McNemar Test Calculator
Compare two paired binary measurements, such as before/after classifications, using the counts that changed in each direction. The tool shows the method and key assumptions so you can inspect how the input values lead to the estimate.
How to use this calculator
- Enter a to b changed from 0 to 1 using the unit and definition shown beside the input.
- Enter a to b changed from 1 to 0 using the unit and definition shown beside the input.
- Check that all values refer to the same time period and scenario.
- Review the outputs alongside the assumptions before using them in a decision.
Formula and assumptions
χ²=(max(0, |b−c|−1))²/(b+c); p≈χ² survival probability with 1 degree of freedom.
- Use only the discordant-pair counts; concordant pairs do not contribute to the McNemar statistic. This large-sample p-value is an approximation and can be unreliable for very small discordant totals.
- The estimate is calculated from values you enter. It does not connect to external accounts, obtain live prices, or validate local regulations or engineering specifications.
Worked examples
Worked example
With 25 changes in one direction and 10 in the other, the continuity-corrected statistic is about 5.6 and the approximate two-sided p-value is around 0.018.
b = 25; c = 10; continuity-corrected χ² is computed from the two discordant counts.
Use the result as a statistical summary, not as a substitute for study design or expert review.
Understanding the result
Use only the discordant-pair counts; concordant pairs do not contribute to the McNemar statistic. This large-sample p-value is an approximation and can be unreliable for very small discordant totals.
Change one input at a time to see how sensitive the output is to that assumption.
Important notes
Use only the discordant-pair counts; concordant pairs do not contribute to the McNemar statistic. This large-sample p-value is an approximation and can be unreliable for very small discordant totals.
Frequently asked questions
What formula does the McNemar Test Calculator use?
χ²=(max(0, |b−c|−1))²/(b+c); p≈χ² survival probability with 1 degree of freedom.
What should I verify before relying on the result?
Use only the discordant-pair counts; concordant pairs do not contribute to the McNemar statistic. This large-sample p-value is an approximation and can be unreliable for very small discordant totals.
Can I compare different scenarios?
Yes. Change one assumption at a time, keep units and definitions consistent, and save the inputs used for each comparison.
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This page provides a calculation tool plus explanatory information so you can understand what the result means and when the underlying method may not fit your situation.