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An analysis of multidimensional contingency talbes Mast, Lilian G. (Feuerverger)
Abstract
In this thesis we consider the following model for a three-dimensional r ˣ s ˣ t contingency table: [formula omitted]. A dot indicates summation over the replaced subscript. The f[formula omitted]’s represent the frequencies and the P[formula omitted]'s represent the proportions. The problem we are concerned with is testing the hypothesis H₀: [formula omitted] = 0 for all i, j, k. i.e. no second order interaction is present. We then seek to extend the model and problem to a w-way table. We use the method of the likelihood ratio . To assist us in determining the numerator of the likelihood ratio we reformulate a theorem about constrained extrema and Lagrange multipliers and prove this reformulation. Some general conclusions we draw are: there are two extensions to our 3-way model; results we obtain using our model and methods are in close agreement with results obtained using the models and methods of other statisticians.
Item Metadata
Title |
An analysis of multidimensional contingency talbes
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
1973
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Description |
In this thesis we consider the following model for a three-dimensional r ˣ s ˣ t contingency table:
[formula omitted]. A dot indicates summation over the replaced subscript. The f[formula omitted]’s represent the frequencies and the
P[formula omitted]'s represent the proportions. The problem we are concerned with is testing the hypothesis H₀: [formula omitted] = 0 for all i, j, k. i.e. no second
order interaction is present. We then seek to extend the model and problem to a w-way table.
We use the method of the likelihood ratio . To assist us in determining the numerator of the likelihood ratio we reformulate a theorem about constrained extrema and Lagrange multipliers and prove this reformulation.
Some general conclusions we draw are: there are two extensions to our 3-way model; results we obtain using our model and methods are in close agreement with results obtained using the models and methods of other statisticians.
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Genre | |
Type | |
Language |
eng
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Date Available |
2011-03-25
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Provider |
Vancouver : University of British Columbia Library
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Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
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DOI |
10.14288/1.0080461
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Campus | |
Scholarly Level |
Graduate
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Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.