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

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

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-plot Small example: ±Herbicide, 9 varieties

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

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