Overview
ISO 8466-2:2001 - Water quality: Calibration strategy for non-linear second‑order calibration functions - provides guidance for calibrating analytical methods when a straight‑line (linear) fit is inadequate. Instead of linear regression, the standard prescribes a least‑squares fit to a second‑order polynomial to determine the calibration function and associated confidence intervals. It is intended primarily for method development in water, wastewater and sludge analysis and may not be required for all routine analyses.
Key topics and technical requirements
- Working range selection
- Define the practical objective and place expected sample concentrations near the centre of the working range.
- Ensure lower limit is distinguishable from blanks (above limit of quantitation).
- Homogeneity of variances
- Use replicate measurements at lowest and highest standards (recommended N = 10 equidistant standards).
- Apply a one‑sided F‑test (see Annex A) to check variance homogeneity; reduce working range if variances differ significantly.
- Second‑order calibration
- Fit response y to y = a + b x + c x² using least squares to estimate coefficients a, b, c.
- Diagnose fit adequacy by plotting residuals (y − ŷ) vs concentration.
- Degrees of freedom for residual standard deviation: f = N − 3.
- Performance characteristics
- Residual standard deviation (s_y) quantifies scatter about the quadratic fit.
- Sensitivity (e) at concentration x: e = b + 2 c x; instrument sensitivity at the working‑range centre x0: E = b + 2 c x0.
- Standard deviation of the procedure (s_x0) = s_y / E and relative standard deviation (V%) = (s_x0 / x0) × 100.
- Single‑valued calibration requirement
- Test for maxima/minima: stationary point x* = −b / (2 c). If x* lies inside the working range the function is not single‑valued and must not be used.
- Sample analysis
- Invert the quadratic to obtain sample concentration x̂ from measured response ŷ (different algebraic solutions for positive/negative curvature).
- Estimate the confidence interval of x̂ by propagating both measurement error and calibration uncertainty.
Applications and users
- Method developers and validation teams in environmental and water quality laboratories
- Quality managers and accreditation bodies assessing analytical performance
- Environmental chemists, instrument manufacturers, and laboratories confronting non‑linearity in calibration
- Use cases: method validation, estimation of limits of quantitation, performance comparison, reporting confidence intervals for non‑linear calibrations
Related standards
- ISO 8466‑1: Statistical evaluation of the linear calibration function - use when linear regression is appropriate.
- Refer to Annex A of ISO 8466‑2 for F‑table values used in variance testing.
Keywords: ISO 8466-2:2001, water quality calibration, second‑order polynomial, non‑linear calibration, residual standard deviation, instrument sensitivity, F‑test, confidence interval.