Three-Dimensional Variance Dispersion Graphs for Split-Plot Designs

Li Liang Li Liang is Senior Statistician, Duke Clinical Research Institute, 2400 Pratt Street, Room 0311 Terrace Level, Durham, NC 27705 . Christine Anderson-Cook is Technical Staff Member, Statistical Sciences Group, Los Alamos National Laboratory, PO Box 1663, MS F600, Los Alamos, NM 87545 . Timothy J. Robinson is Associate Professor, Department of Statistics, University of Wyoming, Department 3332, 1000 E. University Avenue, Laramie, WY 82071 . Raymond H. Myers is Professor Emeritus, Virginia Polytechnic Institute and State University, Blacksburg, VA 24060 .

Christine M Anderson-Cook Li Liang is Senior Statistician, Duke Clinical Research Institute, 2400 Pratt Street, Room 0311 Terrace Level, Durham, NC 27705 . Christine Anderson-Cook is Technical Staff Member, Statistical Sciences Group, Los Alamos National Laboratory, PO Box 1663, MS F600, Los Alamos, NM 87545 . Timothy J. Robinson is Associate Professor, Department of Statistics, University of Wyoming, Department 3332, 1000 E. University Avenue, Laramie, WY 82071 . Raymond H. Myers is Professor Emeritus, Virginia Polytechnic Institute and State University, Blacksburg, VA 24060 .

Timothy J Robinson Li Liang is Senior Statistician, Duke Clinical Research Institute, 2400 Pratt Street, Room 0311 Terrace Level, Durham, NC 27705 . Christine Anderson-Cook is Technical Staff Member, Statistical Sciences Group, Los Alamos National Laboratory, PO Box 1663, MS F600, Los Alamos, NM 87545 . Timothy J. Robinson is Associate Professor, Department of Statistics, University of Wyoming, Department 3332, 1000 E. University Avenue, Laramie, WY 82071 . Raymond H. Myers is Professor Emeritus, Virginia Polytechnic Institute and State University, Blacksburg, VA 24060 .

Raymond H Myers Li Liang is Senior Statistician, Duke Clinical Research Institute, 2400 Pratt Street, Room 0311 Terrace Level, Durham, NC 27705 . Christine Anderson-Cook is Technical Staff Member, Statistical Sciences Group, Los Alamos National Laboratory, PO Box 1663, MS F600, Los Alamos, NM 87545 . Timothy J. Robinson is Associate Professor, Department of Statistics, University of Wyoming, Department 3332, 1000 E. University Avenue, Laramie, WY 82071 . Raymond H. Myers is Professor Emeritus, Virginia Polytechnic Institute and State University, Blacksburg, VA 24060 .

Abstract

Complete randomization for many industrial and agricultural experiments is frequently impractical due to constraints in time, cost, or existence of one or more hard-to-change factors. In these situations, restrictions on randomization may lead to split-plot designs, allowing certain factor levels to be randomly applied to the whole plot units and remaining factor levels randomly applied to the subplot units. Separate random errors in whole and subplot units from the two randomizations results in a compound symmetric error structure, which affects estimation, inference, and choice of design. In this article, we consider the prediction properties of split-plot designs, expanding the comparison between designs beyond parameter estimation properties and present three-dimensional variance dispersion graphs. These graphs can be used for evaluating the prediction capability of split-plot designs as well as for developing design strategies. We demonstrate, through several examples, that three-dimensional variance dispersion plots offer a more comprehensive study of competing designs than what is offered when comparing designs with single number optimality criteria (such as D-, G-, and V-criteria).

Key Words:

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Three-Dimensional Variance Dispersion Graphs for Split-Plot Designs

Related Research Data

Information for

Open access

Opportunities

Help and information

Three-Dimensional Variance Dispersion Graphs for Split-Plot Designs

Abstract

Reprints and Corporate Permissions

Academic Permissions

Related Research Data

Related research

To cite this article:

Download citation

Information for

Open access

Opportunities

Help and information

Keep up to date

Your download is now in progress and you may close this window

Login or register to access this feature