Limiting distribution of the aligned rank transform tests in balanced incomplete blocks
✍ Scribed by Hossein Mansouri
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 102 KB
- Volume
- 74
- Category
- Article
- ISSN
- 0378-3758
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✦ Synopsis
The aligned rank transform statistics are constructed in the same way as the least-squares statistics except that the observations are replaced by ranks of the aligned observations. In this article the asymptotic distribution of the aligned rank transform statistic for the balanced incomplete blocks is derived under the null hypothesis and a sequence of local location alternatives when the number of blocks approaches inÿnity. The relationship of the test statistic to the statistics for the single-factor repeated measurements and the mixed e ects designs with incomplete observation vectors is also pointed out. In addition, the results in this article provide a generalization of the theoretical results for the rank transform statistics in the single-factor repeated measurements design and the mixed e ects complete block design. Finally, a test statistic for ordered alternatives is formulated and its limiting distribution is derived.