LE3 .A278 2009

2009

Cabilio, Paul
Peng, Jianan

Acadia University

Master of Science

Masters

Mathematics and Statistics

Mathematics & Statistics

This thesis considers the situation of incomplete rankings in which n judges independently rank ki 2 f2; :::; tg objects. For testing ordered alternatives, the statistic considered is a generalization of the extended Page test in which the ranks assigned by each judge are replaced by real-valued general score functions of the ranks. The methodology relies on the concept of compatibility to extend the denition of dis- tances and similarities between the criterion determined by the alternative ordering and complete rankings to such situation. The resulting test procedures are therefore applicable to any simple block design. Given score functions with certain property, this generalized statistic is asymptotically normal as either n or t and ki go to innity. The simulation study shows that the performance of these tests is not only related to the forms of general score functions, but is also in uenced by the actual patterns of missing observations. In the complete case, the resulting statistics coincide with the w-tests in Pirie (1974). In the incomplete case with the Wilcoxon score func- tion, it coincides with the extended Page test in Alvo and Cabilio (1995b). Finally, the calculations of null distributions of the generalized statistics are implemented in R programs, which provide exact critical values, and allow the procedures to be conveniently utilized for analysis of real data.

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https://scholar.acadiau.ca/islandora/object/theses:129