= Germination assay
{title2=$\widehat G(t)=g(t)/N$}
A specified test for <germination>, recording the endpoint, conditions and observation window. For a proposed red/far-red <light> test, use <randomization> to allocate one <seed> lot to darkness, red, red then far-red, and red then far-red then red. Match hydration, <temperature>, handling and elapsed time before counting; use sham waiting periods to equalize schedules. Use dish <replication>, retain the dark <scientific control>, and record <radicle> emergence using an observation procedure that does not itself provide an uncontrolled <light> treatment. This is a proposed design, not a claim about the 1952 paper's <randomization> or <replication>.
As an original hypothetical counting example, begin with $N=40$ <seeds> in one dish. Suppose 12 first meet the <radicle> endpoint by 24 hours, eight additional <seeds> by 48 hours, and four additional <seeds> by 72 hours. These invented event counts give
$$
g(24)=12,\qquad g(48)=12+8=20,\qquad g(72)=12+8+4=24,
$$
and cumulative <sample proportions> $\widehat G(24)=0.30$, $\widehat G(48)=0.50$ and $\widehat G(72)=0.60$. The 48-hour increment is $8/40=0.20$, not $0.50$; the latter includes earlier events. Counting the same emerged <radicle> again at each inspection would inflate the total. These numbers illustrate bookkeeping, not biological rates or treatment effects.
With a fixed denominator and irreversible classification of the first endpoint event, the <set> counted at an earlier inspection is a <subset> of the <set> counted later. Hence $0\leq\widehat G(t)\leq1$ and $\widehat G(t)$ cannot decrease. This short proof applies to cumulative <germination> counts even if a later <seedling> dies. A count of currently surviving <seedlings> has a different definition and can decrease.
For treatment comparisons, the dish may be the <experimental unit>: <seeds> in the same dish share conditions. Forty <seeds> in one dish do not supply forty independent dish replicates. Report the <sample size>, <replication>, endpoint time and denominator; a <sample proportion> by a deadline measures this assay's outcome, not an unconditional fraction with <seed viability>.
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