Plausible Component Counts
The component counts a sample does not rule out.
The answer in the analyst's own currency. The rest of the workflow reports a count and then qualifies it: the criterion recommends five, the adequacy verdict says the sample cannot settle the question, the criteria disagree over an interval. None of that answers the question an analyst who arrived with a number actually has, which is whether their number survives. This does, by running the increment test at each count and collecting the ones that were not contradicted.
A wide set is the honest outcome, not a failure of the method. Where the sample cannot settle the count, very little is contradicted and the set is broad — which says the same thing CountAdequacy says, in a form the analyst can act on. The set is evidence about what the data rule out; it is not a ranking, and its smallest member is not a recommendation.
Four outcomes are kept apart rather than collapsed, because collapsing them would let one be read as another:
not rejected — the test ran and the count survived
rejected — the test ran and an extra component bought more than chance
inconclusive — the test ran and could not say, through too few usable replicates
not assessable — no test could be formed, because the count or the one above it cannot be fitted to a sample of this size at all
Only the first is support. In particular a count nobody could evaluate is not evidence of plausibility, so inconclusive and not-assessable counts stay out of the set.
Parameters
every count the caller asked about, in ascending order
the test at each count that could be tested
the level each verdict was read at
Properties
The counts whose test could not say either way.
Whether the surviving counts form an unbroken run.
The largest count not ruled out, or null when none survived.
The counts for which no test could be formed at all, because the count or the one above it is not admissible for a sample of this size.
The counts this sample does not rule out.
The smallest count not ruled out, or null when none survived.