The document discusses two types of classification designs used in experiments: the Randomized Complete Block Design (RCBD) and the Latin Square Design (LSD). The RCBD aims to control variation by grouping experimental units into blocks that can help improve precision, while the LSD further accounts for heterogeneity by using a two-dimensional blocking method. The document outlines the advantages, disadvantages, and randomization processes for both designs, providing examples of their application in agricultural and materials testing experiments.

1. TWO-WAY
CLASSIFICATION
DESIGNS

2. TWO CLASSIFICATION DESIGNS
Experimental units are markedly heterogenous with
respect to some criteria of classification, and
usually the differences among the eu’s is the major
source of experimental error. The design must
account for the heterogeneity. These design is the
RCBD and Latin Square.

3. THE RANDOMIZED COMPLETE BLOCK DESIGN
 One way of increasing precision of an experiment is by
proper grouping or blocking of the experimental units.
 The eu’s are grouped into blocks in such a way that the
differences between the units among different blocks are
greater than the differences between the units within each
block.
 Likewise the blocking should be done in such a way that the
blocks cut across or are perpendicular to the direction of
the eu’s gradient.
 This way, if there are differences among the blocks ,the
variability is removed from the experimental error thereby
improving the precision of the experiment.

4. RCBD
It is used to control variation in an experiment by
accounting for spatial effects in field or greenhouse.
e.g. variation in fertility or drainage
differences in a field
The field or space is divided into uniform units to
account for any variation so that observed
differences are largely due to true differences
between treat- ments. Treatments are then assigned
at random to the subjects in the blocks-once in
each block

5. RCBD
Advantages of the RCBD
 Generally more precise than the completely
randomized design (CRD).
 No restriction on the number of treatments
or replicates.
 Some treatments may be replicated more
times than others.
 Missing plots are easily estimated.

6. RCBD
Disadvantages of the RCBD
 Error degrees of freedom is smaller than
that for the CRD (problem with a small
number of treatments).
 Large variation between experimental
units within a block may result in a large
error term If there are missing data, a
RCBD experiment may be less efficient
than a CRD.

7. RCBD
Randomization and Layout
Suppose there are four treatments which are replicated
three times thus the total eu’s is 12. The randomization
procedure uses draw lots.
T = T1, T2 , T3, , T4
R = 3
Steps:
Eu = 12
1. Group the eu’s into r = 3 blocks
Block I Block
II
Block III

8. RCBD
2. Group the eu’s into r = 3
Block I Block II Block III
3. For each block, allocate the treatments into the eu’s at random
and independently of other blocks as follows:
a. Label the eu’s consecutively from 1 to t = 4
Block I
1
2
3
4
Block II
1
2
3
4
Block III
1
2
3
4

9. RCBD
b. Obtain a sequence of t = 4 numbers using draw lots
Block I
1 T3
2 T1
3 T4
4 T2
Block II
1 T2
2 T4
3 T3
4 T1
Block III
1 T2
2 T3
3 T1
4 T4
c. Using the sequence of draws as the treatment numbers as the
eu numbers assign the treatments to the respective eu’s.
Draw 1= T3 Draw 2= T1 Draw 3= T4 Draw 4= T2
Draw 5= T2 Draw 6= T4 Draw 7= T3 Draw 8= T1
Draw 9= T2 Draw 10= T3 Draw 11= T1 Draw 12= T4

10. RCBD
Sample Problem
1. An experiment was conducted to study the effects of four varieties
of mongo. The experiment was laid out in five farms. In each farm,
four uniform plots were chosen on which the four varieties were
randomly assigned. Make a lay out using the RCBD.
2. A hardness testing machine operates by pressing a tip into a metal
test “coupon.” The hardness of the coupon can be determined from
the depth of the resulting depression. Four tip types are being tested
to see if they produce significantly different readings. The
coupons might differ slightly in their hardness (for example, if
they are taken from ingots produced in different heats). Thus
coupon is a nuisance factor, which can be treated as a blocking
factor. Since coupons are large enough to test four tips on, a RCBD
can be used, with one coupon as a block. Four blocks were used.

11. R = 5 farms
T = 4 varieties of Mongo
EU = 20
V1
V3
V4
V2
V3
V1
V3
V1
V3
V1
V1
V3
F1 F2 F3 F4 F5

12. LATIN SQUARE DESIGN
 If the eu’s exhibit heterogeneity in two direction of
classification heterogeneity the two dimensional
blocking method is to be used- LSD.
 Also known as Complete Block Design, it is a two way
classification design. This is used when the
experimental unit can be grouped into two categories
(double blocking) such that the variations due to
each category are eliminated from the experimental
error.

13. LATIN SQUARE DESIGN
 One grouping or blocking is denoted as the column
classification and the other is row classification. The
grouping of the eu’s should be done so that the
differences among rows and columns represent major
sources of variation. The effect of the double grouping
is to eliminate from the experimental error the
variations due to the differences among the rows and
the columns.
 The rows and the columns are general terms referring
to criteria of classification. They may be kinds of
treatment or factors. Thus the LSD design may be
used to study three factors simultaneously assuming
that the factors have no interactions among
themselves.

14. LSD
Blocking of LSD
 In the LSD design, the whole experimental materials are
divided into as many rows and as many columns as there
are many treatments.
 The treatments are then arranged in blocks in two ways: by
rows and by columns, such that each treatment occurs once
in each row and column.
 Each row is a complete block, each column is likewise a
complete block.
Randomization
Steps:
1. Obtain a basic Latin (T x T) square plan
Example T = 4
r = 4

15. LSD
3 x 3 plot
4 x 4 plot
5 x 5 plot

16. LSD
6 x 6 plot

17. LSD Col 1 Col 2 Col 3 Col 4
Row 1
Row 2
Row 3
Row 4
A
A
A
A B
B
B
B
C
C
C
C
D
D
D
D

18. LSD
R1 –
R2 –
R3 –
R4 –
2. Randomize the assignment of the row classification to
the rows on the plan.
Draw sequence: 1 2 3 4 variable a ( location)
Draw numbers: 3 1 4 2 plan rows
L2
L4
L1
L3

19. LSD
3. Randomize the assignment of the column classification
to the columns on the plan.
Draw sequence: 1 2 3 4 variable b ( type of plant)
Draw numbers: 4 2 1 3 plan columns
Col 1- Col 2- Col 3- Col 4 - P1
P2
P3 P4

20. LSD
A B C D
B C D A
C D A B
D A B C
4. Randomize the assignment of treatments on the plan
Draw sequence: 1 2 3 4 Treatment (kind of fertilizer)
Draw numbers: A B C D plan for treatment
L2
L4
L1
L3
P3
P2 P4 P1
T1
T1
T1
T1
T2
T2
T2
T2
T3
T3
T3
T3
T4
T4
T4
T4

21. B D C A
D B A C
C A D B
A C B D
L1
L2
L3
L4
P1
P2
P3 P4
T2 T4
4. Rearrange the rows and columns in
sequence
T3
T1
T4
T2 T1
T3
T3
T1 T4 T2
T1
T3
T2 T4

22. LSD 1. An agricultural experiment considered the
effects of K2O (potash) on the breaking
strength of cotton fibers. Five K2O levels
were used (36, 54, 72, 108, 144 lbs/acre). A
sample of cotton was taken from each plot,
and a strength measurement was taken.
The experiment was arranged in 3 blocks of
5 plots each.
Sample Problem

23. LSD 2. A plant biologist conducted an experiment
to compare the yields of 4 varieties of
peanuts (A, B, C, D). A plot of land was
divided into 16 subplots (4 rows and 4
columns).
Sample Problem