Agriculture Reference
In-Depth Information
Slide 10.23: Step 2 showing a portion of output for RBD analysis using SAS
experiment. This makes the LSD design's appli-
cability limited in field experimentations. The
number of treatments in LSD design should gen-
erally lie in between four and eight. All these
limitations have resulted in the limited use of
Latin square design in spite of its high potential-
ity for controlling experimental errors.
Analysis
Let there be
10.9
Latin Square Design (LSD)
LSD is a design in which known sources of
variation in two perpendicular directions, that
is, north to south and east to west or south to
north and west to east, could be taken into con-
sideration. In this type of field, we require fram-
ing of blocks into perpendicular directions which
take care of the heterogeneity in both directions.
A Latin square is an arrangement of treatments
in such a way that each treatment occurs once
and only once in each row and each column.
If
t
treatments, so there should be
t
t t
experimental units. The appropriate statistical
model for the analysis of the information from a
t t
rows and
t
columns. So we need a field of
LSD can be given as follows:
is the number of treatments, then the total
number of experimental units needed for this
design is
t
y
ijk
¼ μ þ α
i
þ β
j
þ υ
k
þ e
ijk
; i ¼ j ¼ k ¼ t
2
units are arranged in
t t
. These
t
Where
μ ¼
t
columns. This type of experiments
is rare in laboratory condition but can be
conducted or useful in field conditions or green-
house conditions. The two perpendicular sources
of variations in greenhouse may be the difference
among the rows of the plot and their distances
from the greenhouses.
So while selecting an LSD design, an experi-
menter faces two problems: how to maintain the
minimum replication and how to accommodate
the maximum number of
rows and
t
general effect
α
i
¼
additional effect due to the
i
th treatment
and
P
α
i
¼
0
β
j
¼
additional effect due to the
j
th row and
P
r
j
¼
0
υ
k
¼
additional effect due to the
k
th treatment
and
P
c
k
¼
0
e
ijk
¼
errors that are associated with the
i
th treat-
ment in the
j
th row and the
k
th column and are
2
)
i.i.d.
N
(0,
σ
treatments in the
