Most distribution free nonparametric methods depend on the ranks or orderings of the individual observations. This dissertation develops methods for the situation when there is only partial information about the ranks available. A random-linear-extension exact test and an empirical version of the random-linear-extension test are proposed as a new way to compare groups of data with partial orders. The basic computation procedure is to generate all possible permutations constrained by the known partial order using a randomization method similar in nature to multiple imputation. This random-linear-extension test can be simply implemented using a Gibbs Sampler to generate a random sample of complete orderings. Given a complete ordering, standard nonparametric methods, such as the Wilcoxon rank-sum test, can be applied, and the corresponding test statistics and rejection regions can be calculated. As a direct result of our new method, a single p-value is replaced by a distribution of p-values. This is related to some recent work on Fuzzy P-values, which was introduced by Geyer and Meeden in Statistical Science in 2005. A special case is to compare two groups when only two objects can be compared at a time. Three matching schemes, random matching, ordered matching and reverse matching are introduced and compared between each other. The results described in this dissertation provide some surprising insights into the statistical information in partial orderings. / Statistics
| Identifer | oai:union.ndltd.org:TEMPLE/oai:scholarshare.temple.edu:20.500.12613/901 |
| Date | January 2009 |
| Creators | Cao, Jun |
| Contributors | Smith, Woollcott, 1941-, Parnes, Milton, Raghavarao, Damaraju, Chitturi, Pallavi, Rosenthal, Edward C., 1959- |
| Publisher | Temple University. Libraries |
| Source Sets | Temple University |
| Language | English |
| Detected Language | English |
| Type | Thesis/Dissertation, Text |
| Format | 88 pages |
| Rights | IN COPYRIGHT- This Rights Statement can be used for an Item that is in copyright. Using this statement implies that the organization making this Item available has determined that the Item is in copyright and either is the rights-holder, has obtained permission from the rights-holder(s) to make their Work(s) available, or makes the Item available under an exception or limitation to copyright (including Fair Use) that entitles it to make the Item available., http://rightsstatements.org/vocab/InC/1.0/ |
| Relation | http://dx.doi.org/10.34944/dspace/883, Theses and Dissertations |
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