Statistics · χ² ↔ p-value ↔ σ
Convert between Δχ², confidence level / p-value (for a chosen number of degrees of freedom), and Gaussian significance in σ. All computed instantly in your browser — no dependencies.
1 · Δχ² for a confidence region
Δχ² ↔ confidence level, for a given number of degrees of freedom
For a χ² fit, the Δχ² above the minimum that encloses a confidence region depends on the number of free parameters (degrees of freedom).
| Level | Confidence level | p-value | Δχ² |
|---|
2 · p-value ↔ σ (Gaussian)
Significance in standard deviations
Convert a p-value (or confidence level) to a Gaussian σ, and back. One-sided is the usual significance / discovery convention (5σ ≈ 2.9×10⁻⁷); two-sided is symmetric about the mean.
Tip: enter a p-value of 2.8665e-7 (one-sided) to recover the 5σ discovery threshold.
Numerics: regularised incomplete gamma (Numerical Recipes) for the χ² CDF, inverse via Wilson–Hilferty + Newton; normal tail and inverse via Acklam's algorithm. Self-tested against canonical values on load (see browser console).