How much can a wrongly assigned reference standard shift my content number, and in which direction?

Following on from the certification discussion: I want to quantify the damage. Suppose a lab's standard is assigned 95.0% and its true potency is 88.0%. Does my sample result come out high or low, and by how much? I keep talking myself into both answers and I would like to see it written out.

Second, worse case: suppose the lab took a supplier's chromatographic purity figure — say 99% — and used it as the potency, ignoring water and counter-ion entirely. What does that do to the numbers? My instinct is that it is a systematic error of roughly the size of the water-plus-salt fraction, which from other threads here is 12 to 17%. If that is right it seems like it would be enough to turn a genuinely short vial into one that reads at label claim, which would be a fairly serious thing to have happening quietly.

And third: does an error like this show up anywhere? Would a report with a mis-assigned standard look any different from a correct one, or is it completely invisible from outside?

An important qualifier on the direction argument, because there is a real case where the error goes the other way and it produces false accusations against vendors.

If a lab uses a properly assigned standard on an anhydrous, salt-free basis and then, correctly, reports the sample's content of anhydrous salt-free peptide — but the vendor labelled the vial on gross fill weight — then the report will show roughly 85 to 88% of label on a vial that was filled exactly as the vendor intended. Nobody made an arithmetic error. Two conventions collided.

You can distinguish this from a genuine shortfall with one question to the vendor and one to the lab:

• Vendor: is the label claim gross fill weight or net anhydrous peptide?
• Lab: is your reported content anhydrous salt-free peptide, or net peptide including counter-ion and water?

Four combinations, and only two of them are comparable:

Note that rows two and three are the same magnitude as the calibration errors in the accepted answer, and in the same directions. So an offset of that size has two candidate explanations — a mis-assigned standard, or a convention mismatch — and they are not distinguishable from the number alone.

Which is a slightly deflating conclusion but the right one: a single content number in isolation, with no stated basis on either side, cannot support a claim of shortfall at the 15% level. It can at the 30 to 40% level, because no convention mismatch reaches that far. Below about 20%, ask the two questions before you accuse anyone.

Adding the batch-level consequence that the question gestures at with "every result in a batch", since it is worse than the per-sample arithmetic suggests.

Labs do not re-establish calibration per sample. A standard is prepared, a curve is run, and then a run of samples — often dozens, sometimes an entire day or week of work bracketed by check standards from the same stock — is quantified against it. A mis-assignment therefore does not produce one wrong result; it produces a coherent block of wrong results that all agree with each other.

That coherence is the actively dangerous part, for two reasons.

It defeats replication. The standard advice for a suspicious result is to send another vial. If both vials go to the same lab, they are quantified against the same standard and they agree beautifully. You have replicated the error and increased your confidence in the wrong number. Replication only works across the thing that varies, and the standard does not vary within a lab.

It corrupts comparisons. If you are ranking three vendors on content, and all three were tested in the same run against the same over-assigned standard, the ranking survives — the shift is multiplicative and applies to all of them. That is the one saving grace. But if you compare a result from that run against a result from a different lab, or from the same lab six months later after a standard change, the comparison is meaningless and will look like a real difference in vendor quality.

Practical rules that follow:

• For absolute claims, split across labs. Two vials, two independent testing services, is worth far more than four vials at one. Janoshik and Medutest are separate operations with separate standards and a systematic agreement between them is strong evidence.
• For relative comparisons, keep them in one run. The multiplicative shift cancels. If you are choosing between suppliers, submitting all the candidates together is the better design even though the absolute numbers may be off.
• Record the standard lot if the lab will tell you. When a lab changes standard lots, historical comparisons across the change need treating with suspicion.

None of this requires assuming bad faith anywhere. A single documentation error made once, at the point a standard was received and logged, propagates silently through every report until somebody outside the lab notices an impossible mass balance.