McNemar test (paired 2×2)

Tests whether two paired methods have the same success probability, using only discordant pairs (b and c).

Inputs

Result

Computed ✅

b: 12 · c: 5 · b+c: 17

Chi-square (cc): 2.1176

p (chi-square): 0.1456

p (exact): 0.1435

Decision (alpha=0.05): Fail to reject H0

Interpretation: If you reject H0, the two paired methods have significantly different success rates.

Step-by-step

Discordant total

Formula: n_d = b + c

Substitute: 12 + 5

Result: n_d = 17
Chi-square (continuity corrected)

Formula: χ² = (|b−c|−1)² / (b+c)

Substitute: (|12−5|−1)² / 17

Result: χ² = 2.1176
p-value (chi-square)

Formula: p = P(Chi²₁ ≥ χ²)

Substitute: df = 1

Result: p = 0.1456
Exact p-value (binomial)

Formula: p = BinomTest(min(b,c); n=b+c, p=0.5)

Substitute: min(b,c)=5, n=17, p=0.5

Result: p_exact = 0.1435