Randomization

Experiments have to be randomized to remove conscious and unconscious bias, but without ignoring useful information such as `there will probably be more pollens in this month than that month'. How exactly should this be done? What effect does it have on the assumed model?

Should we randomize an experiment by choosing a plan at random from a set of plans with specified combinatorial properties or by starting with a systematic design and applying a randomly chosen permutation from a suitable group of permutations of the experimental units?

TopicsSome of my publications
Discussion of some of the issues
  • R. A. Bailey: Randomization. In Recent Trends in Statistics (ed. S. Heiler), Vandenhoeck & Ruprecht, Göttingen, 1983, pp. 9–26. [Maths Reviews 0753665 (85g: 62003)]
  • R. A. Bailey: Contribution to the discussion of `On the existence of BLUEs under a randomization model for the randomized block design' by T. Caliński. Listy Biometryczne 33 (1996), pp. 18–21.
  • R. A. Bailey: Inference from randomized (factorial) experiments. Statistical Science, 32 (2017), 352–355. doi: 10.1214/16-STS600
  • What is the link between the group of permutations used for randomization, the assumed model, and the appropriate analysis of variance?
  • R. A. Bailey: A unified approach to design of experiments. Journal of the Royal Statistical Society, Series A 144 (1981), 214–223. [Maths Reviews 0625801 (82h: 62129)]
  • R. A. Bailey: Strata for randomized experiments (with discussion). Journal of the Royal Statistical Society, Series B 53 (1991), 27–78. [Maths Reviews 1094275 (92k: 62134)]
  • R. A. Bailey: Principles of designed experiments in J. A. .Nelder's papers. In Methods and Models in Statistics: In Honour of Professor John Nelder, FRS (eds. N. M. Adams, M. J. Crowder, D. J. .Hand and D A. Stephens), Imperial College Press, London, 2004, pp. 171–194.
  • R. A. Bailey and C. J. Brien: Randomization-based models for multitiered experiments: I. A chain of randomizations. Annals of Statistics, 44 (2016), 1131–1164.
  • How should we randomize an experiment superimposed on a previous one?
  • D. A. Preece, R. A. Bailey, and H. D. Patterson: A randomization problem in forming designs with superimposed treatments. Australian Journal of Statistics 20 (1978), 111–125. [Maths Reviews 0548180 (82k: 62153)]
  • 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)]
  • C. J. Brien and R. A. Bailey: Decomposition tables for experiments. II. Two-one randomizations. Annals of Statistics 38 (2010), 3164–3190. doi: 10.1214/09-AOS785 [Maths Reviews 2722467 (2011j:62187)]
  • Choosing at random from a given set of plans is a valid method of randomization for a prescribed method of data analysis if the estimators of treatment effects and their variances are unbiased over the randomization.
  • R. A. Bailey and C. A. Rowley: Valid randomization. Proceedings of the Royal Society, Series A 410 (1987), 105–124.
  • H. Monod and R. A. Bailey: Valid restricted randomization for unbalanced designs. Journal of the Royal Statisical Society, Series B 55 (1993), 237–251. [Maths Reviews 1210434 (94h: 62121)]
  • H. Monod, J.-M. Azaïs and R. A. Bailey: Valid randomisation for the first difference analysis. Australian Journal of Statistics 33 (1996), 91–106. [Maths Reviews 1410805 (97f: 62120)]
  • J.-M. Azaïs, H. Monod and R. A. Bailey: The influence of design on validity and efficiency of neighbour methods. Biometrics 54 (1998), 1374–1387.
  • What should we do if the usual appropriate method of randomization can give a plan that appears undesirable?
  • R. A. Bailey: Restricted randomization. Biometrika 70 (1983), 183–198. [Maths Reviews 0742988 (85j: 62075)]
  • R. A. Bailey: Restricted randomization versus blocking. International Statistical Review 53 (1985), 171–182. [Maths Reviews 0959036 (89e: 62097)]
  • R. A. Bailey: Restricted randomization for neighbour-balanced designs. Statistics and Decisions Supplement 2 (1985), 237–248. [Maths Reviews 0829496 (87e: 62073)]
  • R. A. Bailey: Randomization, constrained. In Encyclopedia of Statistical Sciences (eds. S. Kotz and N. L. Johnson), J. Wiley, New York, Volume 7, 1986, pp. 524–530.
  • R. A. Bailey: One-way blocks in two-way layouts. Biometrika 74 (1987), 27–32. [Maths Reviews 0885916 (88e: 62187)]
  • R. A. Bailey: Restricted randomization: a practical example. Journal of the American Statistical Association 82 (1987), 712–719.
  • R. A. Bailey and P. R. Nelson: Hadamard randomization: a valid restriction of random permuted blocks. Biometrical Journal 45 (2003), 554–560. [Maths Reviews 1998135]
  • R. A. Bailey: Experiments in rectangular areas: design and randomization. Journal of Agricultural, Biological and Environmental Statistics, 17 (2012), 176–191. doi: 10.1007/s13253-011-0082-6
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