Optimal Semi-Split-Plot Designs with R

Hoffmeister, Sebastian; Geistanger, Andrea

doi:10.1007/978-3-030-25147-5_17

Sebastian Hoffmeister²³ &
Andrea Geistanger²³

Part of the book series: Studies in Classification, Data Analysis, and Knowledge Organization ((STUDIES CLASS))

948 Accesses

Abstract

This paper introduces Semi-Split-Plot designs. They are a new class of experimental designs and support factors where only a reduced number of factor settings can be applied inside of one block. An algorithm to generate optimal Semi-Split-Plot designs is presented. A tutorial for the R package rospd that implements the algorithm is given. Semi-Split-Plot designs are compared to completely randomized and Split-Plot designs in terms of balance, aliasing and predictive quality.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

eBook: USD 16.99; Price excludes VAT (USA)

Softcover Book: USD 16.99; Price excludes VAT (USA)

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

1.
One might argue that using always the same bottles of solvents is a violation of the assumption of independence. The latter is ignored for the moment as experience shows that the product quality of the solvents is very stable.

References

Fisher, R. A. (1992). Statistical methods for research workers (pp. 66–70). New York: Springer. https://doi.org/10.1007/978-1-4612-4380-9_6.
Google Scholar
Hooks, T., Marx, D., Kachman, S., & Pedersen, J. (2009). Optimality criteria for models with random effects. Revista Colombiana de Estadistica32, 17 – 31. http://www.scielo.org.co/scielo.php?script=sci_arttext&pid=S0120-17512009000100002&nrm=iso.
Jones, B., & Goos, P. (2007). A candidate-set-free algorithm for generating d-optimal split-plot designs. Journal of the Royal Statistical Society: Series C (Applied Statistics), 56(3), 347–364. https://doi.org/10.1111/j.1467-9876.2007.00581.x..
Article MathSciNet Google Scholar
Jones, B., & Goos, P. (2011). Optimal design of experiments (pp. 277–282). Wiley-Blackwell. https://doi.org/10.1002/9781119974017.biblio, https://doi.org/10.1002/9781119974017.biblio.
Jones, B., & Goos, P. (2012). I-optimal versus D-optimal split-plot response surface designs. Working Papers 2012002, University of Antwerp, Faculty of Applied Economics. https://ideas.repec.org/p/ant/wpaper/2012002.html.
Jones, B., & Nachtsheim, C. J. (2009). Split-plot designs: What, why, and how. Journal of Quality Technology, 41(4), 340–361. https://doi.org/10.1080/00224065.2009.11917790.
Article Google Scholar
Kowalski, S. M., & Potcner, K. J. (2003). How to recognize a split-plot experiment. https://onlinecourses.science.psu.edu/stat503/sites/onlinecourses.science.psu.edu.stat503/files/lesson14/recognize_split_plot_experiment/index.pdf. Accessed July 29 2018.
Meyer, R. K., & Nachtsheim, C. J. (1995). The coordinate-exchange algorithm for constructing exact optimal experimental designs. Technometrics37(1), 60–69. http://www.jstor.org/stable/1269153.
Miller, A.J., & Nam-Ky, N.: A fedorov exchange algorithm for d-optimal design. Journal of the Royal Statistical Society: Series C (Applied Statistics) 43(4), 669 (1994). http://search.ebscohost.com/login.aspx?direct=true&db=plh&AN=6119956&site=ehost-live&authtype=sso&custid=s87180.
Morgan-Wall, T., & Khoury, G. (2018). skpr: Design of experiments suite: Generate and evaluate optimal designs. https://CRAN.R-project.org/package=skpr. R package version 0.49.1.
Næs, T., & Aastveit, A., & Sahni, N. (2007). Analysis of split-plot designs: An overview and comparison of methods. 23, 801–820.
Google Scholar
R Core Team. (2018). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. https://www.R-project.org/.
SAS. (2018). Split plot designs with different numbers of whole plots. https://www.jmp.com/support/help/14/split-plot-designs-with-different-numbers-of-who.shtml. Accessed July 25 2018.
Schoonees, P., le Roux, N., & Coetzer, R. (2016). Flexible graphical assessment of experimental designs in R: The vdg package. Journal of Statistical Software74(3), 1–22. https://doi.org/10.18637/jss.v074.i03.

Download references

Author information

Authors and Affiliations

Roche Diagnostics GmbH, Penzberg, Germany
Sebastian Hoffmeister & Andrea Geistanger

Authors

Sebastian Hoffmeister
View author publications
You can also search for this author in PubMed Google Scholar
Andrea Geistanger
View author publications
You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sebastian Hoffmeister .

Editor information

Editors and Affiliations

Department of Computer Science, Dortmund University of Applied Sciences and Arts, Dortmund, Germany
Nadja Bauer
Faculty of Statistics, TU Dortmund University, Dortmund, Germany
Katja Ickstadt
Institute for Empirical Research and Statistics, FOM University of Applied Sciences, Essen, Germany
Karsten Lübke
School of Business Studies, HOST University of Applied Sciences Stralsund, Stralsund, Germany
Gero Szepannek
Department of Information Systems, University of Münster, Münster, Germany
Heike Trautmann
Department of Statistical Sciences, Sapienza University of Rome, Rome, Italy
Maurizio Vichi

Rights and permissions

Reprints and permissions

Copyright information

About this chapter

Cite this chapter

Hoffmeister, S., Geistanger, A. (2019). Optimal Semi-Split-Plot Designs with R. In: Bauer, N., Ickstadt, K., Lübke, K., Szepannek, G., Trautmann, H., Vichi, M. (eds) Applications in Statistical Computing. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Cham. https://doi.org/10.1007/978-3-030-25147-5_17

Download citation

DOI: https://doi.org/10.1007/978-3-030-25147-5_17
Published: 12 October 2019
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-25146-8
Online ISBN: 978-3-030-25147-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)

Publish with us

Policies and ethics