Type of Document Dissertation Author Wilcock, Samuel Phillip URN etd-08312001-162742 Title A New Nonparametric Procedure for the k-sample Problem Degree PhD Department Statistics Advisory Committee

Advisor Name Title Terrell, George R. Committee Chair Anderson-Cook, Christine M. Committee Member Arnold, Jesse C. Committee Member Foutz, Robert Committee Member Morgan, John P. Committee Member Keywords

- Error Assumptions
- Distribution Free
- One-way Layout
- k-sample problem
- Nonparametrics
Date of Defense 2001-08-20 Availability unrestricted AbstractThe k-sample data setting is one of the most common datasettings used today. The null hypothesis that is most generally

of interest for these methods is that the k-samples have the

same location. Currently there are several procedures available

for the individual who has data of this type. The most often used

method is commonly called the ANOVA F-test. This test assumes

that all of the underlying distributions are normal, with equal

variances. Thus the only allowable difference in the

distributions is a possible shift, under the alternative

hypothesis. Under the null hypothesis, it is assumed that all k

distributions are identical, not just equally located.

Current nonparametric methods for the k-sample setting require

a variety of restrictions on the distribution of the data. The

most commonly used method is that due to Kruskal and Wallis (1952). The

method, commonly called the Kruskal-Wallis test, does not assume

that the data come from normal populations, though they must

still be continuous, but maintains the requirement that the

populations must be identical under the null, and may differ only

by a possible shift under the alternative.

In this work a new procedure is developed which is exactly

distribution free when the distributions are equivalent and

continuous under the null hypothesis, and simulations are used to

study the properties of the test when the distributions are

continuous and have the same medians under the null. The power of

the statistic under alternatives is also studied. The test bears

a resemblance to the two sample sign type tests, which will be

pointed out as the development is shown.

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