This thesis considers the problem of hypothesis testing for umbrella alternatives when
there are two groups, or strata, of observations. The proposed methods extend a
previously established general framework of hypothesis testing based on rankings to
stratified datasets by first aligning the strata. The tests based on the Spearman and
Kendall distances between ranking vectors lead to the traditional aligned-rank tests
and new methods which account for “misalignment” under the alternative hypothesis.
Asymptotic null distributions and simulation studies are given for the Spearman
distance. Diagnostic tools for the misalignment issue are illustrated alongside the
proposed tests on a dataset of IQ scores of coma patients. Extensions to three or
more strata and ”adaptive” tests are provided as future research directions.
| Identifer | oai:union.ndltd.org:uottawa.ca/oai:ruor.uottawa.ca:10393/45289 |
| Date | 15 August 2023 |
| Creators | Larock, Josh |
| Contributors | Alvo, Mayer |
| Publisher | Université d'Ottawa / University of Ottawa |
| Source Sets | Université d’Ottawa |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf |
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