Consider the following scheme for group testing. The original lot of samples is divided into two groups, and each of the subgroups is tested as a whole. If either subgroup tests positive, it is divided in two, and the procedure is repeated. If any of the groups thus obtained tests positive, test every member of that group. Find the expected number of tests performed, and compare it to the number performed with no grouping and with the scheme described in Example C in Section 4.1.2.
Reference
Group Testing
Suppose that a large number, n, of blood samples are to be screened for a relatively rare disease. If each sample is assayed individually, n tests will be required. On the other hand, if each sample is divided in half and one of the halves is put into a pool with all the other halves, the pooled lot can be tested. Then, provided that the test method is sensitive enough, if this test is negative, no further assays are necessary and only one test has to be performed. If the test on the pooled blood is positive, each reserved half-sample can be tested individually. In this case, a total of n + 1 tests will be required. It is therefore plausible, assuming that the disease is rare, that some savings can be achieved through this pooling procedure.
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