The document describes three experimental designs: Complete Randomized Design (CRD), Randomized Block Design (RBD), and Latin Square Design (LSD). CRD randomly assigns treatments to experimental units and is best for homogeneous materials like lab experiments. RBD divides the field into homogeneous blocks to control local variability and is more precise than CRD. LSD arranges treatments in a square layout with equal rows and columns to control variability in two directions and is more efficient than RBD for a limited number of treatments.

3. COMPLETE RANDOMIZED DESIGN (CRD)
 Where the treatments are assigned completely at random so that each
treatment units has the same chance of receiving any one treatment.
 This is suitable for only the experiment material is homogenous.(ex:
laboratory experiments, green house studies etc.)
 Not suitable for heterogenous study. (ex: field experiments)
Advantages :
 Simple and easy.
 Provides maximum number of degrees of freedom.
Disadvantages :
 Less accurate than other designs.
 Heterogeneity of experimental material will be increased.
 Increased experimental error and reduce precision.
Source: R Rangaswamy. A Textbook of Agricultural Statistics (Second Edition)

4. RANDOMIZED BLOCK DESIGN (RBD) OR
RANDOMIZED COMPLETE BLOCK DESIGN (RCBD)
 Most widely used experimental designs in agricultural research.
 Experimental materials is grouped in to homogenous sub groups. The
sub groups is commonly termed as block. Since each block will consists
the entire set of treatments, a block is equivalent to a replication.(ex:
field experiments)
Advantages :
 More efficient than CRD.
 The statistical analysis is simple and easy.
 Reduced experimental error and increase precision.
Disadvantages :
 Not suitable for large number of treatments.
 It is a versatile design.
Source: R Rangaswamy. A Textbook of Agricultural Statistics (Second Edition)

5. LATIN SQUARE DESIGN (LSD)
 A Latin square experiment is assumed to be a three factor experiment.
The factors are rows, columns and treatments.
 It is assumed that there is no interaction between rows, columns and
treatments.(rows = columns = treatments)
 It is differ from randomized block designs in the experimental units are
grouped in blocks in two different ways, i.e. by rows and columns.
Advantages :
 LSD is more efficient than RBD and CRD.
 The experimental error is small compared than other deigns.
 Analysis is simple even with missing plots.
Disadvantages:
 Number of treatments is limited to the number of replicates which
seldom exceeds 12.
 If have less than 5 treatments, the df for controlling random variation is
relatively large and the df for error is small.
Source: R Rangaswamy. A Textbook of Agricultural Statistics (Second Edition)

6. LAYOUT OF CRD
Treatments = N P K
N = 4 level
P = 3 level
K = 5 level
ANOVA MODEL FOR CRD:-
Sources of
variation
df SS MS F
Treatments t - 1 TSS TMS = TSS/ t-1 TSS/ EMS
Error n - t ESS EMS= ESS/n-t
Total n - 1 Total SS
Source: R Rangaswamy. A Textbook of Agricultural Statistics (Second Edition)
N K P N
P K N K
K N P K

7. LAYOUT OF RBD
 Treatments = 4
 Replications = 3
ANOVA FOR RBD :-
Sources of
variation
df SS MS F
Replication r – 1 RSS RMS RMS/ EMS
Treatment t – 1 TSS TMS TMS/EMS
Error (r-1)(t-1) ESS EMS
Total rt - 1 Total SS
Source: R Rangaswamy. A Textbook of Agricultural Statistics (Second Edition)
Block 1 Block 2 Block 3
B A C
A B D
C C B
D D A

8. LAYOUT OF LSD
ANOVA FOR LSD :-
A B C D E
B A E C D
C D A E B
D E B A C
E C D B A
Source of variation df SS MS F
Rows t - 1 RSS RMS RMS/EMS
Columns t - 1 CSS CMS CMS/EMS
Treatments t - 1 TSS TMS TMS/EMS
Error (t-1)(t-2) ESS EMS
Total t2 - 1 Total SS
Source: R Rangaswamy. A Textbook of Agricultural Statistics (Second Edition)

10. Criteria CRD RBD LSD
1. Condition
of use:
2. Layout:
3.
Replications:
a. The use of amount
of experimental
material to be tested
and nature of the
fertility variation of
the field.
b. The whole field is
divided directly into
plots is equal size
(product of
replications =
treatments).
c. Differ from
treatment to treatment
(4 to 5 replications are
sufficient).
a. The use of fertility
variation moves in one
direction.
b. The field is divided
into homogenous (plots
= number of
treatments).
c. Differ from
treatment to treatment
(4 to 5 replications are
sufficient).
a. The use of fertility
variation move in
two direction.
b. The field is
divided into equal
number of rows and
columns ( number of
rows and columns =
number of
treatments).
c. Number of
replication = number
of treatments ( 5 to
12 replications are
sufficient).

11. Criteria CRD RBD LSD
4.
Randomization:
5. Local control:
6. Analysis:
7. Components
of variation :
d. In this case
treatment wise.
e. Not adopted.
f. Easy and simple.
g. Total variation
is divided into two
components
(treatment and
error).
d. Replication or
block-wise.
e. Adopted by
homogenous blocks.
f. Analysis is easy but
it becomes complicated
when missing plot
technique is applied.
g. Total variation is
divided into three
components (blocks,
treatments and error).
d. Rows, columns and
treatments are
reshuffled with the
help of random
number.
e. Adopted by
homogenous blocks.
f. Analysis is simple
but it becomes
complicated when
several plot yield are
missing.
g. Total variation is
divided into four
groups ( rows,
columns, treatments
and error).