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Optimal main effect plans in blocks of small size

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  • Bose, Mausumi
  • Bagchi, Sunanda

Abstract

In this paper we first construct an universally optimal main effect plan (MEP) for an ss experiment on s2(s-1)/2 nonorthogonal blocks of size two each, s a power of 2. Next we derive another set of sufficient conditions for an MEP on nonorthogonal blocks requiring a smaller number of blocks. These conditions are used to obtain universally optimal saturated MEPs in blocks of size 2 for (i) 42 experiment on 6 blocks and (ii) 52x22 on 10 blocks.

Suggested Citation

  • Bose, Mausumi & Bagchi, Sunanda, 2007. "Optimal main effect plans in blocks of small size," Statistics & Probability Letters, Elsevier, vol. 77(2), pages 142-147, January.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:2:p:142-147
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    References listed on IDEAS

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    1. Rahul Mukerjee, 2002. "Optimal main effect plans with non-orthogonal blocking," Biometrika, Biometrika Trust, vol. 89(1), pages 225-229, March.
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    Cited by:

    1. Jacroux, Mike & Kealy-Dichone, Bonni, 2014. "On the E-optimality of blocked main effects plans when n≡3 (mod 4)," Statistics & Probability Letters, Elsevier, vol. 87(C), pages 143-148.
    2. Jacroux, Mike & Kealy-Dichone, Bonni, 2015. "On the type I optimality of blocked 2-level main effects plans having blocks of different sizes," Statistics & Probability Letters, Elsevier, vol. 98(C), pages 39-43.
    3. Bagchi, Sunanda & Bose, Mausumi, 2008. "Optimal main effect plans in nested row-column set-up of small size," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2720-2724, November.
    4. Dutta, Ganesh & SahaRay, Rita, 2015. "D- and E-optimal blocked main effects plans with unequal block sizes when n is odd," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 37-43.
    5. Jacroux, Mike & Kealy-Dichone, Bonni, 2015. "On the use of blocked 2-level main effects plans having blocks of different sizes," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 362-368.
    6. Chen, Xue-Ping & Lin, Jin-Guan & Yang, Jian-Feng & Wang, Hong-Xia, 2015. "Construction of main-effect plans orthogonal through the block factor," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 58-64.
    7. Jacroux, Mike, 2013. "A note on the optimality of 2-level main effects plans in blocks of odd size," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1163-1166.

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    1. Dutta, Ganesh & SahaRay, Rita, 2015. "D- and E-optimal blocked main effects plans with unequal block sizes when n is odd," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 37-43.
    2. Jacroux, Mike, 2013. "A note on the optimality of 2-level main effects plans in blocks of odd size," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1163-1166.
    3. Jacroux, Mike & Kealy-Dichone, Bonni, 2015. "On the type I optimality of blocked 2-level main effects plans having blocks of different sizes," Statistics & Probability Letters, Elsevier, vol. 98(C), pages 39-43.
    4. Jacroux, Mike & Kealy-Dichone, Bonni, 2015. "On the use of blocked 2-level main effects plans having blocks of different sizes," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 362-368.
    5. Bagchi, Sunanda & Bose, Mausumi, 2008. "Optimal main effect plans in nested row-column set-up of small size," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2720-2724, November.
    6. Chen, Xue-Ping & Lin, Jin-Guan & Yang, Jian-Feng & Wang, Hong-Xia, 2015. "Construction of main-effect plans orthogonal through the block factor," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 58-64.

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