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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 2008Koldkærgård, June 30th to July 3rd 2008
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
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
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
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
What is an incomplete split-plotSmall example: ±Herbicide, 9 varieties
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
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
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”
Performed experiments, trial A
Each plot is
1.5 m × 11.0 m
Each block is
12.0 m × 11.0 m
Performed experiments, trial E
Each plot is
2.5 m × 12.5 m
Each block is
10.0 m × 12.5 m
Measure of efficiency
Depends on the comparisons of interest
Efficiency of the designs,Yield
Efficiency of the designs,%Mildew
Efficiency of the designs,other variables
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)
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
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