Preprint No.
A-00-16
Heiko Großmann, Ulrike Graßhoff, Heinz Holling, Rainer Schwabe
Optimal Designs for Paired Comparisons in Main Effects
Analysis of Variance Models
Abstract:
In psychological research paired comparisons which demand judges
to evaluate the trade-off between two alternatives have been shown
to yield valid estimates of the judges' preferences.
For this situation we
present optimal designs in
a discrete setting
where the alternatives are modeled
by an analysis of variance model with main effects only.
While product type designs are theoretically optimal
they bear the disadvantage of exponentially increasing
sample sizes. We employ orthogonality and combinatorial tools
like Hadamard matrices to achieve optimal designs which are saturated
or which have sufficiently small sample sizes increasing linearly
in the number of factors involved.
Moreover, optimal designs are constructed when the number of varying
factors is restricted for each pair of alternatives.
Keywords: paired comparisons, main effects model, optimal design,
equivalence theorem, symmetrization,
additive model, marginal design, product design, Hadamard matrix,
orthogonal array, saturated design, profile strength
Language: ENG
Available: Pr-A-00-16.ps
Contact: Schwabe, Rainer, Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 2-6, D-14195 Berlin, Germany (schwabe@math.fu-berlin.de)
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