<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>The construction of incomplete split-block-plot (SBP) designs for three-factor experiments is investigated. A semi-Kronecker (Khatri–Rao) product of matrices is used in the construction procedure. With this method some generated designs are obtained where column treatments and subplot treatments are allocated in balanced square lattice designs, while row treatments are in a randomized complete block design. Experiments with an orthogonal block structure are considered. In this paper we consider designs which are generally balanced. This allows us to give the stratum efficiency factors for treatment combination contrasts in the proposed split-block-plot designs.</p>
</abstract>

The construction of incomplete split-block-plot (SBP) designs for three-factor experiments is investigated. A semi-Kronecker (Khatri–Rao) product of matrices is used in the construction procedure. With this method some generated designs are obtained where column treatments and subplot treatments are allocated in balanced square lattice designs, while row treatments are in a randomized complete block design. Experiments with an orthogonal block structure are considered. In this paper we consider designs which are generally balanced. This allows us to give the stratum efficiency factors for treatment combination contrasts in the proposed split-block-plot designs.

On a construction procedure for split-block-plot designs based on the Khatri–Rao product of incidence matrices

katarzyna.ambrozy.deregowska@up.poznan.pl

Department of Mathematical and Statistical Methods

Biometrical Letters

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

The construction of incomplete split-block-plot (SBP) designs for three-factor experiments is investigated. A semi-Kronecker (Khatri–Rao) product of matrices...

On a construction procedure for split-block-plot designs based on the Khatri–Rao product of incidence matrices

Published Online: Jun 30, 2022

Page range: 55 - 63

DOI: https://doi.org/10.2478/bile-2022-0005

Keywords
Generally balanced designs, Semi-Kronecker product of matrices, Square lattice designs, Split-block-plot designs, Stratum efficiency factors

© 2022 Katarzyna Ambroży-Deręgowska et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

On a construction procedure for split-block-plot designs based on the Khatri–Rao product of incidence matrices

Published Online: Jun 30, 2022

Page range: 55 - 63

DOI: https://doi.org/10.2478/bile-2022-0005

KeywordsGenerally balanced designs, Semi-Kronecker product of matrices, Square lattice designs, Split-block-plot designs, Stratum efficiency factors

© 2022 Katarzyna Ambroży-Deręgowska et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Generally balanced designs, Semi-Kronecker product of matrices, Square lattice designs, Split-block-plot designs, Stratum efficiency factors