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Activity Number:
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326
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Type:
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Contributed
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Date/Time:
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Wednesday, August 6, 2003 : 8:30 AM to 10:20 AM
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Sponsor:
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Section on Survey Research Methods
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| Abstract - #301736 |
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Title:
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Analysis of Hierarchical Factorial Layouts When the Class Levels Are Sampled from Unbalanced Finite Populations
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Author(s):
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Shannon E. Allen*+ and Burt S. Holland
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Companies:
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Temple University and Temple University
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Address:
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139 E Tth Ave., Conshohocken, PA, 19428,
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Keywords:
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finite effects ; nested classification ; permutation test ; population imbalance ; Satterthwaite's formula ; variance components
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Abstract:
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Although the properties of the test statistic for a class and/or subclass effect for hierarchical designs with random or fixed effects have been well studied and documented, almost no research has been done involving hierarchical designs having the intermediate case termed "finite effects." Investigating analysis of a multiway nested experimental design from balanced populations of finite effects, Gaylor and Hartwell (1969) derived simple formulae to estimate the variance components that do not depend on balanced sampling and which apply in the special cases of purely fixed and random effects. These authors were unable to extend their work to unbalanced population sizes of subclass effects. We propose an analysis method that begins with a newly defined statistic. When combined with the conventional sums of squares, this statistic enables estimation of the variance components and leads to a ratio test statistic having an expectation exceeding one if and only if the null hypotheses are false. We use permutation tests of these ratio statistics to address the usual ANOVA hypotheses. This methodology is demonstrated with a dataset.
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