Wilson with Continuity Correction F1 CI Method

A Wilson with Continuity Correction F1 CI Method is a conservative confidence interval method that adds continuity correction to Wilson score intervals achieving ≥95% minimum coverage but ~97% average coverage for F1 scores in very small samples.

• AKA: Wilson+CC F1 Method, Conservative Wilson F1 CI, Continuity-Corrected Wilson F1 Method, Brown et al. Recommended F1 CI.
• Context:
  • It can typically be recommended specifically for n < 40 by Brown, Cai, and DasGupta (2001).
  • It can typically guarantee minimum coverage ≥ 95% even for n=5 or n=10.
  • It can typically achieve average coverage ~97% (slightly over-conservative).
  • It can often add 0.5/(2n) continuity correction to standard Wilson bounds.
  • It can often provide widest intervals among analytical methods ensuring safety.
  • It can often be preferred in high-stakes applications requiring coverage guarantee.
  • It can range from being a Standard Wilson with Continuity Correction F1 CI Method to being a Modified Wilson with Continuity Correction F1 CI Method, depending on its correction factor.
  • It can range from being a Small-n Wilson with Continuity Correction F1 CI Method to being a All-n Wilson with Continuity Correction F1 CI Method, depending on its application range.
  • It can range from being a Minimum-Coverage Wilson with Continuity Correction F1 CI Method to being a Average-Coverage Wilson with Continuity Correction F1 CI Method, depending on its optimization target.
  • It can range from being a Fixed-CC Wilson with Continuity Correction F1 CI Method to being a Adaptive-CC Wilson with Continuity Correction F1 CI Method, depending on its correction adaptation.
  • ...
• Example(s):
  • Very Small Sample Applications, such as:
    • n=10: Standard Wilson 93% minimum coverage, Wilson+CC 95.2% minimum.
    • n=5: Standard Wilson 89% minimum coverage, Wilson+CC 95.5% minimum.
    • Critical for maintaining nominal coverage guarantee.
  • Coverage Trade-off Examples, such as:
    • True F1=0.5, n=20: Wilson 95.1% coverage, Wilson+CC 97.3% coverage.
    • Interval width: Wilson [0.38, 0.62], Wilson+CC [0.35, 0.65].
    • Extra 8% width for 2.2% coverage improvement.
  • Extreme Value Protections, such as:
    • F1=0.95, n=15: Wilson might undercover at 92%, Wilson+CC maintains 95%.
    • F1=0.02, n=12: Wilson 91% coverage, Wilson+CC 96% coverage.
    • Most valuable at distribution extremes.
  • ...
• Counter-Example(s):
  • Standard Wilson F1 CI Method, which lacks continuity correction.
  • Agresti-Coull F1 Confidence Interval Method, recommended for n ≥ 40.
  • Liberal CI Method, which prioritizes narrow intervals over coverage.
• See: Wilson Score F1 Confidence Interval Method, Continuity Correction, Conservative Estimation, Brown-Cai-DasGupta Recommendation, Small Sample Inference, Coverage Probability, Minimum Coverage Guarantee, Over-Conservative Method, F1 Interval Selection Guide Method, High-Stakes Application.

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