Laboratory Mathematics, Instrumentation and Quality Control
This domain combines calculation fluency with statistical judgement. You must be able to convert units, perform dilutions, apply Beer-Lambert, and decide whether a control result should stop the run.
Core rules
- Dilution: if x parts sample are added to y parts diluent, the dilution factor is (x + y)/x. Report the measured value multiplied by that factor, and state the dilution on the report.
- Beer-Lambert: absorbance equals molar absorptivity times concentration times path length. For a single-point calibration, unknown concentration = (unknown absorbance / calibrator absorbance) x calibrator concentration, provided the assay is linear at that wavelength and path length is constant.
- Units: convert glucose mg/dL to mmol/L by multiplying by 0.0555; creatinine mg/dL to micromol/L by 88.4; haemoglobin g/dL to g/L by 10. Always carry units through the calculation.
- Westgard rules: 1-2s is a warning only; 1-3s rejects; 2-2s rejects (systematic error); R-4s rejects (random error, one control above +2s and another below -2s with a range exceeding 4s); 4-1s and 10x reject systematic drift.
- Calibration establishes the relationship between signal and concentration; calibration verification confirms the existing curve still performs; linearity studies establish the reportable range.
Worked example
A chemistry control has a mean of 100 micromol/L and SD of 5. Two control levels in the same run give 112 and 91. Reasoning: 112 is +2.4s and 91 is -1.8s, so neither triggers 1-3s. However, one exceeds +2s and the other exceeds -2s in opposite directions, and the total spread is 112 - 91 = 21 micromol/L, which is 4.2s. This violates R-4s, indicating random error such as a pipetting or bubble problem, so the run is rejected and the samples repeated. If both had been on the same side of the mean beyond 2s, 2-2s would indicate systematic error and point toward calibration or reagent lot failure.
Traps that cost marks
- Reporting a diluted result without applying the dilution factor, or applying it twice.
- Reading a result beyond the linearity limit from the calibration curve instead of diluting and re-running.
- Treating 1-2s as a rejection rule and discarding valid runs.
- Confusing the standard deviation with the standard error, or calculating SD with n instead of n-1 for a sample.
- Using a calibrator value from another lot or an expired calibrator.