McNemar's Test (Paired)
Computes McNemar's test, used to compare two paired proportions — when the same subjects are measured twice (before and after, or by two methods). Unlike the two-proportion test, which treats the groups as independent, McNemar looks only at the cases that switched classification (the discordant cells b and c of the 2×2 table), ignoring those that stayed the same. The continuity-corrected version follows a chi-square with 1 degree of freedom. Enter the two discordant counts.
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McNemar's Test (Paired)
Computes McNemar's test, used to compare two paired proportions — when the same subjects are measured twice (before and after, or by two methods). Unlike the two-proportion test, which treats the groups as independent, McNemar looks only at the cases that switched classification (the discordant cells b and c of the 2×2 table), ignoring those that stayed the same. The continuity-corrected version follows a chi-square with 1 degree of freedom. Enter the two discordant counts.
Comparing proportions when the data are paired
Picture measuring the same people's opinion before and after a campaign, or classifying the same exams by two different methods. The two sets of answers aren't independent — they come from the same individuals. Applying the two-proportion test here would be a mistake, because it assumes independence. McNemar's test is the right tool for paired data.
McNemar's insight is to look only at who changed. In a two-by-two table of before versus after, the diagonal cells, which agree, carry no information about change; all that matters are the two discordant cells, b and c, where the classification flipped one way or the other. If the change were symmetric, b and c would be similar; a large difference between them is what the test detects.
Enter the two discordant counts, b and c. The tool computes the continuity-corrected chi-square statistic, which follows a chi-square with one degree of freedom. The correction subtracts one from the absolute difference before squaring, making the test a bit more conservative, which helps when the number of discordances is modest.
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