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Kristian Kristensen, Federica Bigongiali and Hanne Østergård IAMFE Denmark 2008

Efficiency of incomplete split-plot designs A compromise between traditional split-plot designs and randomised complete block design. Kristian Kristensen, Federica Bigongiali and Hanne Østergård IAMFE Denmark 2008 Koldkærgård, June 30 th to July 3 rd 2008. Outline. Introduction

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Kristian Kristensen, Federica Bigongiali and Hanne Østergård IAMFE Denmark 2008

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  1. Efficiency of incomplete split-plot designs A compromise between traditional split-plot designs and randomised complete block design Kristian Kristensen, Federica Bigongiali and Hanne Østergård IAMFE Denmark 2008 Koldkærgård, June 30th to July 3rd 2008

  2. Outline • Introduction • What is an incomplete split-plot • Compared to traditional split-plot and randomised complete block design • Performed experiments • Efficiency of incomplete split-plot designs • Compared to traditional split-plot and randomised complete block design • Discussion and conclusions

  3. Introduction • Example of trial to be performed • 2-factorial design • Treatment factor 1 with few levels (e.g. ± Herbicides) • Treatment factor 2 with many levels (e.g. a large number of varieties) • Some possible designs • Split-plot • Randomised complete block designs • Incomplete split-plot

  4. Introduction • Split-plot • Very convenient • Easy to apply herbicides to many plots in one run • Needs only guard area around each whole-plot • Inefficient comparison of treatments • Herbicides: few and large whole plots, large replicates and thus large distance between whole plots • Varieties: large whole plots and thus large distance between some sub-plots

  5. Introduction • Randomised complete block • Inconvenient • Difficult to apply herbicides to each individual plot • May need guard area around each plot • Efficiency of treatment comparisons • Herbicides: many whole plots increase efficiency but large replicates and thus large distance between most plots decrease efficiency • Varieties: large replicates and thus large distance between most plots decrease efficiency

  6. What is an incomplete split-plotSmall example: ±Herbicide, 9 varieties

  7. What is an incomplete split-plot • Incomplete split-plot • Practical compromise • Easier than RCB, more difficult than split-plot • May require guard-area around each pair (group) of incomplete blocks • Efficiency • Herbicides: several whole plots, comparison within pair (group) of incomplete block and thus moderate distance between incomplete “whole-plots”: More efficient than split-plot • Varieties: few plots within each incomplete “whole plot” and thus small distance between sub-plots: More efficient that RCB and split-plot

  8. Incomplete split-plot • Construction • Can be based on different types of incomplete block designs • We choosed to use to use -designs (generalised lattice) • -designs • Are resolvable • Are available for almost any number of varieties and replicates in combination with a broad range of block sizes

  9. Performed experiments Trial A-D: From the project “Characteristics of spring barley varieties for organic farming (BAR-OF)“ Trial E: From the project “Screening of the potential competitive ability of a mixture of winter wheat cultivar against weeds”

  10. Performed experiments, trial A Each plot is 1.5 m × 11.0 m Each block is 12.0 m × 11.0 m

  11. Performed experiments, trial E Each plot is 2.5 m × 12.5 m Each block is 10.0 m × 12.5 m

  12. Measure of efficiency • Depends on the comparisons of interest

  13. Efficiency of the designs,Yield

  14. Efficiency of the designs,%Mildew

  15. Efficiency of the designs,other variables

  16. Discussion and conclusions • Efficiency • Compared to randomised complete block design • Incomplete split-plot were most often less efficient when comparing the main effect of treatments • Larger number of independent plots/smaller blocks • Incomplete split-plot most often more efficient for other comparisons • Compared to traditional split-plot • Incomplete split-plot were most often more efficient for all types of comparisons • Especially for comparing treatment means (many more degrees of freedom and smaller blocks)

  17. Discussion and conclusions • Increase in efficiency • In most cases larger for grain yield than for mildew • Probably because mildew is less sensible to soil fertility • Small for trial E when comparing mean of varieties and varieties within treatment • Relative small reduction in block sizes • Small for trial B when comparing mean of varieties and varieties within treatment • Reason unknown

  18. Discussion and conclusions • Practical considerations • Treatment applications • Easier than randomised complete block design • More difficult than split-plot design • Guard areas • Less than for randomised complete block design • More than for split-plot design • Design and statistical analysis • More complex than both randomised complete block design and split-plot design • Appropriate software are available and with today's computer power this should not be a problem

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