Agriculture Reference
In-Depth Information
(a)
Four Replicates ~ No Blocking
Factorial design
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1
L.2
T.3
L.3
T.3
L.3
T.2
L.3
T.1
L.1
T.1
L.4
T.1
L.1
T.3
L.2
T.1
L.1
T.2
L.4
T.3
L.2
T.2
L.4
T.2
L.2
T.3
L.3
T.2
L.2
T.1
L.4
T.1
L.2
T.2
L.3
T.3
L.1
T.1
L.4
T.1
L.1
T.3
L.4
T.3
L.1
T.2
L.3
T.1
Split-plot design
Main-plots
(b)
Four Replicates ~ Blocking
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Sub-plots
Figure 9.3
Completely randomized block design (top)
and randomized complete block design (bottom).
Figure 9.4
Multiple factor factorial design (top) and
split-plot design (bottom).
Randomized complete block designs
Although there are often merits in choosing a com-
pletely randomized design, a more common design
(probably the most common design) used by plant
breeders is a randomized complete block. In these
designs, the total area of the field tests is divided into
units according to the number of required replicates.
Each unit is called a block. Each of the test and con-
trol entries are randomly assigned plot positions within
each block (Figure 9.3 (b)). In the cases where there are
distinct fertility gradients or other differences between
blocks, then these can be estimated and subtracted from
the error variance. It is possible therefore, to obtain a
more accurate estimate of the error variance. Blocking
does not necessarily need to be different areas within a
field trial. Different blocks in a randomized complete
block design could, for example, be different days of
testing (where it is not possible to test all replicates in a
single day).
two-dimension designs. In many cases it is important to
simultaneously evaluate a number of breeding lines with
regard to their response to different treatments. These
types of experimental designs are called multidimen-
sional designs or
factorial designs
. To illustrate factorial
designs consider the example where there are only four
breeding lines to be tested (L.1
···
L.4) and the perfor-
mance of each is to be evaluated under three different
treatments, or factors (T.1
T.3). Each genotype
entry is grown with each of the different treatments.
Overall, there are therefore 4
···
12 entries. These
are arranged at random as illustrated in Figure 9.4 (a).
In the example only two replicates are illustrated. In
practice more than two plots of each test unit would be
grown to ensure the necessary level of replication. Repli-
cated factorial designs can be completely randomized or
each replicate can be blocked.
Analysis of factorial designs allows estimates of dif-
ferences between test entries and between treatments
compared to an estimated error. These designs also allow
evaluation of any
interaction
, which may exist between
test entries and treatments. To illustrate consider the
performance of two test lines (A and B) each evaluated
×
3
=
Factorial designs
Single replicate designs are often referred to as single
dimension designs and randomized designs are called
