The document describes the complete randomized design (CRD) method for agricultural experiments. It defines CRD as a design where treatments are randomly assigned to experimental units. Key points: - CRD is best for experiments with limited and homogeneous materials, conducted in laboratories or greenhouses. - Treatments are randomly distributed among experimental units through randomization. - CRD has advantages like easy layout, flexibility, and simplest data analysis compared to other methods. - Steps include determining experimental units, randomly assigning treatments, calculating statistics, and interpreting results.

1. AURORA STATE COLLEGE OF TECHNOLOGY
DEPARTMENT OF AGRICULTURE AND AQUATIC SCIENCES
Instructor
JOSE D. BALAI JR.
Complete Randomized Design (CRD)

2. AURORA STATE COLLEGE OF TECHNOLOGY
DEPARTMENT OF AGRICULTURE AND AQUATIC SCIENCES
Complete Randomized Design (CRD)
 The CRD is a design in which the treatments are randomly arranged over the entire experimental
materials.
 Experimental units are randomly assigned to the factor levels using randomization.
 Used when the experimental material is limited and experimental units homogenous.
 Applicable for laboratory or greenhouse experiments ONLY and should not be used to open fields.
(It may be used to open fields PROVIDED that all conditions unto which the experimental units are
subjected to are homogenous)

3. AURORA STATE COLLEGE OF TECHNOLOGY
DEPARTMENT OF AGRICULTURE AND AQUATIC SCIENCES
Advantages of CRD
 Its layout is very easy.
 There is complete flexibility in this design.
 Whole experimental material can be utilized in this design.
 This design yields maximum degrees of freedom for experimental error.
 The analysis of data is simplest as compared to any other design.
 The analysis can be done even if some values are missing.

4. AURORA STATE COLLEGE OF TECHNOLOGY
DEPARTMENT OF AGRICULTURE AND AQUATIC SCIENCES
Randomization of CRD/Lay-out of CRD
1. Determine the total number of experimental units.
For Equal replication
𝑛 = 𝑛𝑜. 𝑜𝑓 𝑡𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡 × 𝑛𝑜. 𝑜𝑓 𝑟𝑒𝑝𝑙𝑖𝑐𝑎𝑡𝑒𝑠
𝑛 = 𝑡 × 𝑟
Example: If you have 4 treatments with 3 replications then:
𝑛 = 4 × 3 = 12
Thus, the number of experimental units is 12.

5. AURORA STATE COLLEGE OF TECHNOLOGY
DEPARTMENT OF AGRICULTURE AND AQUATIC SCIENCES
Randomization of CRD/Lay-out of CRD
Step 1
Divide the area or experimental materials into the required number of e.u.’s.
1 2 3 4
5 6 7 8
9 10 12
11

6. AURORA STATE COLLEGE OF TECHNOLOGY
DEPARTMENT OF AGRICULTURE AND AQUATIC SCIENCES
Step 2
Assign the treatments to the e.u.’s completely at random – drawing lots
a. Prepare identical pieces of paper and divide them into
t –groups, each group with r - pieces of paper.
b. Label each slip of paper of the same group with the same letter of number corresponding
to the treatment. Uniformly fold the labeled slips of paper, mix them thoroughly and place
them in a container.
Randomization of CRD/Lay-out of CRD
Label
1. 3 slips of paper for T1
2. 3 slips of paper for T2
3. 3 slips of paper for T3
4. 3 slips of paper for T4

7. AURORA STATE COLLEGE OF TECHNOLOGY
DEPARTMENT OF AGRICULTURE AND AQUATIC SCIENCES
Step 2
Assign the treatments to the e.u.’s completely at random – drawing lots
c. Draw one slip of paper at a time, without replacement and with constant shaking of the
container after each draw to mix its contents.
Randomization of CRD/Lay-out of CRD
Slip label T2 T3 T2 T3 T1 T4
Sequence 7 8 9 10 11 12

8. AURORA STATE COLLEGE OF TECHNOLOGY
DEPARTMENT OF AGRICULTURE AND AQUATIC SCIENCES
c. Assign the treatments to plots based on the corresponding treatment label and sequence. For our
example, T1 will be assigned in plots 4, 5 and 11; T2 in plots 1, 7 and 9 and T3 in plots 2, 8 and
10, and T4 in plots 3, 6 and 12.
2 3
T2 T1
1 4
5 6 7 8
9 10 11 12
T2 T3
T1 T4
T3
T4
T2
T1
T3
T4
Step 2
Assign the treatments to the e.u.’s completely at random – drawing lots
Randomization of CRD/Lay-out of CRD

9. AURORA STATE COLLEGE OF TECHNOLOGY
DEPARTMENT OF AGRICULTURE AND AQUATIC SCIENCES
Website Link: https://drs.icar.gov.in/Basic%20Designs/basicdesign.aspx

10. AURORA STATE COLLEGE OF TECHNOLOGY
DEPARTMENT OF AGRICULTURE AND AQUATIC SCIENCES
Linear Model of CRD
𝑌𝑖𝑗 = 𝜇 + 𝜏𝑖 + 𝜀𝑖𝑗
where:
𝜇 is the overall mean effect
𝜏𝑖 is the effect of the 𝑖𝑡ℎ treatment
𝜀𝑖𝑗 error associated tot the 𝑖𝑗𝑡ℎ cell

11. AURORA STATE COLLEGE OF TECHNOLOGY
DEPARTMENT OF AGRICULTURE AND AQUATIC SCIENCES
Linear Model of CRD

12. AURORA STATE COLLEGE OF TECHNOLOGY
DEPARTMENT OF AGRICULTURE AND AQUATIC SCIENCES
Linear Model of CRD
𝑌𝑖𝑗 is the observation
𝑌𝑖. is the total of the 𝑖𝑡ℎ treatment
𝑌.. is the grand total
𝒀.. is the grand mean
t is the number of observations
r is the number of replications
n is the TOTAL number of observation

13. AURORA STATE COLLEGE OF TECHNOLOGY
DEPARTMENT OF AGRICULTURE AND AQUATIC SCIENCES
Numerical Example
Suppose we want to determine the effect of various organic fertilizer on the yield of pechay.
TREATMENT LEVELS REPLICATION LEVELS
T1 – Control R1 – Replication 1
T2 – Chicken Dung R2 – Replication 2
T3 – Alnus Compost R3 – Replication 3
T4 - Vermicompost

14. AURORA STATE COLLEGE OF TECHNOLOGY
DEPARTMENT OF AGRICULTURE AND AQUATIC SCIENCES
Step by Step Analysis in CRD

15. AURORA STATE COLLEGE OF TECHNOLOGY
DEPARTMENT OF AGRICULTURE AND AQUATIC SCIENCES
1. Determine the Correction Factor
2. Determine the Sum of Squares
a. Total Sum of Squares
Step by Step Analysis in CRD

16. AURORA STATE COLLEGE OF TECHNOLOGY
DEPARTMENT OF AGRICULTURE AND AQUATIC SCIENCES
c. Error Sum of Square
b. Treatment Sum of Squares
Step by Step Analysis in CRD

17. AURORA STATE COLLEGE OF TECHNOLOGY
DEPARTMENT OF AGRICULTURE AND AQUATIC SCIENCES
Step by Step Analysis in CRD
3. Determine the degrees of Freedom
a. Total DF
b. Treatment DF
c. Error DF

18. AURORA STATE COLLEGE OF TECHNOLOGY
DEPARTMENT OF AGRICULTURE AND AQUATIC SCIENCES
Step by Step Analysis in CRD
4. Determine the Mean Squares
a. Mean Square of Treatments
b. Mean Square of Treatments

19. AURORA STATE COLLEGE OF TECHNOLOGY
DEPARTMENT OF AGRICULTURE AND AQUATIC SCIENCES
Step by Step Analysis in CRD
5. Determine the computed F value
6. Compute the Coefficient of Variation

20. AURORA STATE COLLEGE OF TECHNOLOGY
DEPARTMENT OF AGRICULTURE AND AQUATIC SCIENCES
Step by Step Analysis in CRD
Decision:
If Fcomp is < F0.05, then there is no significant difference (ns)
If Fcomp is > F0.05, then there is a significant difference (*)
If Fcomp is > F0.01, then there is highly significant difference (*)
Table 1. ANOVA Table on the yield of pechay.

21. AURORA STATE COLLEGE OF TECHNOLOGY
DEPARTMENT OF AGRICULTURE AND AQUATIC SCIENCES
Data Presentation and Interpretation
Table 1. Comparison on the yield of pechay according to organic fertilizer used.

22. AURORA STATE COLLEGE OF TECHNOLOGY
DEPARTMENT OF AGRICULTURE AND AQUATIC SCIENCES
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