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Table 4 Evaluation of type I error rates (TIER)

From: The McNemar test for binary matched-pairs data: mid-p and asymptotic are better than exact conditional

  mean max proportion proportion
Method TIER TIER TIER> 0.05 TIER< 0.03
All 9595 scenarios
McNemar asymptotic 0.0430 0.0537 0.294 0.121
McNemar asymptotic w/CC 0.0190 0.0357 0.000 0.889
McNemar exact 0.0201 0.0367 0.000 0.880
McNemar mid-p 0.0349 0.0495 0.000 0.260
Exact unconditional 0.0373 0.0495 0.000 0.201
Subregion: 10≤N≤30(2525 scenarios)
McNemar asymptotic 0.0352 0.0529 0.037 0.281
McNemar asymptotic w/CC 0.0089 0.0237 0.000 1.000
McNemar exact 0.0090 0.0278 0.000 1.000
McNemar mid-p 0.0212 0.0469 0.000 0.627
Exact unconditional 0.0251 0.0488 0.000 0.541
Subregion: 35≤N≤60(3030 scenarios)
McNemar asymptotic 0.0435 0.0537 0.210 0.084
McNemar asymptotic w/CC 0.0196 0.0306 0.000 0.991
McNemar exact 0.0210 0.0306 0.000 0.989
McNemar mid-p 0.0374 0.0474 0.000 0.176
Exact unconditional 0.0408 0.0482 0.000 0.096
Subregion: 65≤N≤100(4040 scenarios)
McNemar asymptotic 0.0476 0.0535 0.519 0.049
McNemar asymptotic w/CC 0.0249 0.0357 0.000 0.743
McNemar exact 0.0263 0.0367 0.000 0.723
McNemar mid-p 0.0416 0.0495 0.000 0.095
Exact unconditional 0.0423 0.0495 0.000 0.066