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Series of randomized complete block experiments with non-normal data

Author

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  • Bathke, Arne C.
  • Harrar, Solomon W.
  • Wang, Haiyan
  • Zhang, Ke
  • Piepho, Hans-Peter

Abstract

Randomized complete block designs are common in agricultural and other experiments. In this manuscript, we derive asymptotic procedures as well as finite approximations, for the analysis of data arising from series of such experiments. We do not assume normality of the data, and the within-block covariance structures can be arbitrary (no restriction to compound symmetry). The methods are specifically designed for trials with many environments and few blocks per environment, such as multi-environment trials in variety testing and plant breeding. We consider fixed and random effects models for the environment factor. The methodology takes advantage of multivariate notation, and the questions of interest are formulated as profile analysis problems. Finite performance of the proposed procedures is examined in a simulation study, and application is demonstrated using data from a series of crop variety trials.

Suggested Citation

  • Bathke, Arne C. & Harrar, Solomon W. & Wang, Haiyan & Zhang, Ke & Piepho, Hans-Peter, 2010. "Series of randomized complete block experiments with non-normal data," Computational Statistics & Data Analysis, Elsevier, vol. 54(7), pages 1840-1857, July.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:7:p:1840-1857
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    References listed on IDEAS

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    1. Bathke, Arne C. & Harrar, Solomon W. & Madden, Laurence V., 2008. "How to compare small multivariate samples using nonparametric tests," Computational Statistics & Data Analysis, Elsevier, vol. 52(11), pages 4951-4965, July.
    2. Boos, Dennis D. & Brownie, Cavell, 1995. "ANOVA and rank tests when the number of treatments is large," Statistics & Probability Letters, Elsevier, vol. 23(2), pages 183-191, May.
    3. T. Caliński & S. Czajka & Z. Kaczmarek & P. Krajewski & W. Pilarczyk, 2005. "Analyzing Multi-environment Variety Trials Using Randomization-Derived Mixed Models," Biometrics, The International Biometric Society, vol. 61(2), pages 448-455, June.
    4. Gupta, Arjun K. & Harrar, Solomon W. & Fujikoshi, Yasunori, 2006. "Asymptotics for testing hypothesis in some multivariate variance components model under non-normality," Journal of Multivariate Analysis, Elsevier, vol. 97(1), pages 148-178, January.
    5. Harrar, Solomon W. & Bathke, Arne C., 2008. "Nonparametric methods for unbalanced multivariate data and many factor levels," Journal of Multivariate Analysis, Elsevier, vol. 99(8), pages 1635-1664, September.
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    Cited by:

    1. Harrar, Solomon W. & Kong, Xiaoli, 2016. "High-dimensional multivariate repeated measures analysis with unequal covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 1-21.
    2. Johannes Forkman, 2013. "The use of a reference variety for comparisons in incomplete series of crop variety trials," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(12), pages 2681-2698, December.

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