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Evaluation of inequivalent projections of Hadamard matrices of order 24

Author

Listed:
  • H. Evangelaras
  • S. Georgiou
  • C. Koukouvinos

Abstract

Screening designs are useful for situations where a large number of factors (q) is examined but only few (k) of these are expected to be important. It is of practical interest for a given k to know all the inequivalent projections of the design into the k dimensions. In this paper we give all the (combinatorially) inequivalent projections of inequivalent Hadamard matrices of order 24 into k=3,4 and 5 dimensions, as well as their frequencies. Then, we sort these projections according to their generalized resolution, generalized aberration and centered L 2 -discrepancy measure of uniformity. Then, we study the hidden projection properties of these designs as they are introduced by Wang and Wu (1995). The hidden projection property suggests that complex aliasing allows some interactions to be estimated without making additional runs. Copyright Springer-Verlag 2004

Suggested Citation

  • H. Evangelaras & S. Georgiou & C. Koukouvinos, 2004. "Evaluation of inequivalent projections of Hadamard matrices of order 24," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 59(1), pages 51-73, February.
    • Handle: RePEc:spr:metrik:v:59:y:2004:i:1:p:51-73
    DOI: 10.1007/s001840300271
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    Citations

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    Cited by:

    1. H. Evangelaras & S. D. Georgiou, 2021. "Projection properties of two-level supersaturated designs constructed from Hadamard designs using Lin’s method," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(8), pages 1095-1108, November.
    2. SCHOEN, Eric D. & VO-THANH, Nha & GOOS, Peter, 2015. "Two-level orthogonal designs in 24 and 28 runs," Working Papers 2015016, University of Antwerp, Faculty of Business and Economics.
    3. Evangelaras, H. & Kolaiti, E. & Koukouvinos, C., 2006. "Non-isomorphic orthogonal arrays obtained by juxtaposition," Statistics & Probability Letters, Elsevier, vol. 76(3), pages 274-279, February.
    4. P. Angelopoulos & H. Evangelaras & C. Koukouvinos & E. Lappas, 2007. "An effective step-down algorithm for the construction and the identification of nonisomorphic orthogonal arrays," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 66(2), pages 139-149, September.
    5. Evangelaras, H. & Koukouvinos, C., 2004. "On generalized projectivity of two-level screening designs," Statistics & Probability Letters, Elsevier, vol. 68(4), pages 429-434, July.
    6. Eric D. Schoen & Nha Vo-Thanh & Peter Goos, 2017. "Two-Level Orthogonal Screening Designs With 24, 28, 32, and 36 Runs," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1354-1369, July.

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