Agriculture Reference
In-Depth Information
to work correctly. They were left in to emphasize the fact that the
design is incomplete. The chamber variable also is not required for
the calculations and just indicates that there were only three growth
chambers available.
With previously discussed models, it was possible to calculate a
relative efficiency of a more complex design to a simpler design. Such
comparisons with BIB designs are not directly possible because the
designs are incomplete. If the number of treatments and replications
is the same, however, between the BIB and RCBD, then the ratio of
the variances of the difference between two treatment means for the
RCBD and BIB is an indication of efficiency.
(
)
2
2
σ
σλ
r
2
σ
σ
· λ t
rk
rcb
rcb
Efficiency
=
) =
(
2
2
2
k
t
bib
bib
Assuming the variances between the RCBD and BIB designs are
the same, then
λ
t
rk
E
=
and indicates the loss in efficiency by using the BIB design relative to
the RCBD. For example, an experiment with six treatments and five
replications and four experimental units would have t = 6, r = 5 for the
RCBD and t = 6, r = 5, k = 4, λ = 3 for the BIB, which would result
in E = 0.9. This means the amount the BIB variance would have to
be reduced relative to the RCBD design would be about 10% for the
same efficiency.
Balanced Lattice Designs
As the number of treatments increases, there is a concomitant increase
in the size of blocks. This can lead to blocks that are not very uniform
for treatment conditions. From one side of a field to the other, as these
distances increase, the chance for conditions in soil type, moisture,
fertility, etc., to change increases. Balanced lattice designs address this
problem with blocks of relatively small size and increasing the num-
ber of replications as the number of treatments increases. This can
 
Search WWH ::




Custom Search