Some characteristics of two-stage designs of experiments

The procedure of choosing an object with special properties sometimes is carried out in two stages. At the first stage, by simplified treatment, suspicious objects are separated, and then they are studied in more detail, beginning with the most suspicious. An important characteristic of such a procedure is the quantity $\tau$ equal to the number of objects studied in detail in the second stage. In this paper, the distribution of $\tau$ is studied, and the results are applied to estimating the quality of two-stage procedure of choosing between several polynomial hypotheses.
This research was supported by the Russian Foundation for Basic Research, grant 96–15–96092.