Building a calibration line
- Prepare standards that cover the expected range, ideally in a matrix close to the real sample, with a blank among them.
- Measure in random order, with at least three replicates per level, so that drift does not look like a trend.
- Plot signal against concentration and fit a straight line over the range where it is linear. Look at the residuals, not only at R². A curved residual pattern means the range is too wide.
- Report the slope with its uncertainty, the intercept, the linear range and the number of points.
The slope is the sensitivity. For amperometric and voltammetric sensors it is often divided by the electrode area, as µA µM⁻¹ cm⁻², so that electrodes of different size can be compared.
Limit of detection and quantification
The limit of detection (LOD) is the smallest concentration that can be told apart from a blank with reasonable confidence. The limit of quantification (LOQ) is the smallest that can be measured with acceptable precision.
The result depends strongly on which σ is used: the standard deviation of repeated blanks, the residual standard deviation of the calibration line sy/x, or the standard error of the intercept. Mocak and co-workers (1997) compared these for voltammetric methods. Always say which one you used, and check the LOD by measuring a sample near it. An LOD far below the lowest standard you measured is an extrapolation, not a result.
Selectivity, repeatability and stability
- Interference. Measure the analyte with likely interferents at realistic, and higher, concentrations, and report the change in signal in percent.
- Repeatability on one electrode and reproducibility across several electrodes, as relative standard deviation (RSD).
- Stability of the response over days or weeks of storage, with the storage conditions.
Real samples
A sensor that works in buffer may not work in serum, urine, river water or coffee. Two methods test this.
- Recovery. Add known amounts of analyte to the real sample and measure what you find. Recoveries close to 100%, with a small RSD, suggest that the matrix does not disturb the measurement.
- Standard addition. Add several known amounts to the sample itself and extrapolate the line to zero signal. This corrects for matrix effects on the slope.
Where possible, compare the result with an established method such as HPLC.
A reporting checklist
| Item | What to give |
|---|---|
| Electrode | Material, modification and how it was made, geometric area, single use or reused |
| Method | Technique and all its parameters, electrolyte and pH, potential window, accumulation time |
| Calibration | Linear range, slope with uncertainty, intercept, number of points and replicates |
| LOD and LOQ | Formula, k, and which σ was used |
| Selectivity | Interferents, their concentrations and the signal change |
| Real samples | Sample type and preparation, recovery and RSD, comparison with a reference method |
Check your understanding
Quiz for lesson 4.2
Pick one answer per question. You see the explanation straight away.
References and further reading
- J. Mocak, A. M. Bond, S. Mitchell, G. Scollary, A statistical overview of standard (IUPAC and ACS) and new procedures for determining the limits of detection and quantification, application to voltammetric and stripping techniques, Pure Appl. Chem. 69 (1997) 297–328. IUPAC page
- International Council for Harmonisation, Guideline Q2(R2), Validation of analytical procedures, 2023.
- D. R. Thévenot, K. Toth, R. A. Durst, G. S. Wilson, Electrochemical biosensors, recommended definitions and classification, Pure Appl. Chem. 71 (1999) 2333–2348, also in Biosens. Bioelectron. 16 (2001) 121–131. IUPAC page
- A. J. Bard, L. R. Faulkner, Electrochemical Methods: Fundamentals and Applications, 2nd ed., Wiley, 2001, chapter 7.