Why we want a straight line
Most instruments don't read out concentration directly; they give a signal — a peak height, an absorbance — and we convert it using a calibration curve built from standards of known concentration. Life is easiest when that relationship is a straight line: double the concentration, double the signal. This straight-line behaviour is called linearity. A linear method is simple to use, easy to check, and forgiving — a small reading error turns into a proportionally small concentration error, with no nasty surprises.
But no method stays linear forever. Push the concentration high enough and the line bends — detectors saturate, light gets fully absorbed, signals plateau. The stretch of concentrations where the method is both linear *and* precise enough to be useful is its working range. A validated method states this range plainly, and you simply don't report results outside it.
Don't let r fool you
When you fit a line to your standards, software hands you a correlation coefficient, r (or r-squared), often a glamorous 0.999. It's tempting to treat that one number as proof of linearity. Resist. A high r mostly tells you the points trend together — it can stay impressively high even when the data gently curve, especially if your standards are bunched at the extremes.
Recovery: did we get back what we put in?
A perfect calibration with clean standards still doesn't prove the method works on *real* samples, because real samples are messy. Some analyte gets lost during extraction; some gets stuck to glassware; the surrounding stuff can dampen or boost the signal. Recovery measures how much of the analyte your method actually finds, as a percentage of what is truly there. A recovery of 100% is the dream; 85% means you're systematically losing about a seventh of the analyte somewhere along the way.
How do you measure recovery when you don't know the true amount in a real sample? You cheat, honestly: you take a real sample, add ("spike") a known amount of analyte, and see how much extra signal comes back. This is the spike recovery test, and it is one of the most trusted, hands-on checks in the whole field.
Running a spike-recovery test
- Measure the real sample as-is to get its starting analyte level.
- Take a second portion of the same sample and add a precisely known amount of analyte (the spike).
- Measure the spiked portion through the full method.
- Recovery = (measured spiked - measured original) / amount added x 100%. Compare against the acceptable range, often 80-120% for trace work.
If recovery drifts far from 100%, suspect a matrix effect — the sample's own ingredients interfering — or a loss step in your sample prep. A consistent low recovery can sometimes be corrected for, but it's always better to fix the leak than to paper over it with a correction factor.
Linearity and recovery together
Notice how these two checks cover different failure modes. Linearity guards the *math* — that the calibration faithfully turns signal into concentration across the working range. Recovery guards the *chemistry* — that the analyte survives the journey from real sample to final reading. A method needs both to pass validation; a beautiful line is worthless if 40% of your analyte vanishes before it ever reaches the detector.