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Biometrika 2006 93(2):289-302; doi:10.1093/biomet/93.2.289
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© 2006 Biometrika Trust

Optimal blocking of two-level factorial designs

Neil A. Butler

School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, U.K. neil.butler{at}nottingham.ac.uk

Blocking of two-level factorial designs is considered for block sizes 2 and 4 using the method of fractional partial confounding. A-, D- and E-optimal designs are obtained for block size 2 within the class of orthogonal designs for which main effects and two-factor interactions are all orthogonal to each other before allowing for blocking. A-, D- and E-optimal designs are obtained for block size 4 within the class of orthogonal designs with main effects orthogonal to blocks. The designs obtained also have other favourable properties including orthogonal estimation of effects and orthogonality to superblocks.

Key Words: Defining contrast; Fractional factorial; Main effect; Minimum aberration; Optimum design; Two-factor interaction.

Received January 2005. Revised October 2005.


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