| """Deterministic fixed-effect heterogeneity calculation, independently checked with Wolfram. |
| |
| No external service/API calls. Input arrays MUST be effect sizes and standard |
| errors obtained from authentic comparable studies before scientific use. |
| A pooled value is descriptive only, not proof of consensus or causal effect. |
| """ |
| from math import isfinite, sqrt |
|
|
| def inverse_variance_heterogeneity(effects: list[float], standard_errors: list[float]) -> dict: |
| if len(effects) != len(standard_errors) or len(effects) < 2: |
| raise ValueError("Need at least two matching effects and standard errors") |
| if any(not isfinite(float(v)) for v in effects): |
| raise ValueError("Effects must be finite") |
| if any(not isfinite(float(se)) or float(se) <= 0 for se in standard_errors): |
| raise ValueError("Standard errors must be finite positive numbers") |
| weights = [1.0 / (float(se) ** 2) for se in standard_errors] |
| pooled = sum(w * v for w, v in zip(weights, effects)) / sum(weights) |
| q = sum(w * (float(v) - pooled) ** 2 for w, v in zip(weights, effects)) |
| dof = len(effects) - 1 |
| i2 = max(0.0, (q - dof) / q) if q > 0 else 0.0 |
| stderr = sqrt(1.0 / sum(weights)) |
| return { |
| "pooled_effect": pooled, |
| "standard_error": stderr, |
| "ci95": [pooled - 1.96 * stderr, pooled + 1.96 * stderr], |
| "Q": q, |
| "degrees_of_freedom": dof, |
| "I2": i2, |
| "warning": "Do not pool incomparable outcomes or interpret this result as independent scientific validation.", |
| } |
|
|
