PDF FULL TEXT - World Agroforestry Centre

178 Pages·2002·1.77 MB·English

Data analysis of agroforestry experiments
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by Lecture notes
Richard Coe
Roger Stern
Eleanore Allan
edited by
Jan Beniest
Janet Awimbo
The World Agroforestry Centre (ICRAF) is the international leader in Agroforestry – the
science and practice of integrating ‘working trees’ on smallholder farms and in rural landscapes.
Agroforestry is an effective and innovative means to reduce poverty, create food security, and
improve the environment. The Centre and its many partners provide improved, high quality
tree seeds and seedlings, and the knowledge needed to use them effectively. We combine excellence
in scientific research and development to address poverty, hunger and environmental needs
through collaborative programs and partnerships that transform lives and landscapes, both
locally and globally.
© World Agroforestry Centre 2002
ISBN 92 9059 145 5
ICRAF
The World Agroforestry Centre
United Nations Avenue
PO Box 30677
Nairobi, Kenya
Tel: + 254 2 524 000
Fax: + 254 2 524 001
Contact via the USA
Tel: + 1 650 833 6645
Fax: + 1 650 833 6646
E-mail: [email protected]
Internet: www.worldagroforestrycentre.org
Design: Mariska Koornneef
Printed by: Kul Graphics Ltd, Nairobi, Kenya
Table of contents
Session 1. Review of experimental design 5
Session 2. Objectives and steps in data analysis 13
Session 3. Software familiarization 19
Session 4. Descriptive analysis and data exploration 25
Session 5. Analysis of variance as a descriptive tool 43
Session 6. Ideas of simple inference 53
Session 7. An introduction to statistical modelling 63
Session 8. An introduction to multiple levels 81
Session 9. Writing up and presenting results 91
Session 10. Where are we now?- Review of basic statistics 95
Session 11. Design and analysis complexity 97
Session 12. Dealing with categorical data 119
Session 13. Getting more out of on-farm trials and multilevel problems 135
Session 14. Complications in agroforestry trials 153
Session 15. Complications in data 163
Session 16. Data analysis 173

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R. Coe, R. D. Stern, E. Allan
Introduction
It is necessary to understand both the design of a trial, and some of the ideas behind the
design, before attempting to analyse the data. This session provides a brief review of these
design ideas.
The key element in the design of a trial is the ‘Statement of Trial Objectives’. We will use
this session to show that the objectives of the trial determine the treatments to be applied in the e
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experiment, as well as the measurements that are to be taken. Satisfying these objectives will n
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also require an appropriate layout of the plots (or other units) in the experiment. In the remaining u
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sessions we will often breakdown a trial into its component parts of treatments, layout and e
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measurements.
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Later, in Session 2, we will use these overall objectives of the trial to construct the objectives
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of the analysis. The idea that the analysis of the data must be able to satisfy the objectives of the si
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trial is the dominant theme of this whole course.
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Objectives eri
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Objectives drive the whole of the design of any experiment. For this reason the design o
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process has to start by determining objectives. vi
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The objectives for a trial must be:
(cid:123) Clear. If the objectives are vague it will not be possible to decide on the rest of the design.
(cid:123) Complete. Often the statement of objectives is incomplete so that when designing the
experiment many questions can not be answered.
Example
An example of an incomplete objective statement would be something like:
“To evaluate the effectiveness of improved fallows for restoring soil fertility”.
A trial cannot be designed until the objective is completed with such details as:
(cid:122) Where is the evaluation needed? Over what range of environmental
conditions?
(cid:122) What range of ‘improvements’ need to be evaluated?
(cid:122) What are the criteria for evaluation? Whose criteria are these?
Over what time scale?
A more complete statement of objectives might be something like:
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ur “ Planted fallows, using Sesbania sesban seedlings, planted at 1m x 1m and grown
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e for two years before clearing (removing wood and incorporating other biomass)
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have improved maize yields, compared to those obtained following a two-year
66 natural fallow in on-station trials in E. Zambia. Now we wish to carry out a trial to
determine:
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d (cid:122) Grain yield increase (relative to natural fallows) in the first, second and third
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t cropping season achieved using this technology on degraded (i.e. about to
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m be put into fallow) clay and sandy soil maize fields in Eastern province of
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f (cid:122) Change in soil organic matter and N pools (compared to natural fallow) at
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the end of the improved fallow and after 1, 2 and 3 following maize crops.”
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(cid:123) Relevant. In the area of development research, experiments are carried out to help solve
development problems. The objectives of the experiment must be relevant to solving the
problem. It must be clear how we will be a step nearer solving the problem once we have
the results from the experiment.
(cid:123) Capable of being met by an experiment. Not every research question needs an experiment.
Treatments
The objectives will determine the treatments or conditions to be compared. The key
concepts that will determine the choice of treatments are:
(cid:123)(cid:123)(cid:123)(cid:123)(cid:123) Contrast or comparison between treatments
Many objectives simply require the comparison of the mean results of two treatments.
In certain cases, more complex comparisons are needed. In general, each hypothesis corresponds
to a contrast. The hypothesis or question determines the contrast and the contrast determines
the treatments that will be incorporated in the experiment and not the reverse, as often happens.
For example, a trial is conducted to determine whether farmers find the addition of
mulch from hedgerow species a useful addition to the management of fertility in vegetable plots,
and if so, which of two common hedgerow species (Lantana or Tithonia) is superior. The first
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objective requires a contrast ‘mulch vs no mulch’. The second requires a contrast ‘Lantana vs ot
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Tithonia’. Together these define three treatments which are; e
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1. Lantana mulch,
2. Tithonia mulch, 77
3. no mulch.
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(cid:123)(cid:123)(cid:123)(cid:123)(cid:123) Controls e
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Very often, treatments require some sort of standard against which they can be compared. en
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Choice of these control treatments is determined by the experimental objectives. Control does eri
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not necessarily mean zero input or do nothing or use farmer practices. Any of these might be x
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useful for certain objectives, but others may be equally or more appropriate. o
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The Tithonia and Lantana mulch example refers to ‘mulch as addition to management of R
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fertility’, meaning the appropriate control, should be whatever the farmer usually does.
(cid:123)(cid:123)(cid:123)(cid:123)(cid:123) Factorial treatment structure
Factorial treatments refer to sets of treatments defined by the combination of two or
more treatment factors, each with two or more levels.
For example, in a fodderbank trial, two cutting heights combined with three plant
densities gives a total of six treatments.
Such sets of treatments often arise naturally from the proposed hypotheses but they can
also be used to test several unrelated hypotheses in the same experiment more efficiently than in
separate ones. Understanding factorial structure and the idea of interaction can further suggest
other hypotheses that should be tested.
Complications may arise if:
(cid:123) not all factorial combinations are distinct or can be included (they may not be possible),
(cid:123) control treatments have to be included in addition to a factorial set,
(cid:123) the total number of treatments will be too large if all possible combinations are included
in the experiment.
(cid:123)(cid:123)(cid:123)(cid:123)(cid:123) Quantitative factors
When treatment factors are quantitative (e.g. amount of manure, tree density), the aspects
e to be decided are the range of levels, the number of different levels, the spacing of the levels and
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the replication at each level. There are many options in the choice of levels when two or more
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tu quantitative factors are involved. The choice of levels is not usually defined by objectives that
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88 Layout
The layout of the trial describes both the ‘objects’ (plots) of the experiment and the way
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si the treatments are allocated to them. In agroforestry experiments the basic ‘objects’ or units are
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al usually plots of land. However the same ideas apply to other types of experiments, such as those
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ex When describing experiments on plots of land there is a hierarchy in the layout. At the
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top level are the sites where the trial is conducted. There might be one or several. A single site
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farm is a site, and they may be grouped according to criteria relevant to the objectives.
Within sites there will often be known (or suspected) patterns of variation that define
blocks. The size and shape of the blocks should be determined by the variation expected.
Within each block will be a number of plots. The layout of a single plot (its size, shape,
position of trees and crops within it, the size of guard areas and so on) will depend on objectives
and practical considerations of conducting the trial.