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
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
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