Sample size determination in zero tolerance circumstances and the implications of stepwise sampling: Bacterial ring rot as a special case

A formula suitable for determining sample size in zero tolerance situations is developed. It is PEA = e-nP; where PEA = probability of erroneous acceptance of a field, e = base of natural logarithm, n = sample size, and p = probability that a plant is diseased. For a trace amount of disease,i.e., p = 0.001, a PEA of 0.01 is achieved with a sample size of 4605. Such a sample size might be achieved by sampling in a stepwise fashion whereby multiple samples are taken and sampling ceases when disease is found. In such schemes, if the total sample size of all samples is 4605, then the PEA will still be 0.01 when p = 0.001. General formulas for stepwise sampling and formulas for special circumstances such as stratified (non-random) sampling schemes, sampling small fields, and sampling in the presence of reduced disease expression can also be obtained. A case study is used to exemplify the use of these formulas in the development of a zero tolerance sampling strategy.