Refereed journal article or data article (A1)
Design and cost optimization for hierarchical data
List of Authors: Kari Tokola, Andreas Lundell, Jaakko Nevalainen, Hannu Oja
Publisher: WILEY-BLACKWELL
Publication year: 2014
Journal: Statistica Neerlandica
Journal name in source: STATISTICA NEERLANDICA
Journal acronym: STAT NEERL
Volume number: 68
Issue number: 2
Start page: 130
End page: 148
Number of pages: 19
ISSN: 0039-0402
DOI: http://dx.doi.org/10.1111/stan.12026
In this paper, we consider balanced hierarchical data designs for both one-sample and two-sample (two-treatment) location problems. The variances of the relevant estimates and the powers of the tests strongly depend on the data structure through the variance components at each hierarchical level. Also, the costs of a design may depend on the number of units at different hierarchy levels, and these costs may be different for the two treatments. Finally, the number of units at different levels may be restricted by several constraints. Knowledge of the variance components, the costs at each level, and the constraints allow us to find the optimal design. Solving such problems often requires advanced optimization tools and techniques, which we briefly explain in the paper. We develop new analytical tools for sample size calculations and cost optimization and apply our method to a data set on Baltic herring.