INTERPRETING RESULTS
A difference, a reference interval and a clinical decision
These are three questions. Answering one does not settle the others.
Revised 30 September 2026. The original publication date and address are retained.
Analytical difference
Could the observed difference be explained by the specified measurement process?
Population comparison
Where does a result sit relative to an appropriate reference population?
Clinical importance is a further question
Does the result or change matter for this person and this decision? That depends on clinical context, biological variation, decision thresholds and other evidence. A statistical finding alone cannot supply that judgement.
For the difference between two numerical results
For d = y₂ − y₁, uncertainty propagation gives u²(d) = u²(y₁) + u²(y₂) − 2cov(y₁,y₂), for the specified model. Shared calibration or other effects can create covariance. Decide what is being compared: the same specimen measured twice, different specimens over time, or two procedures.
Synthetic example: independent standard uncertainties of 0.4 and 0.5 units give u(d) = 0.64 units. If a normal approximation and k = 2 are justified, an approximate expanded interval for the difference has half-width 1.28 units. This describes the analytical model; it does not account for unmodelled bias or automatically include biological variation.
Do not widen a reference interval to change the conclusion
A central 95% reference interval describes a defined reference population. It does not mean that every result outside it indicates disease, or that a result must exceed three SDs to count as outside the interval. Do not replace validated limits with a wider interval simply to reclassify a result.
The arithmetic behind a symmetric normal interval
For an ideal normal distribution, mean ±1.96 SD covers about 95%, so the full width is about 3.92 SD. If illustrative limits were 10.2 to 13.4, their width of 3.2 would imply SD ≈0.82 under that model—not 1.6. This calculation does not validate those limits or justify estimating a clinical interval from a small convenience sample.
For change within a person
A reference change value combines specified analytical and within-person biological variation under assumptions about stability and distribution. Exceeding it is evidence about change relative to that model; it does not by itself prove clinical importance. Disease, treatment, sampling conditions and the time between measurements may change the interpretation.
Sources & further reading
- JCGM 100 — uncertainty propagation and covariance
- NIST/SEMATECH — the normal distribution
- CLSI EP28 — defining, establishing and verifying reference intervals (public overview)
Educational material. Examples are synthetic. Consult applicable full guidance and your locally approved procedure for operational decisions.