Designs for special layouts

Sometimes a single system of blocks is not enough, and a more complicated layout is needed. Then a design suitable for that layout is needed. Examples include Latin squares and semi-Latin squares.

LayoutsSome of my publications
Observational units inside experimental units (m / n)
  • T. H. Sparks, R. A. Bailey and D. A. Elston: Pseudoreplication: common (mal)practice. SETAC (Society of Environmental Toxicology and Chemistry) News, 17(3) (1997), 12–13.
  • R. A. Bailey and J. J. D. Greenwood: Effects of neonicotinoids on bees: an invalid experiment. Ecotoxicology, 27 (2018), 1–7. doi: 10.1007/s10646-017-1877
  • Small blocks inside large blocks (n / b / k)
  • 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)]
  • 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)]
  • R. A. Bailey: Resolved designs viewed as sets of partitions. In Combinatorial Designs and their Applications (editors F. C. Holroyd, K. A. S. Quinn, C. Rowley and B. S. Webb), Chapman & Hall/CRC Press Research Notes in Mathematics 403, CRC Press LLC, Boca Raton, (1999), pp. 17–47. [Maths Reviews 1678589 (2000e: 05017)]
  • R. A. Bailey: Choosing designs for nested blocks. Listy Biometryczne 36 (1999), 85–126.
  • R. A. Bailey: Six families of efficient resolvable designs in three replicates. Metrika 62 (2005), 161–173. doi: 10.1007/s00184-005-0405-0 [Maths Reviews 2274987]
  • Rows and columns (r × c)
  • R. A. Bailey, D. A. Preece and P. J. Zemroch: Totally symmetric Latin squares and cubes. Utilitas Mathematica 14 (1978), 161–170. [Maths Reviews 0511521 (80a: 05032)]
  • R. A. Bailey: Enumeration of totally symmetric Latin squares. Utilitas Mathematica 15 (1979), 193–216. [Maths Reviews 0531629 (80d: 05014a) and 0557001 (80d: 05014b)]
  • R. A. Bailey: Latin squares with highly transitive automorphism groups. Journal of the Australian Mathematical Society, Series A 33 (1982), 18–22. [Maths Reviews 0662355 (83g: 05021)]
  • R. A. Bailey: Quasi-complete Latin squares: construction and randomization. Journal of the Royal Statistical Society, Series B 46 (1984), 323–334. [Maths Reviews 0781893 (86i: 62161)]
  • R. A. Bailey, D. A. Preece and C. A. Rowley: Randomization for a balanced superimposition of one Youden square on another. Journal of the Royal Statistical Society, Series B 57 (1995), 459–469. [Maths Reviews 1323350 (96i: 62083)]
  • Ian Anderson and R. A. Bailey: Completeness properties of conjugates of Latin squares based on groups, and an application to bipartite tournaments. Bulletin of the Institute of Combinatorics and its Applications 21 (1997), 95–99. [Maths Reviews 1470311 (98d: 05032)]
  • 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]
  • C. J. Brien, R. A. Bailey, T. T. Tran and J. Bolund: Quasi-Latin designs. Electronic Journal of Statistics, 6 (2012), 1900–1925. doi: 10.1214/12-EJS732 [Maths Reviews 2988468]
  • 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]
  • Small blocks inside rows and columns ((r × c) / n)
  • R. A. Bailey: Semi-Latin squares. Journal of Statistical Planning and Inference 18 (1988), 299–312. [Maths Reviews 0926634 (89b: 62160)]
  • R. A. Bailey: An efficient semi-Latin square for twelve treatments in blocks of size two. Journal of Statistical Planning and Inference 26 (1990), 263–266. [Maths Reviews 1086100]
  • R. A. Bailey: Efficient semi-Latin squares. Statistica Sinica 2 (1992), 413–437. [Maths Reviews 1187951 (93j: 62199)]
  • R. A. Bailey: Recent advances in experimental design in agriculture. Bulletin of the International Statistical Institute 55 (1) (1993), 179–193.
  • R. A. Bailey: A Howell design admitting A5. Discrete Mathematics 167-168 (1997), 65–71. [Maths Reviews 1446733 (98h: 05039)]
  • R. A. Bailey and P. E. Chigbu: Enumeration of semi-Latin squares. Discrete Mathematics 167-168 (1997), 73–84. [Maths Reviews 1446734 (98g: 05026)]
  • 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 and H. Monod: Efficient semi-Latin rectangles: designs for plant disease experiments. Scandinavian Journal of Statistics 28 (2001), 257–270. [Maths Reviews 1842248 (2002c: 05038)]
  • R. A. Bailey: Semi-Latin squares. Wiley StatsRef: Statistics Reference Online, 2017, pp. 1–8. doi: 10.1002/9781118445112.stat02644.pub2
  • Rows and columns inside large blocks b / (r × c)
  • R. A. Bailey and H. D. Patterson: A note on the construction of row-and-column designs with two replicates. Journal of the Royal Statistical Society, Series B 53 (1991), 645–648. [Maths Reviews 1125721]
  • H. Monod and R. A. Bailey: Pseudofactors: normal use to improve design and facilitate analysis. Applied Statistics 41 (1992), 317–336.
  • R. A. Bailey: Recent advances in experimental design in agriculture. Bulletin of the International Statistical Institute 55 (1) (1993), 179–193.
  • R. A. Bailey: Resolved designs viewed as sets of partitions. In Combinatorial Designs and their Applications (editors F. C. Holroyd, K. A. S. Quinn, C. Rowley and B. S. Webb), Chapman & Hall/CRC Press Research Notes in Mathematics 403, CRC Press LLC, Boca Raton, (1999), pp. 17–47. [Maths Reviews 1678589 (2000e: 05017)]
  • R. A. Bailey and E. R. Williams: Optimal nested row-column designs with specified components. Biometrika 94 (2007), 459–468. doi: 10.1093/biomet/asm039 [Maths Reviews 2331490]
  • C. J. Brien, R. A. Bailey, T. T. Tran and J. Bolund: Quasi-Latin designs. Electronic Journal of Statistics, 6 (2012), 1900–1925. doi: 10.1214/12-EJS732 [Maths Reviews 2988468]
  • R. A. Bailey and A. Łacka: Nested row-column designs for near-factorial experiments with two treatment factors and one control treatment. Journal of Statistical Planning and Inference, 165 (2015), 63–77. doi: 10.1016/j.jspi.2015.04.003
  • Small blocks inside large blocks, with rows running across all small blocks (r × (b / k))
  • 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)]
  • R. A. Bailey: Recent advances in experimental design in agriculture. Bulletin of the International Statistical Institute 55 (1) (1993), 179–193.
  • C. J. Brien, R. A. Bailey, T. T. Tran and J. Bolund: Quasi-Latin designs. Electronic Journal of Statistics, 6 (2012), 1900–1925. doi: 10.1214/12-EJS732 [Maths Reviews 2988468]
  • Smalls rows inside large rows at the same time as small columns inside large columns ((r / n) ×  (c / m))
  • R. A. Bailey, J. Kunert and R. J. Martin: Some comments on gerechte designs. I. Analysis for uncorrelated errors. Journal of Agronomy & Crop Science 165 (1990), 121–130.
  • R. A. Bailey, J. Kunert and R. J. Martin: Some comments on gerechte designs. II. Randomization analysis, and other methods that allow for inter-plot dependence. Journal of Agronomy & Crop Science 166 (1991), 101–111.
  • R. A. Bailey, Peter J. Cameron and Robert Connolly: Sudoku, gerechte designs, resolutions, affine space, spreads, reguli, and Hamming codes. The American Mathematical Monthly 115 (2008), 383–404.
    (Translated into Chinese in Mathematical Advance in Translation 28 (2009), 21–39.) [Maths Reviews 2408485]
  • Page maintained by R. A. Bailey