Doctor of Philosophy / Department of Statistics / James Higgins / Many studies are performed on units that cannot be replicated due to cost or other restrictions.
There often is an abundance of subsampling to estimate the within unit component of
variance, but what is needed for statistical tests is an estimate of the between unit component
of variance. There is evidence to suggest that the ratio of the between component of variance
to the total variance will remain relatively constant over a range of studies of similar types.
Moreover, in many cases this intraclass correlation, which is the ratio of the between unit variance to the total variance, will be relatively small, often 0.1 or less. Such situations exist in education, agriculture, and medicine to name a few.
The present study discusses how to use such prior information on the intraclass correlation
coefficient (ICC) to obtain inferences about differences among treatments in the face of no
replication. Several strategies that use the ICC are recommended for different situations and
various designs. Their properties are investigated. Work is extended to under-replicated
experiments. The work has a Bayesian flavor but avoids the full Bayesian analysis, which has
computational complexities and the potential for lack of acceptance among many applied
researchers. This study compares the prior information ICC methods with traditional
methods. Situations are suggested in which prior information ICC methods are preferable to
traditional methods and those in which the traditional methods are preferable.
| Identifer | oai:union.ndltd.org:KSU/oai:krex.k-state.edu:2097/45 |
| Date | January 1900 |
| Creators | Perrett, Jamis J. |
| Publisher | Kansas State University |
| Source Sets | K-State Research Exchange |
| Language | en_US |
| Detected Language | English |
| Type | Dissertation |
| Format | 2509477 bytes, application/pdf |
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