### Sample Size and Efficiency for Hypotheses Testing in ANOVA Model

### Minghui Wang

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ISBN 978-3-8325-0119-8

142 pages, year of publication: 2002

price: 40.50 €

In this thesis two closely related experimental design problems are addressed. The first problem concerns the determination of the size of an experiment to guarantee the power of an approximate F-test in the ANOVA model. Satterthwaite's result is generalized such that a linear combination of one non-central Chi-square distribution and one or more central Chi-square distributions can be approximated. Sample size for the approximate F-test is then derived from this generalized form. Along with an estimate of the sample size, an upper and a lower bound of the size of an experiment are derived. Furthermore, a simulation is carried out to study the distribution of the estimated sample size for Satterthwaite's approximate F-test, as well as to evaluate the derived bounds of the sample size.

The second problem deals with efficiencies of experimental designs. A general definition of efficiency of an experimental design is given. This definition of the efficiency is defined as a function of the size of the experiment. This efficiency can be applied to compare the relative efficiencies of experimental designs not only for the estimation problem, but also for hypothesis testing. In particular, the efficiency of an experimental design in ANOVA for testing hypotheses is investigated. As an example the relative efficiency of a split-block design versus a split-plot design for hypothesis testing is explored.