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