Incomplete-block designs

If the experimental units are not all alike, we group them into blocks in such a way that units within each block are tolerably alike. Usually we do this in such a way that all blocks have the same size. Blocks may be fields on different farmers' farms, or groups of patients looked after by different nurses, or laboratory procedures done on different days.

If the blocks are too small to contain every treatment, the design is an incomplete-block design.

TopicsSome of my publications
Balanced incomplete-block designs
  • R. A. Bailey and Peter J. Cameron: A family of balanced incomplete-block designs with repeated blocks on which general linear groups act. Journal of Combinatorial Designs 15 (2007), 143–150. doi: 10.1002/jcd.20120 [Maths Reviews 2291526 (2007k: 05025)]
  • Partially balanced incomplete-block designs
  • R. A. Bailey: Partially balanced designs. In Encyclopedia of Statistical Sciences (eds. S. Kotz and N. L. Johnson), J. Wiley, New York, Volume 6, 1985, pp. 593–610.
  • R. A. Bailey: Cyclic designs and factorial designs. In Probability, Statistics and Design of Experiments (proceedings of the R. C. Bose Symposium on Probability, Statistics and Design of Experiments, Delhi, 27–30 December, 1988) (ed. R. R. Bahadur), Wiley Eastern, New Delhi, 1990, pp. 51–74.
  • C.-S. Cheng and R. A. Bailey: Optimality of some two-associate-class partially balanced incomplete-block designs. Annals of Statistics 19 (1991), 1667–1671. doi: 10.1214/aos/1176348270 [Maths Reviews 1126346 (92k: 62130)]
  • R. A. Bailey: Association Schemes: Designed Experiments, Algebra and Combinatorics, Cambridge University Press, Cambridge, 2004. 387pp. ISBN 0 521 82446 X. [Maths Reviews 2047311 (2005d: 05001)]
  • R. A. Bailey, Peter J. Cameron and Tomas Nilson: Sesqui-arrays, a generalisation of triple arrays. Australasian Journal of Combinatorics, 71 (2018), 427–451. [Maths Reviews 3801275]
  • Blocks of size two
  • R. A. Bailey, D. C. Goldrei and D. F. Holt: Block designs with block size two. Journal of Statistical Planning and Inference 10 (1984), 257–263. [Maths Reviews 0760410]
  • R. A. Bailey: Designs for two-colour microarray experiments. Applied Statistics 56 (2007), 365–394. doi: 10.1111/j.1467-9876.2007.00582.x [Maths Reviews 2409757]
  • R. A. Bailey, Katharina Schiffl and Ralf-Dieter Hilgers: A note on robustness of D-optimal block designs for two-colour microarray experiments. Journal of Statistical Planning and Inference, 143 (2013), 1195–1202. doi: 10.1016/j.jspi.2013.01.005
  • When do nice combinatorial properties guarantee low variance?
  • R. A. Bailey and T. P. Speed: Rectangular lattice designs: efficiency factors and analysis. Annals of Statistics 14 (1986), 874–895. [Maths Reviews 0856795 (88e: 62186)]
  • C.-S. Cheng and R. A. Bailey: Optimality of some two-associate-class partially balanced incomplete-block designs. Annals of Statistics 19 (1991), 1667–1671. doi: 10.1214/aos/1176348270 [Maths Reviews 1126346 (92k: 62130)]
  • R. A. Bailey, H. Monod and J. P. Morgan: Construction and optimality of affine-resolvable designs. Biometrika 82 (1995), 187–200. doi: 10.1093/biomet/82.1.187 [Maths Reviews 1332849 (96k: 62212)]
  • Using the concurrence graph or the Levi graph to find optimal designs
  • R. A. Bailey and G. Royle: Optimal semi-Latin squares with side six and block size two. Proceedings of the Royal Society, Series A 453 (1997), 1903–1914. [Maths Reviews 1478138 (98k: 62130)]
  • R. A. Bailey: Variance and concurrence in block designs, and distance in the corresponding graphs. Michigan Mathematical Journal 58 (2009), 105–124. doi: 10.1307/mmj/1242071685 [Maths Reviews 2526080 (2010g:05043)]
  • R. A. Bailey and Peter J. Cameron: Combinatorics of optimal designs. In Surveys in Combinatorics 2009 (eds. S. Huczynska, J. D. Mitchell and C. M. Roney-Dougal), London Mathematical Society Lecture Note Series, 365, Cambridge University Press, Cambridge, 2009, pp. 19–73. [Maths Reviews 2588537]
  • R. A. Bailey and Peter J. Cameron: Using graphs to find the best block designs. In Topics in Structural Graph Theory (eds. L. W. Beineke and R. J. Wilson), Cambridge University Press, Cambridge, 2013, pp. 282–317. arXiv:1111.3728
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