<abstract xmlns="http://www.w3.org/1999/xhtml">This paper considers block designs and row-column designs where the information matrix <bold>C</bold> has two different nonzero eigenvalues, one of multiplicity 1 and the other of multiplicity <italic>h</italic>−1, where <italic>h</italic> is the rank of the matrix <bold>C</bold>. It was found that for each such design there exists a diagonal positive definite matrix <bold>X</bold> such that the design is <bold>X</bold>
−1-balanced.</abstract>

This paper considers block designs and row-column designs where the information matrix C has two different nonzero eigenvalues, one of multiplicity 1 and the other of multiplicity h−1, where h is the rank of the matrix C. It was found that for each such design there exists a diagonal positive definite matrix X such that the design is X
−1-balanced.

X−1-balance of some partially balanced experimental designs with particular emphasis on block and row-column designs

Department of Mathematical and Statistical Methods, Poznan University of Life Sciences, Wojska Polskiego 28, 60-637 Poznań, Poland

Biometrical Letters

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

X-balance of some partially balanced experimental designs with particular emphasis on block and row-column designs

This paper considers block designs and row-column designs where the information matrix C has two different nonzero eigenvalues, one of multiplicity 1 and the...

X⁻¹-balance of some partially balanced experimental designs with particular emphasis on block and row-column designs

Published Online: Jun 08, 2015

Page range: 1 - 12

DOI: https://doi.org/10.1515/bile-2015-0001

Keywords
block design, row-column design, efficiency balance, variance balance, X-balance

© Ryszard Walkowiak

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

X−1-balance of some partially balanced experimental designs with particular emphasis on block and row-column designs

Published Online: Jun 08, 2015

Page range: 1 - 12

DOI: https://doi.org/10.1515/bile-2015-0001

Keywordsblock design, row-column design, efficiency balance, variance balance, X-balance

© Ryszard Walkowiak

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

X⁻¹-balance of some partially balanced experimental designs with particular emphasis on block and row-column designs

Keywords
block design, row-column design, efficiency balance, variance balance, X-balance