18. Lattice Designs

  1. Klaus Hinkelmann1 and
  2. Oscar Kempthorne2

Published Online: 27 JAN 2005

DOI: 10.1002/0471709948.ch18

Design and Analysis of Experiments: Advanced Experimental Design, Volume 2

Design and Analysis of Experiments: Advanced Experimental Design, Volume 2

How to Cite

Hinkelmann, K. and Kempthorne, O. (2005) Lattice Designs, in Design and Analysis of Experiments: Advanced Experimental Design, Volume 2, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/0471709948.ch18

Author Information

  1. 1

    Virginia Polytechnic Institute and State University, Department of Statistics, Blacksburg, VA, USA

  2. 2

    Iowa State University, Department of Statistics, Ames, IA, USA

Publication History

  1. Published Online: 27 JAN 2005
  2. Published Print: 4 MAR 2005

Book Series:

  1. Wiley Series in Probability and Statistics

Book Series Editors:

  1. Walter A. Shewhart and
  2. Samuel S. Wilks

ISBN Information

Print ISBN: 9780471551775

Online ISBN: 9780471709947

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Keywords:

  • Lattice design;
  • quasi-factorial design;
  • square lattice;
  • cubic lattice;
  • lattice square;
  • rectangular lattice;
  • incomplete block design;
  • BIB design;
  • PBIB design;
  • system of confounding

Summary

This chapter considers an important combination of incomplete block designs and factorial designs in an effort to construct resolvable designs, usually for a large number of treatments. These designs are referred to as quasi-factorial or lattice designs. We discuss the construction of several forms of such designs, including one-restrictional two- and three-dimensional lattices, two-restrictional two-dimensional lattices, and one-restrictional two-dimensional rectangular lattices. We give a thorough description of the intra- and inter-block analyses for these designs.