dc.contributor.author | Wanyoike, John N | |
dc.date.accessioned | 2022-04-11T11:47:36Z | |
dc.date.available | 2022-04-11T11:47:36Z | |
dc.date.issued | 2021 | |
dc.identifier.uri | http://erepository.uonbi.ac.ke/handle/11295/160150 | |
dc.description.abstract | The main focus of this research is to construct balanced asymmetrical factorial
designs in which main effects and higher order interactions are estimated with high
efficiencies if not full efficiencies. The specific objectives in this work is to illustrate
straight forward procedures for constructing balanced arrays/resolvable balanced
incomplete block designs and hence balanced asymmetrical factorial designs.
The available literature has given methods of calculating efficiencies for balanced
asymmetrical factorial designs. These methods are not clear and have used the
traditional approaches. Therefore in this work we have made a contribution in
which we have given a direct method that uses Kronecker product of matrices to
evaluate such efficiencies.
Another major contribution is the use of Resolvable balanced incomplete block
designs in construction of balanced asymmetrical factorial designs
A notable contribution in this research work is in the construction of transitive
arrays which are extensively used in the construction of balanced asymmetrical
factorial designs by the use of Latin squares. In literature, such arrays have been
constructed by using t − ply transitive groups
An additional contribution in this work is in the construction of resolvable balanced
incomplete block designs (BIBD’s) that have block size k = 3 More specifically we
have used the geometry of chords constructed in a circle. We have used resolvable
BIBD’s of block size k = 3 to construct many more balanced asymmetrical factorial
designs
This research work has come up with a noble method of constructing balanced
arrays/resolvable BIBD’s which have been used to construct a wide range of balanced
asymmetrical factorial designs.
This research work is however based on the construction of balanced asymmetrical
factorial designs that are connected, so the results that we have illustrated in this
thesis are not valid in the disconnected case. This calls for suitable modifications
of these results to make them applicable to the disconnected case.
In this thesis we have restricted our considerations of balanced asymmetrical factorial
designs to one way designs only. These concepts can also be extended to
two way designs i.e. designs with rows and columns as blocks | en_US |
dc.language.iso | en | en_US |
dc.publisher | University of Nairobi | en_US |
dc.rights | Attribution-NonCommercial-NoDerivs 3.0 United States | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/us/ | * |
dc.subject | asymmetrical factorial designs | en_US |
dc.title | Construction of sub class of balanced asymmetrical factorial designs | en_US |
dc.type | Thesis | en_US |