Experimental design for one-sided confidence intervals or hypothesis tests in binomial group testing

A common statistical issue in seed-quality control is to prove that the proportion of individuals showing an unwanted trait is less than a small threshold. Group testing can be used to reduce costs of assay and upper confidence limits for the proportion of detrimental individuals can be used for either estimation or hypothesis testing. A crucial problem of group testing is the appropriate choice of group size in dependence of the number of groups, an assumed true proportion, and the threshold. This paper reports on experimental design to achieve high power for tests or low confidence interval width. Two agricultural applications are presented for which experimental design is discussed.