Digit preference: what a round number tells you
Terminal-digit analysis on declared purity figures, and what happens when you put the round numbers next to independent measurements of the same lots.
A chromatographic purity figure is the ratio of two integrated areas. It has no reason to land on a half or a whole percent, and across a large set of genuine measurements the terminal digit should be approximately uniform. On some certificates it is not.
The analysis
The index examined the terminal-digit distribution of every declared purity figure it holds. Round values — those ending in .0 or .5 — are substantially over-represented in the certificates of the lower-documentation suppliers and approximately at chance in the higher-documentation ones.
| Rule | Flagged this quarter | Rate | Severity |
|---|---|---|---|
| AX-R01 — Mass accuracy outside class limit | 30 | 3.94% | HIGH |
| AX-R02 — Declared impurity arithmetic does not close | 35 | 4.59% | MEDIUM |
| AX-R03 — Declared largest single impurity exceeds declared total | 0 | 0.00% | HIGH |
| AX-R04 — Digit preference in declared purity | 47 | 6.17% | LOW |
| AX-R05 — COA purity diverges from independent median | 0 | 0.00% | HIGH |
| AX-R06 — Recovered mass outside label claim tolerance | 47 | 6.17% | MEDIUM |
| AX-R07 — Declared gravimetric mass balance does not close | 28 | 3.67% | MEDIUM |
| AX-R08 — Endotoxin above index specification | 6 | 0.79% | HIGH |
| AX-R09 — Impurity fingerprint shared across suppliers | 30 | 3.94% | LOW |
| AX-R10 — Supplier-supplied sample reads high against buyer-sourced | 1 | 0.13% | MEDIUM |
| AX-R11 — Retention time outside compound window | 33 | 4.33% | MEDIUM |
| AX-R12 — Peak asymmetry above the integration limit | 0 | 0.00% | MEDIUM |
The test that makes it informative
Digit preference on its own is a curiosity. It becomes a finding when the round declarations are compared against independent measurements of the same lots.
| Declaration type | Mean divergence from independent median |
|---|---|
| Round (terminal digit .0 or .5) | 0.63 pp |
| Non-round (two decimal places) | 0.29 pp |
Round declarations are more than twice as optimistic. Three explanations are consistent with that. The figure may have been rounded for presentation from a real measurement, which is defensible and should be stated. It may be a specification reported as a result — "≥99.0 %" becoming "99.0 %" somewhere between laboratory and certificate, which is the most common case in the index's experience. Or it may not correspond to a measurement.
Rule design
Rule AX-R04 requires a pattern of at least three round declarations from one supplier before any of them is flagged, because a single round result is unremarkable and flagging it would be unfair. The rule is classified low-severity and the rule page states all three explanations rather than asserting the worst one.
One category deserves separate mention. Two substances in the index are not defined chemical entities — a thymic peptide extract and a recombinant glycoprotein — and purity is not a defined quantity for either. Certificates that nonetheless print a purity figure for them are listed on the rule page, because a purity claim on an extract is not a rounded measurement, it is not a measurement at all.