1. Calibration + Methodology

What is calibration?

Establishing a mathematical function that describes the dependence of analyte concentration on the measured value/signal.

General calibration equation

y = a + bx; y = signal, a = intercept, b = slope/sensitivity, x = concentration or variable.

What is sensitivity in a calibration curve?

The slope b of the calibration curve, not the intercept.

What is the intercept in a calibration curve?

The signal at x = 0; it is not sensitivity and not LOD.

External calibration

Standards are prepared separately from the sample; signal from standards is used to determine unknown sample concentration.

When is external calibration appropriate?

When matrix effects are small or the standards match the sample matrix well.

External calibration exam trap

External calibration is NOT typically chosen when severe matrix effects are present.

Standard addition

Known small amounts of standard solution are added directly to the sample to compensate for matrix effects.

When is standard addition used?

When severe matrix effects are present and matrix-matched standards are difficult.

Internal standard

A different compound is added in known amount to all samples and standards to correct for injection, preparation or instrument variation.

Internal standard response equation

S_A/S_IS = F · c_A/c_IS; S_A = analyte signal, S_IS = internal standard signal, F = response factor.

Internal standard vs standard addition

Internal standard corrects variation using another compound; standard addition adds the same analyte standard to the sample.

Matrix effect

The sample matrix changes the analytical signal compared with standards of the same analyte concentration.

LOD meaning

Limit of detection: the smallest concentration that can be detected reliably, not necessarily quantified accurately.

LOD signal formula

y_LOD = y_blank + 3s_blank; uses blank signal and blank standard deviation.

LOD concentration formula

c_LOD = (y_LOD - a)/b; a = intercept, b = slope.

LOQ formula

y_LOQ = y_blank + 10s_blank; LOQ is the limit of quantification.

Residual analysis

Residual analysis checks deviations between measured points and calibration curve; it helps assess model fit, linearity and possible LOD/fit problems.

Confidence limits of calibration curve

Confidence limits are narrowest near the centroid/mean of calibration data and wider at the ends/extrapolated regions.

Centroid of calibration data

The point around the mean x and mean y of calibration data; uncertainty is lowest near this region.

Why should you not extrapolate a calibration curve?

Uncertainty increases outside the calibrated concentration range and assumptions may fail.

What must be reported with a calculation?

Equation used, assumptions, units, dilution factors and final concentration.

Blank sample

Contains matrix/reagents but no analyte; used to correct background and estimate LOD.

Dilution factor

DF = V_final/V_sample; c_original = c_measured · DF.

Convert mol/L to mg/L

mg/L = c(mol/L) · molar mass(g/mol) · 1000.

Analytical workflow

Choose method/försöksplan → sampling → sample preparation → interference removal → calibration/measurement → calculation → evaluation.

Representative sample

A sample that reflects the whole material/parti; critical when the material is heterogeneous.

Total variance formula

s_tot² = s_prov² + s_analys²; total uncertainty comes from sampling and analytical measurement.

When should more samples be prioritized?

If sampling uncertainty dominates analytical uncertainty, improve/take more samples instead of only improving the instrument method.