Date of Award:
Master of Science (MS)
Mathematics and Statistics
Department name when degree awarded
This work considers the application of a µ-model approach on the cell means to a special yet important class of experimental designs. These include full factorial, completely nested, and mixed models with one or more observations per cell. By limiting attention to full models, an approach to the general data situation is developed which is both conceptually simple and computationally advantageous.
Conceptually, the method is simple because the design related effects are defined as if the cell means are single observations. This leads to a rather simple algorithm for generating main effect contrasts, from which associated interaction contrasts can also be formed. While the sums of squares found from these contrasts are not additive with non-orthogonal data, they do lead to the class of design related hypotheses with the clearest interpretation in terms of the cells.
The computational method is advantageous because the sum of squares for each source of variation is evaluated separately. This avoids the storage and inversion of a potentially large matrix associated with alternative methods, and allows the user to evaluate only those sources of interest.
The methodology outlined in this work is programmed into a user-easy, interactive terminal version for the analysis of these n-factor design models.
Van Koningsveld, Richard, "A µ-Model Approach on the Cell Means: The Analysis of Full, Design Models with Non-Orthogonal Data" (1979). All Graduate Theses and Dissertations. 6872.
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