How this calculation works
Only discordant pairs identify change direction. Exact mode sums a two-sided conditional binomial tail; approximate modes use one chi-square degree of freedom with the selected correction convention.
Uncorrected statistic = (b − c)²/(b+c); exact test conditions on discordant total b+c with probability one halfA worked example
With ten positive-to-negative and two negative-to-positive pairs, the discordant difference is eight and uncorrected statistic is 64/12. The exact two-sided conditional p value is 0.038574219.
Good to know
Independent matched pairs required. Exact mode supports at most 2,000 discordant pairs. No discordants gives a labeled p=1 convention, not evidence of equivalence.
Reference: R statistical documentation: McNemar test (opens in a new tab) ↗
Use matched outcomes rather than independent groups
Each subject or unit contributes one before/after pair. A table comparing unrelated groups does not become paired merely because its rows and columns have binary labels.
Concordant pairs agree before and after. Discordant pairs switch direction, and it is the balance between those two switching counts that the symmetry test examines.
Declare the exact or approximate convention
Exact mode uses the conditional binomial distribution with the discordant total fixed. Approximate modes use a chi-square tail, with an optional absolute-difference correction reduced by one.
These conventions can differ for small discordant totals. The page labels the selected method rather than presenting one unlabeled p value as universal.
No switching information is not proof of no effect
Changing the concordant counts alone does not change this conditional p value. With no discordant pairs, the direction balance contains no information.
The p=1 convention for that degenerate case is displayed alongside an explicit explanation. It does not establish equivalence or guarantee a sufficiently precise estimate of change.
Use the result with the next measurement
The paired t test differences calculator concerns numerical within-pair measurements. Binary switching counts require their own model rather than treating a 2×2 table as continuous differences.
Independent matched pairs required. Exact mode supports at most 2,000 discordant pairs. No discordants gives a labeled p=1 convention, not evidence of equivalence.
A few questions, answered
Do concordant pairs change p?
Not for the conditional symmetry calculation here.
Is an independent 2×2 table appropriate?
No, the counts must describe matched pairs.
What does no discordance mean?
There is no switch-direction information, not demonstrated equivalence.