McNemar Test

Compare proportions on paired data.

Definition

McNemar's test is the non-parametric equivalent of the paired t-test for binary data. It compares two proportions measured on the same subjects (before/after, two conditions) and tests whether the change is significant.

When to use it

• Compare two paired proportions (before/after)
• Evaluate the effectiveness of a treatment on a binary outcome
• Analyze agreement between two binary raters

Requirements

• Binary dependent variable (Yes/No, Success/Failure)
• Paired measurements (same subjects, two conditions)
• Continuity correction if discordant cells < 25

What StatsLab computes

• McNemar χ² statistic and p-value
• OR (odds ratio) with 95% CI
• Paired 2×2 contingency table
• Before/after proportions with 95% CI

Worked example

Context : Vaccine evaluation: 100 patients tested positive for a virus before and after vaccination.

Result : McNemar χ²(1) = 8.1, p = 0.004, OR = 0.21

Interpretation : Significant reduction in positive cases after vaccination (p < 0.01). The odds ratio of 0.21 indicates the risk of being positive after vaccination is 5 times lower.

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