1. bookVolume 57 (2020): Issue 2 (December 2020)
Journal Details
License
Format
Journal
eISSN
2199-577X
First Published
17 Aug 2013
Publication timeframe
2 times per year
Languages
English
access type Open Access

Constructing non-orthogonal split-split-plot designs using some resolvable block designs

Published Online: 31 Dec 2020
Volume & Issue: Volume 57 (2020) - Issue 2 (December 2020)
Page range: 177 - 194
Journal Details
License
Format
Journal
eISSN
2199-577X
First Published
17 Aug 2013
Publication timeframe
2 times per year
Languages
English
Summary

We consider a new method of constructing non-orthogonal (incomplete) split-split-plot designs (SSPDs) for three (A, B, C) factor experiments. The final design is generated by some resolvable incomplete block design (for the factor A) and by square lattice designs for factors B and C using a modified Kronecker product of those designs (incidence matrices). Statistical properties of the constructed designs are investigated under a randomized-derived linear model. This model is strictly connected with a four-step randomization of units (blocks, whole plots, subplots, sub-subplots inside each block). The final SSPD has orthogonal block structure (OBS) and satisfies the general balance (GB) property. The statistical analysis of experiments performed in the SSPD is based on the analysis of variance often used for multistratum experiments. We characterize the SSPD with respect to the stratum efficiency factors for the basic estimable treatment contrasts. The structures of the vectors defining treatment contrasts are also given.

Keywords

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