Using group testing to estimate a proportion, and to test the binomial model

Group testing has been extensively studied as an efficient way to classify units as defective or satisfactory when the proportion (p) of defectives is small. It can also be used to estimate p, often substantially reducing the mean squared error (MSE) of p and cost per unit information. Group testing is useful for larger p in the estimation problem than in the classification problem, but for larger p more care must be taken in choosing the group size (k); k being too large not only increases MSE (p), but adversely affects the robustness of p to both errors in testing (misclassification) and errors in the assumed binomial model. Procedures that retest units from defective groups, if even feasible, are shown to reduce cost per unit information very little in the estimation problem, but can provide useful information for testing the model. Methods are given for using data from tests of unequal-sized groups to estimate p and for testing the validity of the binomial model.