stats

Chi-Squared Variance Test

Test a sample variance against a known population variance — χ² statistic, p-value, confidence interval for σ².

Inputs

Input mode

Sample data (comma-separated)Hypothesized variance σ₀²

Hypothesis tail

Confidence level (for CI)

Results

Sample variance s²—

Sample SD s—

Degrees of freedom—

χ² statistic—

p-value (two-tailed)—

95% CI for σ² — lower—

95% CI for σ² — upper—

Conclusion α = 0.05—

Conclusion α = 0.01—

χ² = (n−1)s²/σ₀² · df = n−1
CI: ((n−1)s²/χ²_upper , (n−1)s²/χ²_lower)
p via Q(df/2, χ²/2) — upper incomplete gamma

Series branch (x < a+1): P = e^(−x)x^a/Γ(a)·Σ x^n/Γ(a+n+1)
CF branch (x ≥ a+1): Lentz algorithm. ε = 1e-10, max 200 iters.