Calculator
Enter the 2×2 paired contingency table. Rows = first measurement (Before / Test 1); Columns = second measurement (After / Test 2).
After / Test 2 +
After / Test 2 −
Before / Test 1 +
Before / Test 1 −
McNemar Test Calculator
Test for a significant net change in paired binary outcomes — pre/post treatment response, or compare two paired diagnostic tests performed on the same patients.
About the McNemar Test
The McNemar test evaluates whether there is a statistically significant difference in proportions of a binary outcome between two paired measurements. Unlike the chi-square test, it is designed for paired data — the same subjects measured at two time points (e.g., before and after treatment), or matched diagnostic tests on the same patients.
Only the discordant pairs (cells b and c) contribute statistical information. Subjects who remained the same across both measurements (concordant pairs a and d) do not affect the test result. The formula is:
χ² = (b − c)² / (b + c) [without continuity correction]
χ² = (|b − c| − 1)² / (b + c) [with Edwards correction, recommended when b+c < 25]
Reporting format (APA/journal): McNemar χ²(1, N=100) = 16.03, p < 0.001
Frequently Asked Questions
When should I use the McNemar test?
Use McNemar when you have paired binary (yes/no) data from the same subjects measured twice — for example, treatment response before and after an intervention, or two diagnostic tests on the same patients. The key requirement is that observations are paired, not independent.
What is the difference between McNemar and chi-square?
Chi-square tests association between two independent categorical variables. McNemar tests whether the proportion of a binary outcome differs in paired data. Using a standard chi-square test on paired data ignores the within-subject correlation and inflates the Type I error rate.
What are discordant pairs?
Discordant pairs are subjects who changed outcome: positive before but negative after (cell b), or negative before but positive after (cell c). Only these pairs drive the McNemar test. Concordant subjects — those who stayed the same (a or d) — do not affect the result.
How do I report McNemar test results?
Report: McNemar χ²(1, N=total) = value, p = value. State the before and after proportions and the direction of change. Example: "Before the intervention, 40% of patients had uncontrolled hypertension; after the intervention, 18% did. The net reduction was statistically significant: McNemar χ²(1, N=100) = 14.67, p < 0.001."
When should I apply the continuity correction?
Apply the Edwards continuity correction (|b−c|−1)² / (b+c) when the total discordant pairs (b+c) is less than 25. For larger samples, the correction makes little difference and the uncorrected version is also acceptable.