Wald F1 Confidence Interval Method

A Wald F1 Confidence Interval Method is a symmetric confidence interval method that uses normal approximation with delta-method standard error but suffers from severe undercoverage in small samples and near boundaries.

• AKA: Normal Approximation F1 CI Method, Symmetric F1 Interval Method, First-Order Delta F1 CI, Naive F1 Confidence Interval Method.
• Context:
  • It can typically construct intervals as F1 ± z*SE using first-order approximation.
  • It can typically achieve only ~85% actual coverage for nominal 95% CI in small samples.
  • It can typically fail catastrophically near boundaries with coverage dropping to ~0%.
  • It can often produce impossible intervals outside [0,1] range (e.g., [-0.05, 1.03]).
  • It can often collapse to degenerate intervals [0,0] or [1,1] at extreme F1 values.
  • It can often be used as baseline comparison showing why better methods are needed.
  • It can range from being a Standard Wald F1 Confidence Interval Method to being a Adjusted Wald F1 Confidence Interval Method, depending on its variance estimation.
  • It can range from being a Small-Sample Wald F1 Confidence Interval Method to being a Large-Sample Wald F1 Confidence Interval Method, depending on its sample size.
  • It can range from being a Uncorrected Wald F1 Confidence Interval Method to being a Continuity-Corrected Wald F1 Confidence Interval Method, depending on its adjustment.
  • It can range from being a Failed Wald F1 Confidence Interval Method to being a Adequate Wald F1 Confidence Interval Method, depending on its coverage achievement.
  • ...
• Example(s):
  • Coverage Failure Examples, such as:
    • n=20, F1=0.8: Wald CI [0.72, 0.88], actual coverage 82% (13% below nominal).
    • n=30, F1=0.95: Wald CI [0.91, 0.99], actual coverage 45% (catastrophic failure).
    • n=15, F1=0: Wald CI [0, 0] (degenerate), missing true F1>0 possibility.
  • Boundary Violation Examples, such as:
    • F1=0.98, SE=0.03: Wald CI [0.92, 1.04] exceeds upper bound.
    • F1=0.02, SE=0.04: Wald CI [-0.06, 0.10] goes below zero.
    • Invalid intervals requiring post-hoc truncation.
  • Comparison Studies, such as:
    • Mean coverage: Wald 85.1%, Wilson 95.3%, BCa 94.8%.
    • Extreme cases: Wald 0% coverage, Wilson maintains >90%.
    • Consistent underperformance across all scenarios.
  • ...
• Counter-Example(s):
  • Wilson Score F1 Confidence Interval Method, which achieves nominal coverage.
  • Agresti-Coull F1 Confidence Interval Method, which uses plus-four correction.
  • BCa Bootstrap F1 Confidence Interval Method, which handles skewness.
• See: Confidence Interval Method, Normal Approximation, Delta-Method F1 Standard Error Estimation Method, Undercoverage Problem, Coverage Probability, Symmetric Interval, Boundary Violation, Small Sample Problem, Wilson Score F1 Confidence Interval Method, Statistical Anti-Pattern, Coverage Probability Validation Method.

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