Understand the hypothesis test
What makes this an exact test
McNemar’s Test. An exact procedure calculates null probabilities from the discrete sampling model rather than relying on a large-sample continuous approximation.
1Fix the null model and margins2Enumerate compatible outcomes3Sum outcomes at least as extreme
Test statistic and reference model
Exact test treats b of b+c discordant pairs as Binomial(b+c, 0.5).
The test assesses marginal change within pairs, not association between the two measurements.
Responsible interpretation
Exact does not mean assumption-free, unbiased, or automatically more informative. The sampling design and the definition of ‘as extreme’ still matter.
Required assumption: Pairs must be independent of other pairs and measured twice on the same unit or a defensible match.
Quick guide
How to use this calculator
- Enter the observations, probabilities, model parameters, or summary statistics requested by the visible labels.
- Keep every value on the same scale and confirm that the selected sampling relationship, distribution, and tail convention match the question you are investigating.
- Read the result together with its assumptions and interpretation. Statistical output summarizes uncertainty under a model; it does not repair biased data or establish causation.
Calculation method
How the mcnemar’s test calculator works
Exact test treats b of b+c discordant pairs as Binomial(b+c, 0.5).
The test assesses marginal change within pairs, not association between the two measurements.
Worked example
McNemar’s Test example
Ten changes from no to yes and two from yes to no are tested using only 12 discordant pairs.
Exact test treats b of b+c discordant pairs as Binomial(b+c, 0.5).
Supported inputs
Precision and limits
Model and design
Pairs must be independent of other pairs and measured twice on the same unit or a defensible match.
Numerical scope
Inputs use double-precision numerical methods with guarded domains. Datasets accept up to 10,000 finite plain-decimal values. Extremely large parameters or probabilities deep in a numerical tail may require specialist statistical software.
Interpretation
The test assesses marginal change within pairs, not association between the two measurements.
Decision boundary
The calculator does not validate how data were collected, diagnose dependence or bias, choose a scientifically meaningful effect, or replace review by a qualified statistician for consequential research, medical, regulatory, safety, or policy decisions.
Privacy
Entered values and calculated results stay in this browser and are not sent to an analytics service.
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