1. A A R H U S U N I V E R S I T E T Faculty of Agricultural Sciences 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

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-plot Small 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