Expected variance between seed germination test replicate results

According to the International Seed Testing Association (ISTA), the germination percentage of a seed lot is determined by testing usually four replicates of 100 seeds (ISTA, 2017). The theoretical variance of the binomial distribution is used by ISTA to define the maximum tolerated range in the germination percentages of the replicates. If the tolerated range is exceeded, the test has to be repeated. We show that the theoretical variance between the four replicates is different from the variance of the binomial distribution. In the case of four replicates with 100 seeds each and germination percentages of about 50%, the difference is small but becomes bigger with decreasing sample size and with lower or higher germination percentages. We also present asymptotic and exact tests to compare the empirical variance between the four replicates with its expected variance. The exact test can lead to notably different results compared with the test based on the binomial assumption, when sample size is small and germination percentages are close to 100 or 0%. If the four replicates of 100 seeds each are drawn from 400 seeds, the tolerance values in ISTA's Table 5B would increase in almost every fourth case by 1 if tolerances were computed with the correct formula.