Abstract
Suppose two treatments are to be compared where the responses to the treatments fall into a 2 × k contingency table with ordered categories. Test the null hypothesis that the treatments have the same effect against the alternative that the second treatment is “better” than the first. “Better” means that the probability of falling into the higher of the ordered categories is larger for the second treatment than for the first treatment. (In technical terms what we define as better is stochastically larger.) For k = 3 we propose a new test that has very desirable properties. The small sample version of the new test is unbiased, conditionally unbiased, admissible, and has a monotone power function property. It is not cosily carried out. The large sample version of the test is approximately unbiased, has desirable monotonicity properties, and is easy to carry out. The new test seems preferable to the likelihood ratio test and to the VVilooxon-Mann-Whitney test.
| Original language | American English |
|---|---|
| Title of host publication | Probability and Statistical Models with Applications |
| Publisher | CRC Press |
| Pages | 549-564 |
| Number of pages | 16 |
| ISBN (Electronic) | 9781420036084 |
| ISBN (Print) | 1584881240, 9781584881247 |
| State | Published - Jan 1 2000 |
ASJC Scopus subject areas
- General Mathematics
Keywords
- Independence
- Likelihood ratio order
- Likelihood ratio test
- Stochastic order
- Unbiased test
- Wilcoxon-Mann-Whitney test