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## Variance-distance relationships in agricultural field plot experiments

Methods for examining how the errors of agricultural field plot experiments are related to the distances between plots are developed for a two-dimensional layout. Knowledge of the errors is useful for investigating the suitability of experimental designs and methods of analysis for various field situations. The methods of postblocking and pairblocking are extended to two dimensions to allow the calculation of error laws for the semi-variance of the difference in yields of plots <i>p</i> rows and <i>q</i> columns apart. The techniques are applied to results of past variety trials. The two dimensional version is applied to two UK trials series, while the one-dimensional version is applied to a tropical series of trials. The error laws derived, the exponential variance error laws, are used to improve recommendations for design and analysis of future trials. The classical method of analysis of the variety trials used is also described in this work and the efficiency of such analysis assessed. In particular, for row and column designs that have the property of adjusted orthogonality, the estimate of the ratio of the row stratum variance to the row x column stratum variance can be expressed as a function of the error mean squares from the analysis of the incomplete block column component design and row and column design. Similarly, the estimate of the ratio of the column stratum variance to the row x column stratum variance can also be expressed as a function of the error mean squares from the analysis of the incomplete block row component design and row and column design. Knowledge of the error variance law can be used to derive spatial methods of analysis for individual trials. The simplest first difference neighbour analysis, derived from the linear variance rule has row and column analysis without recovery of information as its simplest case when no trend effect is present.

Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:661746 |

Date | January 1992 |

Creators | Seraphin, Jose Carolos |

Publisher | University of Edinburgh |

Source Sets | Ethos UK |

Detected Language | English |

Type | Electronic Thesis or Dissertation |

Source | http://hdl.handle.net/1842/11382 |

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