. McNemar is built for precisely that situation, where each row of your data file is one person contributing both measurements.

The rule of thumb is short. If you could move somebody in the first column without touching the second, the groups are independent and Pearson applies. If moving them forces you to move their after-cell as well, the data are paired and McNemar applies. The same logic covers one participant measured twice, matched case-control pairs, and two raters coding the same set of cases.

Running Pearson on a paired table does not give you a slightly biased answer. It gives you the answer to a different question. Pearson tests whether the two measurements are associated, and in a pre-post design they almost always are, because people who scored high before tend to score high afterwards. You get a tiny p value that proves only that people resemble themselves. McNemar tests whether the marginals moved, which is what you meant to ask.

The rest of the formatting lives in how to report a chi-square test in APA 7, and nearly all of it carries over: the N inside the parentheses, the decimals, the upright χ. The one thing that does not carry over is the effect size, because neither phi nor Cramér's V belongs here. If your variable has three or more categories measured twice — a diagnosis with three levels, say — what you want is McNemar-Bowker, with df = k(k − 1) / 2, which is 3 for three categories.

The effect size: discordant-pair odds ratio or difference in proportions

APA 7 asks for an effect size here as well, and this is where people paste in Cramér's V out of habit. It does not belong: phi and V measure association between two variables, and McNemar measures imbalance between two cells. The two options that do work are the odds ratio of the discordant pairs and the difference between paired proportions.

The odds ratio is a division: 51 / 22 = 2.32. Read it as a ratio of discordant pairs rather than as a risk — for every client who moved into caseness, 2.32 moved out of it. The interval comes from exp(ln OR ± 1.96 × √(1/51 + 1/22)), which gives 95% CI [1.41, 3.82]. Be careful with ordinary odds ratio calculators, mine included: they are built for independent groups and use all four cells, so feeding them a paired table returns something else entirely. For McNemar it is a division you do by hand.

The difference in paired proportions is (51 − 22) / 140 = .21, with a standard error of √(73 − 29² / 140) / 140 and an interval of 95% CI [.09, .32]. This is the one that reads best in a clinical journal: twenty-one people in every hundred left caseness, net. It takes no leading zero, because a difference in proportions cannot exceed 1.

Which one to lead with depends on your reader. For clinical and applied journals, the difference in proportions needs no translation. If you come from epidemiology, or you plan to add covariates later, the odds ratio connects to what comes next, which is conditional logistic regression — McNemar with more variables inside it (how to report a logistic regression in APA 7). Reporting both costs you half a line and pre-empts the reviewer's question.

Continuity correction and the exact test: when each one applies

Your software decides this for you and does not always say so plainly. With few discordant pairs the chi-square approximation stops being trustworthy, and the most cited convention puts the cut-off at 25: below 25 discordant pairs you use the exact binomial test on those two cells. SPSS switches on its own and labels the result as exact significance; the trouble is that plenty of people copy the number out of the table without checking which test produced it, and then write up a χ² their output never calculated.

Edwards's continuity correction subtracts 1 from the absolute difference before squaring it: χ² = (|51 − 22| − 1)² / 73 = 784 / 73 = 10.74, p = .001, against 11.52 and p < .001 uncorrected. It does not change the conclusion here, but it changes both numbers you write down, so say which one you used in a single clause: “a continuity correction was applied” or “the uncorrected statistic is reported”. In large samples the correction is irrelevant; in mid-sized ones it is the difference between .049 and .052, and whole paragraphs get written about that difference.

Watch what happens in a pilot. Thirty participants, 11 changing in one direction and 3 in the other: 14 discordant pairs, below the cut-off. No χ² appears anywhere — you write “exact binomial test, p = .057, OR = 3.67, on n = 30 pairs”. The ratio is larger than in the main example and the result still is not significant, because fourteen pairs cannot carry that much. This is where the phrase “approaching significance” gets invented most often. Do not write it. Write the interval and let the reader see how wide it is.

A worked example for the Results section

The setting: 140 clients in a talking therapies service, screened with the GAD-7 at intake and again at discharge. The outcome is binary, caseness or not, and the question is whether the proportion meeting caseness fell.

“Caseness fell from 66.4% (93 of 140) at intake to 45.7% (64 of 140) at discharge. Changes were discordant in 73 pairs: 51 clients moved out of caseness and 22 moved into it. McNemar's test, without a continuity correction, indicated that this imbalance was unlikely to be due to chance, χ²(1, N = 140) = 11.52, p < .001. The discordant-pair odds ratio was OR = 2.32, 95% CI [1.41, 3.82], and the difference in paired proportions was .21, 95% CI [.09, .32].”

Four sentences and everything is there: the marginals the reader wants, the two cells that carry the calculation, the statistic with its df and its N of pairs, and two effect sizes with intervals. Notice what is missing as well — no “highly significant difference”, no “trend”, no Cramér's V doing nothing useful. If you want to check the italics, leading zeros and decimals before it goes into your manuscript, the APA 7 formatter reads it in a second.

Already drafted it? Paste your Results section into Review one section before it goes to your supervisor or the journal. You get the first thing a reviewer would object to, with your own sentence quoted.

Frequently asked questions

What is McNemar's test used for?

It is the test for a binary variable measured twice in the same people: the same participant before and after, matched case-control pairs, or two raters coding the same cases. It asks whether the marginal proportions changed, and to answer that it uses only the discordant cells, the people who switched category. If your two columns come from different people, you do not want McNemar, you want Pearson's chi-square.

How do you report McNemar's test in APA 7?

With the chi-square, its degrees of freedom and the N of pairs inside the parentheses, the p value and an effect size: χ²(1, N = 140) = 11.52, p < .001, OR = 2.32, 95% CI [1.41, 3.82]. Before that line come the percentages at both time points and the frequencies of the two discordant cells, without which nobody can check your arithmetic. The χ stays upright because it is Greek; N and p are italicized.

What is the difference between McNemar's test and a chi-square test?

Pearson's chi-square assumes independent observations and tests whether two variables are associated. McNemar assumes paired data and tests whether the marginal proportions moved. Running Pearson on a pre-post table does not give a slightly biased answer; it answers a different question, and it comes out significant almost every time because a person's before and after scores are correlated by construction.

What is the effect size for McNemar's test?

Either the discordant-pair odds ratio, which is one discordant cell divided by the other (51 / 22 = 2.32), or the difference in paired proportions, which is their difference over the total number of pairs (.21). Both are reported with a confidence interval. What does not belong here is phi or Cramér's V, because those measure association and McNemar does not measure association.

How many degrees of freedom does McNemar's test have?

One, always, because the test compares exactly two cells. If your output shows 2 or 3 degrees of freedom, you have either run a Pearson chi-square on the crosstabulation or run the McNemar-Bowker extension for variables with more than two categories, which carries k(k − 1) / 2 degrees of freedom.

What do you do when there are very few discordant pairs?

Report the exact binomial test instead of the chi-square. The usual convention puts the cut-off at 25 discordant pairs, and most packages switch tests on their own below that number. When they do, drop the χ² entirely: give the name of the test, the p value, the effect size with its interval and the number of pairs. Few discordant pairs produce a wide interval, and that is information rather than a flaw to be disguised.

With the chi-square, its df = 1 and its N of pairs, the p value, both discordant cells and an effect size with an interval, your McNemar test is properly reported. If you have the table in front of you and cannot quite tell whether it calls for McNemar, Pearson or a conditional logistic regression with covariates, that is what my statistical consulting is for.