1The seven lines that matter

Parts 1 and 2 of this series were about finding the right limit. This part is about the other half of the comparison: the result. The examples are drawn from EU food law — maximum levels from Regulation (EU) 2023/915, the rules of interpretation from Regulation (EC) No 333/2007 — but the logic is the same wherever a number meets a limit: drinking water, toys, cosmetics, packaging.

A report from an accredited laboratory is a dense document, and for compliance purposes seven lines do the work. The analyte — and, where it matters, the species, because total arsenic and inorganic arsenic are different regulated quantities. The matrix as the laboratory classified it, because limits attach to legal categories, not to marketing names. The units and basis — mg/kg on wet weight is the default in EU contaminant law, and confusing mg/kg with µg/kg is a factor-of-a-thousand mistake that happens more often than anyone admits. The result with its uncertainty, written x ± U. The LOQ for each element. The recovery, and whether the result was corrected for it. And, if you asked for one, a statement of conformity — with the decision rule it used.

2<LOQ is not zero

The limit of detection is the lowest concentration at which the method can tell the analyte apart from a blank. The limit of quantification is the lowest concentration it can put a reliable number on — conventionally around three times higher. Below the LOQ an honest laboratory does not report a value; it reports “<LOQ”.

Two consequences follow. The first: “not detected” and “<LOQ” are statements about the method, not about the sample. A result of <0.05 mg/kg means the true value lies somewhere between zero and 0.05. It does not mean zero — and if the level you are being asked about is 0.02, that report tells you nothing at all. This is why EU exposure assessments use the upper-bound convention: everything below the LOQ is counted as if it sat exactly at the LOQ.

The second: the LOQ decides whether a laboratory is even eligible to check a given level. Regulation 333/2007 sets the requirement relative to each maximum level, and Part 1 of this series listed the criteria in full. The short version:

Checking lead in wine at 0.10 mg/kg therefore needs an LOQ of 0.020 mg/kg or better. A cheaper screening method with an LOQ of 0.05 would “see” the lead, but a result near the level would be metrologically worthless — and inadmissible for official control.

3The ± is the honest part

No measured concentration is a single point. Weighing, digestion, calibration, instrument drift, matrix effects — each contributes a small scatter, and the laboratory combines them into a standard uncertainty u, then multiplies it by a coverage factor k = 2 to get the expanded uncertainty U printed on the certificate. The interval x ± U covers the true value with roughly 95 % confidence. That is what “0.095 ± 0.024 mg/kg” says: with 95 % confidence, the truth lies between 0.071 and 0.119.

Uncertainty is not a confession of sloppiness. It is a regulated performance characteristic, and EU law caps how large it may be. A method is fit for purpose only if its standard uncertainty stays below a maximum computed from the level itself:

U_f = √( (LOD/2)² + (α·C)² ) — the maximum standard measurement uncertainty, where C is the concentration of interest and α a factor that falls as concentrations rise.

At the wine level of 0.10 mg/kg — that is, 100 µg/kg — with an LOD of 0.01 mg/kg, the formula allows an expanded uncertainty of about 0.036 mg/kg, roughly a third of the value being measured. Our worked example’s ± 0.024, about 25 % relative, sits comfortably inside that, and is typical of a good ICP-MS measurement near a limit. Which leads to a rule of thumb worth keeping: a result near a legal limit that carries no uncertainty statement is a screening result, not a compliance result.

One more line of small print: recovery. Where the method involves an extraction step, the regulation requires the result to be corrected for recovery, and the report must say that the correction was applied and at what rate. Two laboratories, one correcting an 85 % recovery and one not, will disagree by 15 % on identical samples — while both being internally consistent.

4The decision rule: where chemistry meets law

So the true value lies, with 95 % confidence, between 0.071 and 0.119 mg/kg, and the level is 0.10. Someone has to decide. The instruction for how to decide — how the uncertainty counts for or against the limit — is the decision rule. Since the 2017 revision of ISO/IEC 17025, a laboratory issuing a pass/fail statement must state which rule it used, and must agree it with the customer before the work begins. The standard taxonomy is ILAC-G8; the full treatment is the Eurachem/CITAC guide. Three rules cover nearly every case in practice.

Simple acceptance is common in commercial work precisely because it is simple: 0.095 ≤ 0.10, pass. Near a limit it is closer to a coin toss than a verdict.

Guarded rejection is how EU enforcement works. Regulation 333/2007 instructs the official laboratory to reject a lot only where the result clears the level with its whole uncertainty interval:

“The lot or sublot is rejected if the analytical result of the laboratory sample exceeds beyond reasonable doubt the respective maximum level … taking into account the expanded measurement uncertainty.”

Our wine passes official control: 0.095 − 0.024 = 0.071, below 0.10. No authority can prove non-compliance from this measurement. One nuance Part 1 already flagged: the regulation states the principle, and the familiar arithmetic — subtract U, then compare — comes from the Commission’s expert report on the use of uncertainty in food law rather than from the legal text itself.

Guarded acceptance is the rule for the opposite chair. The enforcement laboratory asks “can I prove this is over the limit?”; a producer or importer should ask “can I be confident it is under?” — which means demanding x + U ≤ ML before calling a lot clean. Our wine fails that test decisively: 0.095 + 0.024 = 0.119.

5One number, four zones

Put the two guarded rules on one axis and every possible result falls into one of four zones. For our example — level 0.10 mg/kg, U = 0.024:

Our 0.095 sits in the probable-pass band, and it is worth being blunt about what that band contains. Treating the measurement’s scatter as roughly normal — the same model the compliance guides use — a result of 0.095 with u = 0.012 leaves about a 34 % probability that the true concentration is above 0.10. The lot is unenforceable and, one time in three, actually over the level. Whether to ship it is a commercial decision about recall risk, retailer specifications and export markets — but it should be made knowing that number, not from the single word “complies”.

6The report speaks for the sample, not the lot

Everything above concerns analytical uncertainty — the laboratory’s own scatter on the material it received. It says nothing about whether the 25 grams that went into the digestion vessel represent the ten thousand bottles in the consignment. Contaminants are rarely distributed evenly, and that is why Regulation 333/2007 devotes its longest part to sampling: incremental samples across the lot, aggregate samples of a set weight, and the principle that a legally meaningful result starts from a legally taken sample.

A courier envelope with one retail unit inside supports a statement about that unit. It becomes evidence about a lot only as far as your own sampling was representative — Part 2 made the same point about a single sealed bottle. For official disputes, EU law also gives the operator a right to a documented second expert opinion, and where appropriate a second analysis, under Article 35 of Regulation (EU) 2017/625. Retained counter-samples are worth the freezer space.

7What to ask before you order

Five questions, asked before the sample ships, prevent almost every dispute about a report afterwards.

8Questions we hear

Is 0.095 mg/kg against a 0.10 mg/kg limit a pass?

Under the EU official-control rule, yes — non-compliance cannot be proven once the uncertainty is taken into account. Under a due-diligence rule, no: with a typical ± 0.024 uncertainty there is about a one-in-three chance the true value exceeds the limit.

Does “<LOQ” mean the substance is absent?

No. It means that the concentration, if any, is below the smallest value the method can quantify. For compliance purposes you know only that the true value lies between zero and the LOQ.

Why doesn’t the laboratory just report the exact value?

There is no exact value accessible to any method. The x ± U interval is the complete, honest result; a bare number is the same result with information deleted.

Which decision rule should I ask for?

Releasing product on your own responsibility: guarded acceptance, x + U at or below the limit. Contesting an enforcement finding: verify that guarded rejection was applied. Never leave it unstated — ISO/IEC 17025 requires the rule to be agreed before testing.

Can two different results from two laboratories both be right?

Yes, whenever their uncertainty intervals overlap. 0.093 ± 0.024 and 0.104 ± 0.024 are statistically the same measurement.