A completely randomized design (CRD) is one where the treatments are assigned completely at random so that each experimental unit has the same chance of receiving any one treatment. For the CRD, any difference among experimental units receiving the same treatment is considered as experimental error. 

1. Statistical Methods for Engineering Research
Randomized Complete Block Design

2. Prepared By
Dr. Manu Melwin Joy
Assistant Professor
School of Management Studies
Cochin University of Science and Technology
Kerala, India.
Phone – 9744551114
Mail – manumelwinjoy@cusat.ac.in
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3. Completely randomized design
• A completely randomized design (CRD) is
one where the treatments are assigned
completely at random so that each
experimental unit has the same chance of
receiving any one treatment.
• For the CRD, any difference among
experimental units receiving the same
treatment is considered as experimental
error.

4. Completely randomized design
• Hence, CRD is appropriate only for
experiments with homogeneous
experimental units, such as laboratory
experiments, where environmental effects
are relatively easy to control.
• For field experiments, where there is
generally large variation among
experimental plots in such environmental
factors as soil, the CRD is rarely used.

5. Randomized complete block
design
• The randomized complete block design
(RCBD) is one of the most widely used
experimental designs in forestry research.
• The purpose of blocking is to reduce the
experimental error by eliminating the
contribution of known sources of variation
among the experimental units.

6. Randomized complete block
design
• This is done by grouping the experimental
units into blocks such that variability within
each block is minimized and variability
among blocks is maximized.
• Since only the variation within a block
becomes part of the experimental error,
blocking is most effective when the
experimental area has a predictable pattern
of variability.

7. Randomized complete block
design
• This design divides the group of
experimental units into n homogeneous
groups of size t.
• These homogeneous groups are called
blocks.
• The treatments are then randomly assigned
to the experimental units in each block -
one treatment to a unit in each block.

8. Example 1:
• Suppose we are interested in how weight gain (Y)
in rats is affected by Source of protein (Beef,
Cereal, and Pork) and by Level of Protein (High
or Low).
• There are a total of t = 3×2 = 6 treatment
combinations of the two factors (Beef -High
Protein, Cereal-High Protein, Pork-High Protein,
Beef -Low Protein, Cereal-Low Protein, and Pork-
Low Protein) .

9. • Suppose we have available to us a total of N = 60
experimental rats to which we are going to apply the
different diets based on the t = 6 treatment
combinations.
• Prior to the experimentation the rats were divided
into n = 10 homogeneous groups of size 6.
• The grouping was based on factors that had
previously been ignored (Example - Initial weight
size, appetite size etc.)
• Within each of the 10 blocks a rat is randomly
assigned a treatment combination (diet).

10. • The weight gain after a fixed period is
measured for each of the test animals and is
tabulated on the next slide:

11. Block Block
1 107 96 112 83 87 90 6 128 89 104 85 84 89
(1) (2) (3) (4) (5) (6) (1) (2) (3) (4) (5) (6)
2 102 72 100 82 70 94 7 56 70 72 64 62 63
(1) (2) (3) (4) (5) (6) (1) (2) (3) (4) (5) (6)
3 102 76 102 85 95 86 8 97 91 92 80 72 82
(1) (2) (3) (4) (5) (6) (1) (2) (3) (4) (5) (6)
4 93 70 93 63 71 63 9 80 63 87 82 81 63
(1) (2) (3) (4) (5) (6) (1) (2) (3) (4) (5) (6)
5 111 79 101 72 75 81 10 103 102 112 83 93 81
(1) (2) (3) (4) (5) (6) (1) (2) (3) (4) (5) (6)
Randomized Block Design

12. Example 2:
• The following experiment is interested in
comparing the effect four different
chemicals (A, B, C and D) in producing
water resistance (y) in textiles.
• A strip of material, randomly selected from
each bolt, is cut into four pieces (samples)
the pieces are randomly assigned to receive
one of the four chemical treatments.

13. • This process is replicated three times
producing a Randomized Block (RB) design.
• Moisture resistance (y) were measured for
each of the samples. (Low readings indicate
low moisture penetration).
• The data is given in the diagram and table on
the next slide.

14. Diagram: Blocks (Bolt Samples)
9.9 C 13.4 D 12.7 B
10.1 A 12.9 B 12.9 D
11.4 B 12.2 A 11.4 C
12.1 D 12.3 C 11.9 A

15. Table
Blocks (Bolt Samples)
Chemical 1 2 3
A 10.1 12.2 11.9
B 11.4 12.9 12.7
C 9.9 12.3 11.4
D 12.1 13.4 12.9