### Norell, Lennart

- Department of Economics, Swedish University of Agricultural Sciences

Report2006

Norell, Lennart

Design effects are studied for the maximum likelihood estimates of the variance components in a one-way analysis of variance model. The factor effects and the errors are assumed to follow normal distributions. The main problem studied is how to assign a given number of observations on a given number of levels of the factor. The optimality criteria are based on the Fisher information matrix corresponding to the large-sample variances of the estimators. The resulting optimal designs depend on the ratio of variance components. If the estimation of the factor variance component is involved, then designs with the sample sizes as equal as possible are the most efficient unless the ratio is small. The optimal number of levels of the random factor is shown to increase with the ratio of variance components. For very small ratios and when the criterion concerns the estimation of the error variance only, the design with two levels of the factor and with the sample sizes as unequal as possible is optimal. Sufficient conditions in terms of the ratio of the variance components are presented for balanced and unbalanced designs to be optimal

Publisher: Dept of Mathematics, Uppsala university

### Norell, Lennart

- Department of Economics, Swedish University of Agricultural Sciences

- Department of Economics, Swedish University of Agricultural Sciences

https://res.slu.se/id/publ/10862