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Inter-block information: to recover or not to recover it?

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Abstract

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Comparing standard errors of treatment differences using fixed or random block effects with the approximation of Kackar and Harville helps in choosing the preferable assumption for blocks in the analysis of field experiments.

Abstract

Blocked designs are common in plant breeding field trials. Depending on the precision of variance estimates, recovery of inter-block information via random block effects may be worthwhile. A challenge in practice is to decide when recovery of information should be pursued. To investigate this question, a series of sugar beet trials laid out as α-designs were analysed assuming fixed or random block effects. Additionally, small trials laid out as α-designs or partially replicated designs were simulated and analysed assuming fixed or random block effects. Nine decision rules, including the Kackar–Harville adjustment, were used for choosing the better assumption regarding the block effects. In general, use of the Kackar–Harville adjustment works well and is recommended for partially replicated designs. For α-designs, using inter-block information is preferable for designs with four or more blocks.

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Acknowledgments

JM and HPP were supported by DFG grant PI 377/13-1. Strube Research is thanked for providing their dataset. We thank two anonymous reviewers for their helpful hints, which enhanced the quality of this paper.

Conflict of interest

The authors declare that they have no conflict of interest.

Author information

Authors and Affiliations

  1. Biostatistics Unit, Institute for Crop Science, University of Hohenheim, Stuttgart, Germany

    Jens Möhring & Hans-Peter Piepho

  2. Statistical Consulting Unit, School of Mathematical Sciences (MSI), The Australian National University, Canberra, ACT, 0200, Australia

    Emlyn Williams

Authors
  1. Jens Möhring
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  2. Emlyn Williams
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  3. Hans-Peter Piepho
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Corresponding author

Correspondence to Hans-Peter Piepho.

Additional information

Communicated by M. Bink.

Appendix

Appendix

See Tables 9, 10, 11, 12 and 13.

Table 9 Probability of selecting the better model for nine decision rules and scenario 3 (varying number of plots per block) depending on the value of the block variance estimate (zero or positive)
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Table 10 Probability of selecting intra-block analysis for nine decision rules and scenario 3 (varying number of plots per block) depending on the value of the block variance estimate (zero or positive)
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Table 11 Probability of selecting intra-block analysis for nine decision rules and scenario 4 (varying block-to-error variance ratio) depending on the value of the block variance estimate (zero or positive)
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Table 12 MSED for nine decision rules and scenario 4 (varying block-to-error variance ratio) depending on the value of the block variance estimate (zero or positive)
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Table 13 MSED for using different number of blocks and block sizes with a fixed number of treatments (scenario 5) depending on the value of the block variance estimate (zero or positive)
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Möhring, J., Williams, E. & Piepho, HP. Inter-block information: to recover or not to recover it?. Theor Appl Genet 128, 1541–1554 (2015). https://doi.org/10.1007/s00122-015-2530-0

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  • DOI: https://doi.org/10.1007/s00122-015-2530-0

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