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McNemar's Test Calculator

Free McNemar's test calculator. Paired 2×2 table, chi-square, exact binomial, odds ratio, continuity

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Why This Statistical Analysis Matters

Why: Statistical calculator for analysis.

How: Enter inputs and compute results.

χ²

PAIRED NOMINAL DATAInference & Tests

McNemar's Test — Paired 2×2 Tables

Before/after, matched pairs. Tests marginal homogeneity. Discordant pairs drive the test. Chi-square or exact binomial.

Fisher Exact →Chi-Square →

Real-World Scenarios — Click to Load

2×2 Paired Table

	After +	After −
Before +
Before −

Continuity correction

Exact binomial test

mcnemar_results.sh

CALCULATED

$ mcnemar --table="45,12,8,35" --correction= --exact=

Decision

FAIL TO REJECT

p-value

0.8585

Method

Chi-square with continuity correction

Discordant pairs

χ² statistic

0.4500

df = 1

Odds ratio (b/c)

1.5000

95% CI: [0.613, 3.670]

McNemar's Test Result

Paired 2×2 Table

p = 0.8585

Not significantχ² = 0.450Discordant: 20

numbervibe.com/calculators/statistics/mcnemar-test-calculator

Discordant Pairs Visualization (b vs c)

χ²(1) Distribution — Rejection Region & p-value

Paired Table (Cell Counts a, b, c, d)

Calculation Breakdown

TABLE SUMMARY

Discordant pairs (b + c)

12 + 8 = 20

Concordant pairs (a + d)

45 + 35 = 80

Total N

100

a + b + c + d

CHI-SQUARE TEST

Method

Chi-square (Edwards correction)

χ² statistic

0.4500

(|12−8|−1)²/(12+8) = 0.4500

ext{Always} 1 ext{for} 2 imes 2 ext{McNemar}

p-value

0.8585

1 - F_χ^{2}(χ^{2}, 1)

DECISION

FAIL TO REJECT H₀ (not significant)

EFFECT SIZE

Odds ratio (b/c)

1.5000

12/8

95% CI for OR

[0.6131, 3.6696]

\text{exp}(\text{ln}( ext{OR}) pm 1.96 imes √(1/b + 1/c))

⚠️For educational and informational purposes only. Verify with a qualified professional.

Key Takeaways — Paired Nominal Data

• 2×2 paired table: Rows = Before (+/−), Columns = After (+/−). Cells a,b,c,d. Only discordant pairs (b, c) matter.
• McNemar's χ² (with correction): χ² = (|b−c|−1)² / (b+c). df = 1.
• McNemar's χ² (no correction): χ² = (b−c)² / (b+c).
• Exact binomial: Under H₀, b ~ Binomial(b+c, 0.5). p-value = 2×P(X ≤ min(b,c)). Preferred when b+c is small.
• Odds ratio (discordant): OR = b/c. 95% CI: exp(ln(OR) ± 1.96×√(1/b + 1/c)).
• Interpretation: Significant result means the treatment/intervention changed the outcome proportions.

Did You Know?

🔗McNemar's test is for paired/matched data — same subjects measured twice. Not for independent groups.Source: McNemar 1947

📊Only discordant pairs (b and c) contribute to the test. Concordant pairs (a, d) are ignored.Source: Agresti

🧪Common in before/after studies, diagnostic test comparison, crossover trials.Source: NIST Handbook

📱A/B tests with same users (pre/post) should use McNemar, not chi-square for independence.Source: Best practice

⚠️When b+c < 25, use exact binomial test. Chi-square approximation may be unreliable.Source: Agresti

📐Edwards' continuity correction subtracts 1 from |b−c| to improve approximation.Source: Edwards 1948

Formulas

χ² = (|b − c| − 1)² / (b + c)

With continuity correction (Edwards)

χ² = (b − c)² / (b + c)

Without correction

OR = b / c

Odds ratio (discordant pairs)

95% CI: exp(ln(OR) ± 1.96 × √(1/b + 1/c))

Woolf method

Frequently Asked Questions

When to use McNemar vs chi-square?

McNemar: paired/matched data (same subjects, two time points or two conditions). Chi-square: independent groups.

When to use exact test?

When b+c is small (e.g., < 25). Exact binomial gives accurate p-values; chi-square can be unreliable.

What does continuity correction do?

Subtracts 1 from |b−c| to improve the chi-square approximation. Often used for small samples.

How to interpret the odds ratio?

OR = b/c. OR > 1 means more changed from + to − than − to +. OR < 1 means the opposite.

What is H₀?

H₀: marginal proportions are equal — P(Before +) = P(After +), i.e., b = c on average.

McNemar vs Chi-Square Independence

Chi-square test of independence assumes two independent samples. McNemar assumes paired data — same subjects measured twice. Using chi-square on paired data inflates the test statistic and gives incorrect p-values. Always use McNemar for before/after or matched designs.