Table 1.
An illustrative example of the pool adjacent violators algorithm.
| Subject | y* | g(0): step 0 (D*) | g(1): step 1 | g(2): step 2 | g(3): step 3 | g(4): step 4 |
|---|---|---|---|---|---|---|
| 8 | 2 | 0 | 0 | 0 | 0 | 0 |
| 4 | 12 | 1 | 1/2 | 1/3 | 1/3 | 1/3 |
| 1 | 18 | 0 | 1/2 | 1/3 | 1/3 | 1/3 |
| 6 | 20 | 0 | 0 | 1/3 | 1/3 | 1/3 |
| 7 | 27 | 1 | 1 | 1 | 1 | 2/3 |
| 9 | 30 | 1 | 1 | 1 | 1/2 | 2/3 |
| 2 | 42 | 0 | 0 | 0 | 1/2 | 2/3 |
| 3 | 50 | 1 | 1 | 1 | 1 | 1 |
| 10 | 55 | 1 | 1 | 1 | 1 | 1 |
| 5 | 78 | 1 | 1 | 1 | 1 | 1 |
The scores (y) are sorted ascendingly (y*) and the probabilities are initialized with the truth states D* (step 0). In each step, the adjacent violators (i.e., the order of the probabilities is opposite to that of the scores) are pooled into one group (boxes in the table) and the estimated probabilities in the box are averaged before going to the next step until no violators are found.