Every measurement is a range
The idea that a measured quantity comes with an uncertainty is unremarkable in any technical field and almost entirely absent from consumer labelling. A sun protection factor is a good example of the gap.
The determination produces individual factors from a panel of volunteers. Those individual results are not identical, because people are not identical: baseline reddening thresholds differ, skin differs, and the visual reading of an endpoint carries its own variation. The reported figure is the mean of the valid individual results, and around that mean sits a confidence interval whose width depends on how variable the panel was and how many volunteers were tested.
The standard does not treat that width as incidental. It requires the interval to reach a stated precision before the result can be reported, and it provides for testing further volunteers until it does.
Where the variation comes from
Four sources dominate, and each is managed rather than removed.
The panel. Individual response to ultraviolet varies, and the ratio being measured has a personal denominator. Screening narrows the range; it does not close it.
The assessor. The endpoint is read visually. Training and standardised viewing conditions reduce assessor variation, and different trained assessors will still occasionally read a marginal site differently.
The application. Spreading a weighed quantity by hand over a marked area is a manual operation. Two competent operators produce slightly different films.
The source. Solar simulators are matched to a specified output within tolerances, so two compliant simulators are similar rather than identical.
None of this is unusual for a biological measurement. What is unusual is how completely the resulting uncertainty vanishes at the labelling stage.
What rounding down actually does
Labelling convention takes the tested result and expresses it as one of a small set of permitted figures, rounding down. A product tested at a value between 30 and 50 is labelled 30. A product tested somewhat above 50 is labelled 50 plus.
Two things follow, and they pull in opposite directions.
The convention is conservative. The printed figure is at or below the tested result, never above it, so the label understates rather than overstates. That is the correct direction for a safety related figure to err in.
The convention also destroys information. Two products labelled 30 may have tested materially differently, and the label cannot distinguish them. A reader comparing packs is comparing bands, not measurements, and the bands are wide at the top of the scale.
| Produced by the test | Reaches the pack |
|---|---|
| Individual factors for each volunteer | No |
| Panel mean | Only after rounding down to a permitted figure |
| Confidence interval | No |
| Panel size | No |
| Method and version | No |
| Laboratory identity | No |
| Rounded labelling figure | Yes, printed prominently |
Framework of this publication. It describes how published rules and guidance fit together and is not a measurement, a survey or a study.
Why the convention is defensible
It would be possible to print the tested value, the confidence interval, the panel size and the laboratory. Almost nobody argues for it, and the reasons are worth stating because they explain the design of the whole label.
A confidence interval on a pack would be read as a range of performance rather than as a statement about measurement precision, which would be a new misunderstanding replacing an old one. An exact tested value would present differences between products that the method cannot reliably resolve. And the space on a pack is finite, with mandatory information already competing for it.
Grouping into bands with a conservative rounding rule solves the real problem, which is preventing false precision, at the cost of a lesser one, which is that the reader cannot see the margin.
Reproducibility between laboratories
A separate question from the uncertainty within one determination is how well two laboratories agree on the same product. Inter-laboratory variation has been a recognised issue in sun protection testing for a long time, and it is one of the drivers behind successive revisions of the methods.
The practical implication for a business is that a retest is not guaranteed to reproduce a previous result, and that a result close to the boundary between two permitted labelling figures is a commercial risk. The practical implication for a reader is that the difference between two products labelled with adjacent figures is smaller and less certain than the labels imply.
Uncertainty in the UVA determination
The in vitro ultraviolet A determination carries its own uncertainty, arising from the substrate, the film application, the spectrophotometry and the calibration step that ties the result to the in vivo figure.
Because the output is compared against thresholds rather than printed, the uncertainty shows up in a different way: as a risk of a marginal product falling on the wrong side of a threshold on a retest. A product close to the boundary carries the circled mark or does not, with nothing in between, which makes the threshold structure sensitive at exactly the point where the measurement is least certain.
Products that sit on a boundary
The interaction between uncertainty and a banded labelling scheme produces a specific commercial situation worth describing, because it explains behaviour that otherwise looks strange.
A product whose tested result sits just above a permitted labelling figure is comfortable. A product whose tested result sits just below the next one is not, because a small improvement in formulation would move it up a band and a small variation on retest could move it down. The bands are wide at the top of the scale, so the gap between a labelled 30 and a labelled 50 covers a considerable range of tested results.
The consequences run in both directions. A formulator may push a formulation harder than the difference in delivered protection warrants, because the labelling step is worth more commercially than the underlying improvement is worth physically. And a marginal product may be retested in the hope of a more favourable panel, which is a practice the statistical requirements in the standards are partly designed to constrain.
None of this is visible from a pack. It is one of the reasons a reader should treat adjacent labelled figures as bands rather than as measurements, and treat the difference between them as smaller than the numerals suggest.
Uncertainty and claims
The common criteria for cosmetic claims require that a claim is supported by adequate and verifiable evidence, and the advertising codes require objective claims to be capable of substantiation. Neither requires that a claim be certain, which would be an impossible standard for any measured property.
What they do require is that the evidence supports the claim as made. A claim expressed with more precision than the measurement supports is a claim the evidence does not reach. That is one of the reasons superlatives and fine comparisons in this category are difficult: a claim that one product outperforms another by a small margin requires evidence capable of resolving a small margin, and the methods are not built for that.
What a test report contains
Since none of it reaches the pack, it is worth setting out what a laboratory report actually holds, because it is the document a business is relying on and the one an enforcement authority would ask for.
It identifies the sample tested, including a batch reference, so that the report can be tied to a specific formulation rather than to a product name. It states the method and its edition. It records the panel: how many volunteers, their screening characteristics, and which individual results were excluded and why. It gives the individual factors, the mean, the standard deviation and the confidence interval. It records the source calibration and the environmental conditions. And it states the reported result, which is not the same thing as the labelled figure.
That last distinction is the one businesses lose track of. The report states a determined value. The pack states a labelling figure derived from it by a rounding rule. When somebody says a product is SPF 30, they may mean either, and in a dispute the difference matters.
What to take from this
A tested factor is a panel mean with an interval, held to a required precision. The pack prints a rounded down band. The convention is conservative and it hides the margin, and the differences between adjacent labelled figures are smaller and less certain than the numerals suggest.