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1. Experimental design
Presentation by
Seth Koomson
( MPhil. Part II ) 1

2. INTRODUCTION
Research is a planned investigation into a subject to discover new facts, or
establish, confirm, or revise existing information or theories.
the results of research are used to develop a plan of action based on the
facts discovered in the research.
 For example, research is the basis for recommending new technologies to
farmers.
 In government, it is useful in policy formulation, and national development
depends a whole lot on research findings.
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3. FIELD EXPERIMENTATION
 To enhance the proper understanding of the materials presented here,
basic definitions, concepts, and steps in field experimentation are first
discussed briefly
Experimental unit–the lowest level or smallest subdivision of the
experiment to which independent application of the treatment is made.
Examples in agriculture3 research are plot, pot, and soil samples.
Experimental design–the plan for grouping experimental units and
assigning them to treatments.
Experimental factor–an external item or variable under investigation.
A factor of an experiment is a controlled independent variable, a
variable whose levels are set by the experimenter. Examples are
variety, fertilizer, and planting density.
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4. FIELD EXPERIMENTATION CONTD.
Experimental treatment–magnitude of external factors imposed by the
researcher; usually with two or more levels or rates. In research, a
treatment is something that researchers administer to experimental
units.
 A factor is a general type of treatments. Different treatments
constitute different levels For example, in a study evaluating the
response of five maize varieties to four levels of zinc fertilizer, variety
and fertilizer are factors while the different varieties and fertilizer rates
are treatments. Experimental units contain the treatments.
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5. FIELD EXPERIMENTATION CONTD.
Randomization is the process by which experimental units are
allocated to treatments. The treatments are allocated to units in such a
way that each treatment is equally likely to be applied to each unit.
Replication means repetition, another copy, to look (exactly) alike. It
is the number of times a treatment appears in an experiment.
Population A population may be defined as all possible individuals in
a specified situation. The individuals have one or more characteristics
in common. A population could be homogeneous or heterogeneous.
Thus, we could have a population of maize clearly distinct from other
maize populations.
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6. FIELD EXPERIMENTATION CONTD.
Sample–part of a population drawn to represent the whole population.
In practice, a sample could be obtained at random by a process
referred to as probability sampling. Samples could also be non-random
or fixed.
Variable–a characteristic of a sample or population whose value is not
the same from one individual to another in the population or sample.
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7. EXPERIMENTAL DESIGNS
The commonly used designs in agriculture research are as follows.
1. Completely Randomized Design (CRD)
2. Randomized Complete Block Design (RCBD)
3. RCBD with factorial arrangement (also known as Factorial Design)
4. Split-plot and
5.Split Split-plot Designs
6. Strip Plot design.
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8. COMPLETE RANDOMIZED
DESIGN(CRD)
The structure of the experiment in a completely randomized design is
assumed to be such that the treatments are allocated to the
experimental units completely at random but not haphazardly.
 In other words, the treatments are assigned to experimental units
without restriction on randomization
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9. COMPLETE RANDOMIZED
DESIGN(CRD)
Following is the CRD layout of an experiment with four treatments a,
b, c, d replicated three times each.
The numbers refer to plots or experimental units. Note that the
treatments are not in any particular order or grouping.
1a 2d 3b 4c
5b 6a 7c 8d
9d 10b 11a 12c
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12. ADVANTAGES OF CRD
1. Flexibility.
2. Number of replications need not be equal for all treatments.
3. A missing plot may be disregarded without any adverse effect on
the analysis and results.
4. Statistical analysis is simple. A major disadvantage of CRD is that it
is very inefficient if plots are not homogeneous
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13. RANDOMIZED COMPLETE BLOCK
DESIGN(RCBD)
The randomized complete block design involves matching the subjects
according to a factor which the experimenter wishes to investigate.
The subjects are put into groups (or blocks) of the same size as the number
of treatments making up the factor. In other words, a block contains as
many experimental units or plots as the number of treatments.
The treatments are then randomly assigned to the different experimental
units within the block.
Blocking may then be defined as the procedure by which experimental units
are grouped into homogeneous clusters in an attempt to improve the
comparison of treatments by randomly allocating the treatments within each
cluster or ‘block’.
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14. RANDOMIZED COMPLETE BLOCK
DESIGN(RCBD)
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17. ADVANTAGES OF RCBD
1.Each block contains all the treatments and is, therefore, the same size as all other
blocks in the experiment (hence the name “complete block”).
2.The number of blocks is the same as the number of replications;
3.Treatments are randomized within each block independently of other blocks.
4.All units (plots) within the same block are handled in the same manner except for
the treatments applied.
5.In the analysis, treatment effects are assumed to be independent of block effects;
therefore, the two can be cleanly isolated in the analysis.
6.Variability within each block is minimized while that among blocks is maximized.
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18. ADVANTAGES OF RCBD
The real advantage of RCBD is evident in situations where the field
for the trial is heterogeneous for factors such as soil fertility and slope.
Where the soil is homogeneous and relatively uniform in flatness,
RCBD may have little or no advantage over CRD
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19. RANDOMIZED COMPLETE BLOCK DESIGN WITH
FACTORIALARRANGEMENT (OR FACTORIAL DESIGN)
This design is used to evaluate two or more factors simultaneously.
The treatments are combinations of levels of the factors.
The advantages of factorial designs over experiments containing one
factor at a time are that they are more efficient and they allow
interactions to be detected.
In the analysis of data from this design, three sources of variation may
be obtained in addition to block and residual (error) effects.
These are variations due to factor A, to factor B (both of which are
referred to as main effects) and the interactions of factor A with factor
B, which are referred to as interaction effects.
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20. RANDOMIZED COMPLETE BLOCK DESIGN
WITH FACTORIALARRANGEMENT (OR
FACTORIAL DESIGN)
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22. SPLIT-PLOT DESIGNS
Split-plot design involves introducing a second factor into an experiment by
dividing the large experimental units (whole unit or whole plot) for the first
factor into smaller experimental units (sub-units or sub-plots) on which the
different levels of the second factor will be applied. Each whole unit is a
complete replicate of all the levels of the second factor (RCBD).
The whole unit design may be CRD or RCBD. Randomization–The first
factor levels are randomly assigned to the whole plots according to the rules
for the whole plot design (i.e., CRD or RCBD). Similarly, the second factor
levels are randomly assigned to sub-plots within each whole plot according
to the rules of an RCBD.
The name of the split-plot design is prefixed with the design name
associated with the whole plot design; for example, Randomized Complete
Block Split-Plot Design. The design for the sub-plot is, by definition,
always RCBD.
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23. SPLIT-PLOT DESIGNS
N1 V1 V2 V4 V3
N3 V3 V2 V4 V1
N4 V1 V4 V2 V3
N2 V2 V1 V3 V4
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24. SPLIT-PLOT DESIGNS
• Other replications are the same except that a new randomization is
done for each replication.
•
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25. SPLIT-SPLIT PLOT DESIGN
The Split-split plot design is an extension of the Split-plot design to
accommodate a third factor.
Levels of the third factor are randomized and assigned to sub-
divisions of the sub-plot, which are referred to as sub-sub plots.
 Example with a third factor, micronutrient fertilizer at two levels, M1
and M2, may now be laid out in a Split-split plot design as shown in
the following diagram for one replication:
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26. SPLIT-SPLIT PLOT DESIGN
N1 V1M1 V2M2 V4M2 V3M1
V1M2 V2M1 V4M1 V3M2
N3 V3M2 V2M2 V4M1 V1M1
V3M1 V2M1 V4M2 V1M2
N4 V1M2 V4M1 V2M2 V3M1
V1M1 V4M2 V2M1 V3M2
N2 V2M2 V1M1 V3M2 V4M1
V2M1 V1M2 V3M1 V4M2
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27. STRIP PLOT DESIGN
A strip plot design, also known as a split-block design, is used in
agricultural research when there are two factors in an experiment and
both factors require large plot sizes, making it difficult to carry out
the experiment in a split-plot design.
This design is suitable when the precision for measuring the
interaction effect between the two factors is higher than that for
measuring the main effect of either one of the two factors.
In a strip plot design, each block or replication is divided into a
number of vertical and horizontal strips depending on the levels of
the respective factors.
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28. STRIP PLOT DESIGN
The vertical strip plot is for the first factor, the horizontal strip plot is
for the second factor, and the interaction plot is for the interaction
between the two factors.
The vertical and horizontal strips are always perpendicular to each
other, and the interaction plot is the smallest and provides information
on the interaction of the two factors.
The analysis of a strip plot design is carried out in three stages:
horizontal strip analysis, vertical strip analysis, and interaction
analysis.
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29. STRIP PLOT DESIGN
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