Multiphase Experiments with at Least One Later Laboratory Phase. I. Orthogonal Designs

  • C. J. Brien
  • B. D. Harch
  • R. L. Correll
  • R. A. Bailey
Article

Abstract

The paper provides a systematic approach to designing the laboratory phase of a multiphase experiment, taking into account previous phases. General principles are outlined for experiments in which orthogonal designs can be employed. Multiphase experiments occur widely, although their multiphase nature is often not recognized. The need to randomize the material produced from the first phase in the laboratory phase is emphasized. Factor-allocation diagrams are used to depict the randomizations in a design and the use of skeleton analysis-of-variance (ANOVA) tables to evaluate their properties discussed. The methods are illustrated using a scenario and a case study. A basis for categorizing designs is suggested. This article has supplementary material online.

Key Words

Analysis of variance Experimental design Laboratory experiments Multiple randomizations Multi-phase experiments Multitiered experiments Two-phase experiments 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Supplementary material

13253_2011_60_MOESM1_ESM.pdf (530 kb)
Web-based Supplementary Materials for Multiphase experiments with at least one later laboratory phase. I. Orthogonal designs (PDF 520 KB)

References

  1. Bailey, R. A., and Brien, C. J. (2011), “Data Analysis for Multitiered Experiments Using Randomization Models: A Chain of Randomizations,” Unpublished manuscript. Google Scholar
  2. Brien, C. J. (1983), “Analysis of Variance Tables Based on Experimental Structure,” Biometrics, 39, 53–59. CrossRefGoogle Scholar
  3. Brien, C. J., and Bailey, R. A. (2006), “Multiple Randomizations (with discussion),” Journal of the Royal Statistical Society, Series B, 68, 571–609. MathSciNetCrossRefGoogle Scholar
  4. — (2009), “Decomposition Tables for Experiments. I. A Chain of Randomizations,” The Annals of Statistics, 37, 4184–4213. MathSciNetMATHCrossRefGoogle Scholar
  5. — (2010), “Decomposition Tables for Experiments. II. Two-One Randomizations,” The Annals of Statistics, 38, 3164–3190. MathSciNetMATHCrossRefGoogle Scholar
  6. Brien, C. J., and Demétrio, C. G. B. (2009), “Formulating Mixed Models for Experiments, Including Longitudinal Experiments,” The Journal of Agricultural, Biological and Environmental Statistics, 14, 253–280. CrossRefGoogle Scholar
  7. Brien, C. J., Harch, B. D., and Correll, R. L. (1998), “Design and ANOVA for Experiments Involving a Field Trial and Laboratory Analyses,” Paper presented to The Ninth International Conference on Quantitative Methods for the Environmental Sciences, Gold Coast, Australia. Google Scholar
  8. Brien, C. J., May, P., and Mayo, O. (1987), “Analysis of Judge Performance in Wine-Quality Evaluations,” Journal of Food Science, 52, 1273–1279. CrossRefGoogle Scholar
  9. Cochran, W. G., and Cox, G. M. (1957), Experimental Designs (2nd ed.), New York: Wiley. MATHGoogle Scholar
  10. Cox, D. R. (1958), Planning of Experiments, New York: Wiley. MATHGoogle Scholar
  11. — (2009), “Randomization in the Design of Experiments,” International Statistical Review, 77, 415–429. CrossRefGoogle Scholar
  12. Cox, D. R., and Solomon, P. (2003), Components of Variance, Boca Raton: Chapman and Hall/CRC. MATHGoogle Scholar
  13. Cullis, B. R., Smith, A. B., Panozzo, J. F., and Lim, P. (2003), “Barley Malting Quality: Are We Selecting the Best?” Australian Journal of Agricultural Research, 54, 1261–1275. CrossRefGoogle Scholar
  14. Harch, B. D., Correll, R. L., Meech, W., Kirkby, C. A., and Pankhurst, C. E. (1997), “Using the Gini Coefficient with BIOLOG Substrate Utilisation Data to Provide an Alternative Quantitative Measure for Comparing Bacterial Soil Communities,” Journal of Microbial Methods, 30, 91–101. CrossRefGoogle Scholar
  15. Jarrett, R. G., and Ruggiero, K. (2008), “Design and Analysis of Two-Phase Experiments for Gene-Expression Microarrays—Part I,” Biometrics, 64, 208–216. MathSciNetMATHCrossRefGoogle Scholar
  16. Kerr, M. K. (2003), “Design Considerations for Efficient and Effective Microarray Studies,” Biometrics, 59, 822–828. MathSciNetMATHCrossRefGoogle Scholar
  17. Littell, R., Milliken, G., Stroup, W., Wolfinger, R., and Schabenberger, O. (2006), SAS for Mixed Models (2nd ed.), Cary: SAS Press. Google Scholar
  18. McIntyre, G. A. (1955), “Design and Analysis of Two Phase Experiments,” Biometrics, 11, 324–334. CrossRefGoogle Scholar
  19. Nelder, J. A. (1965), “The Analysis of Randomized Experiments with Orthogonal Block Structure. I. Block Structure and the Null Analysis of Variance,” Proceedings of the Royal Society, Series A, 283, 147–161. MathSciNetMATHCrossRefGoogle Scholar
  20. Ojima, Y. (2000), “Generalized Staggered Nested Designs for Variance Components Estimation,” Journal of Applied Statistics, 27, 541–553. MATHCrossRefGoogle Scholar
  21. Patterson, H. D., and Bailey, R. A. (1978), “Design Keys for Factorial Experiments,” Applied Statistics, 27, 335–343. MATHCrossRefGoogle Scholar
  22. Peeling, P., Dawson, B., Goodman, C., Landers, G., Wiegerinck, E. T., Swinkels, D. W., and Trinder, D. (2009), “Training Surface and Intensity: Inflammation, Hemolysis, and Hepcidin Expression,” Medicine and Science in Sports and Exercise, 41, 1138–1145. CrossRefGoogle Scholar
  23. Searle, S. R., Casella, G., and McCulloch, C. E. (1992), Variance Components, New York: Wiley. MATHCrossRefGoogle Scholar
  24. Smith, A. B., Cullis, B. R., Appels, R., Campbell, A. W., Cornish, G. B., Martin, D., and Allen, H. M. (2001), “The Statistical Analysis of Quality Traits in Plant Improvement Programs with Application to the Mapping of Milling Yield in Wheat,” Australian Journal of Agricultural Research, 52, 1207–1219. CrossRefGoogle Scholar
  25. Smith, A. B., Lim, P., and Cullis, B. R. (2006), “The Design and Analysis of Multi-Phase Plant Breeding Experiments,” The Journal of Agricultural Science, 144, 393–409. CrossRefGoogle Scholar
  26. Williams, E. R. (1986), “Row and Column Designs with Contiguous Replicates,” Australian Journal of Statistics, 28, 154–163. CrossRefGoogle Scholar

Copyright information

© International Biometric Society 2011

Authors and Affiliations

  • C. J. Brien
    • 1
  • B. D. Harch
    • 2
  • R. L. Correll
    • 3
  • R. A. Bailey
    • 4
  1. 1.School of Mathematics and StatisticsUniversity of South AustraliaMawson LakesAustralia
  2. 2.Ecosciences PrecinctCSIRO Sustainable Agriculture FlagshipBrisbaneAustralia
  3. 3.Rho EnvironmentricsHighgateAustralia
  4. 4.School of Mathematical SciencesQueen Mary University of LondonLondonUK

Personalised recommendations