a a r h u s u n i v e r s i t e t faculty of agricultural sciences efficiency of incomplete...
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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
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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
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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
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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
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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
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What is an incomplete split-plotSmall example: ±Herbicide, 9 varieties
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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
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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
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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”
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Performed experiments, trial A
Each plot is
1.5 m × 11.0 m
Each block is
12.0 m × 11.0 m
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Performed experiments, trial E
Each plot is
2.5 m × 12.5 m
Each block is
10.0 m × 12.5 m
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Measure of efficiency
Depends on the comparisons of interest
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Efficiency of the designs,Yield
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Efficiency of the designs,%Mildew
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Efficiency of the designs,other variables
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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)
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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
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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