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- """Statistical utilities for drill result analysis."""
- from __future__ import annotations
- import math
- def wilson_ci(passed: int, total: int, z: float = 1.96) -> tuple[float, float]:
- if total == 0:
- return (0.0, 0.0)
- if passed > total:
- passed = total
- p = passed / total
- denom = 1 + z**2 / total
- center = (p + z**2 / (2 * total)) / denom
- margin = (z / denom) * math.sqrt(p * (1 - p) / total + z**2 / (4 * total**2))
- return (max(0.0, center - margin), min(1.0, center + margin))
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