Statistics & Uncertainty Calculators
Sample sizes, ANOVA, GUM uncertainty, and the QA/QC math.
- Cp / Cpk Process CapabilityTurn spec limits and process spread into Cp, Cpk, and the sigma level that predicts your reject rate.Cp = (USL − LSL) / 6σ , Cpk = min[(USL − μ)/3σ, (μ − LSL)/3σ]
- Sample Size for a Mean (Known σ)How many samples you need to estimate a mean within a target margin of error, when the population standard deviation is known.n = ( z(α/2) · σ / E )² , rounded up
- One-Way ANOVA F-StatisticCompare 2–4 group means from summary stats (n, mean, s) — get F, mean squares, and degrees of freedom for the table lookup.F = MSB / MSW, MSB = Σ nᵢ(x̄ᵢ − x̄)² / (k − 1), MSW = Σ (nᵢ − 1)sᵢ² / (N − k)
- Student-t Mean Confidence IntervalConfidence interval for a population mean from a small sample — uses the t-distribution, not the normal.CI = x̄ ± t(α/2, n−1) · s/√n , SE = s/√n
- Normal Distribution Tail ProbabilityTurn a z-score into CDF, tail area, and two-sided probability — the guts of a Z-table without the table.z = (x − μ)/σ , Φ(z) = ½[1 + erf(z/√2)] , upper = 1 − Φ(z)
- Combined Uncertainty (GUM)Root-sum-square of up to five uncertainty components, with coverage factor for an expanded uncertainty.uₙ = √(u₁² + u₂² + … + uₙ²) , U = k · uₙ
- Type A / Type B Combined UncertaintyCombine a statistical (Type A) uncertainty with an instrument/spec (Type B) contribution per the GUM — get u_c, expanded U, and effective degrees of freedom.u_A = s/√n u_B = a/√3 (rect), a/√6 (tri), a/√2 (U), a (normal 1σ) u_c = √(u_A² + u_B²) U = k·u_c ν_eff = u_c⁴ / (u_A⁴/(n−1))
- ISO 17025 CMC (Calibration & Measurement Capability)Roll reference-standard, repeatability, resolution, and other contributors into an ILAC P14-style CMC claim for your scope of accreditation.u_ref = U_ref/2 u_rep = s/√n u_res = r/(2√3) , u_c = √(u_ref² + u_rep² + u_res² + u_other²) CMC = k · u_c