McNemar's Test Calculator
Statistical test for paired categorical data with 2×2 contingency tables
2×2 Contingency Table
Enter the observed frequencies for each cell of the 2×2 contingency table
Choose appropriate test method
Example Calculation
Medical Treatment Study
Scenario: 220 patients tested before and after treatment
Data: a=60, b=70, c=50, d=40
Question: Does treatment significantly affect test results?
Calculation
χ² = (b-c)²/(b+c) = (70-50)²/(70+50) = 400/120 = 3.33
p-value = 1 - χ²cdf(3.33) = 0.068
Decision: p-value (0.068) > α (0.05), not significant
Conclusion: No evidence that treatment affects test results
Test Selection Guide
Standard McNemar's
Use when b+c ≥ 25
Exact Binomial
Use when b+c < 25
Edwards Correction
Conservative correction
Mid-p Test
Less conservative than exact
Contingency Table
Cell Definitions:
a: Positive before, Positive after
b: Negative before, Positive after
c: Positive before, Negative after
d: Negative before, Negative after
Key Focus:
McNemar's test uses only discordant pairs (b + c)
Formulas
Standard McNemar's:
χ² = (b-c)²/(b+c)
Edwards Correction:
χ² = (|b-c|-1)²/(b+c)
Yates Correction:
χ² = (|b-c|-0.5)²/(b+c)
Understanding McNemar's Test
What is McNemar's Test?
McNemar's test is a statistical test used for paired categorical data to determine whether the marginal proportions differ significantly between two related groups or time points.
When to Use McNemar's Test
- •Before-after treatment comparisons
- •Matched pairs with binary outcomes
- •Test-retest reliability studies
- •Comparing two diagnostic methods
Key Assumptions
Paired Data
Each subject must be measured twice (e.g., before and after treatment).
Binary Outcome
The outcome variable must have exactly two categories (e.g., pass/fail, positive/negative).
Independence
Different pairs should be independent of each other.
Important Notes
- • McNemar's test focuses only on discordant pairs (cells b and c)
- • Use exact test when b+c < 25 for better accuracy
- • The test assumes the changes are symmetric under the null hypothesis
- • Not appropriate for independent groups (use Chi-square test instead)