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A germination test is binomial evidence

Sow n seeds, count k that germinate. That single act is a binomial experiment, and everything downstream inherits its uncertainty. 40/50 germinating is not "80%" — it's "probably somewhere near 80%, with a spread set by n." The spread is the whole story: 8/10 and 80/100 both read 80%, but the second pins the true rate about three times more tightly.

The right uncertainty interval for a proportion is Wilson's, not the naive ±1.96√(p(1−p)/n) — the naive one collapses to zero width at 0% and 100% (exactly where seed data lives) and can leak outside [0,1]. Wilson stays honest at the extremes and never leaves the unit interval.

Rule of thumb this buys you: with 50 seeds, a single test can't distinguish rates closer than about ±12 percentage points. Any threshold comparison sharper than that, from one plate, is noise wearing a suit.

Try it — how sample size sets what a test can distinguish
Seeds sown50Germination80%
40/50 germinated → Wilson 95%: 67.088.8% (width 21.8 points). This one test cannot distinguish true rates inside that band.
Demonstration accession — realistic shape, not real bank data
Where this appears in the pipeline: Counts are the truth; percentages are a courtesy · Observed vs supported: two independent confidence checks
The clock: an accession's age at test