Complete Randomized Block Design (CRBD) and Randomized Block Design (RBD)

In experimental research, the design of an experiment is crucial for obtaining valid and reliable results. This presentation focuses on two important experimental designs: Complete Randomized Block Design (CRBD) and Randomized Block Design (RBD). These designs help control variability and improve the accuracy of experimental outcomes.

Overview of Experimental Designs Experimental designs are structured approaches to conducting experiments that aim to minimize bias and maximize the reliability of results. They are essential for ensuring that the findings are valid and can be generalized to a larger population.

1. GURU GHASIDAS VISHWAVIDYALAY , BILASPUR ,(C.G)
Under the supervision of
Dr.Naveen kumarVishwakarma
Assistant professor
Department of Biotechnology
PRESENTED BY :
ADYALIPSA SANDHIBIGRAHA
ANJALI GUPTA
ARPANA SINGH
MONOBODHO SWAGATIKA
PRATIKSHA RAJAK
SESSION-2024-25
COMPLETE RANDOMISE BLOCK DESIGN AND RANDOMISE BLOCK DESIGN
DEPARTMENT OF BIOTECHNOLOGY
SUBJECT :BIOSTATISTICS

2. CRD (COMPLETELY RANDOMISE DESIGN )& RBD (RANDOMIZED
BLOCK DESIGN) :
Experimental design
Completely randomized design
Advantages & Disadvantages of CRD
Statistical analysis in CRD
Randomise block design
Advantages & Disadvantages of RBD
Statistical analysis in RBD
Comparison between CRD & RBD
Application of CRD & RBD
Conclusion

3. SOME BASIC TERMS :
Treatment is a testable material applied to particular subjects (experimental unit).
Example –fertilizer variety of seed , teaching methods , strategies to enhance savings , investment and production.
Experimental unit :-it is a subject on which treatment is applied
Example : plants , students , customers, plots ,groups of people .
 Experimental error: is the variation among experimental units , no two plants are alike ,no two students are
alike etc.
Experimental design : it is a refine form of analysis of variance . Used to test the difference between more than
two population means. It is a state of strategies adopted by experimenter to get valid estimates of treatment
effects with minimum experimental error .

4. EXPERIMENTAL DESIGN :
 Experimental design is a study in statistics which deals
with the design and analysis of experiments. It is a way to
carefully plan experiments in advance so that your results
are both valid and objective.
 Sir Ronald Fischer introduced this system of
experimental design in 1935.
 He is a well known statistician, eugenicist, evolutionary
biologist, geneticist. Founder of Experimental .
ir Ronald Fischer introduced the system of experimental
design in 1935 .
He is known as the father of modern statistics .

5. VARIABLES USED IN EXPERIMENTAL DESIGNS :-
Independent variables :
An independent variable is the one which is controlled or changed in a scientific experiment to examine the
effects on the dependent variable.
Dependent variables :
A dependent variable is the one which is being measured & tested in a scientific experiment, under specific
conditions. Variables Used in Experimental Design Dependent Variable Independent Variable .
FOR EXAMPLE If we examine any plant field and the growth of plants then the problem is that if the plant grows
more by the use of fertilizers or not? Does cause/affect ?
 Independent Variable: Fertilizer
Dependent Variable: Plant Growth

6. Experimental designs are important for determining the cause and effect relationship between
dependent variable and independent variable.
 It is a statistical method in which a researcher plans to observe effect of desired factors on
response.
Principles of Experimental Design :
There are three basic principles :
 Replication:- Repetition of the treatment under investigation Or To provide an estimate of
experimental error. •
 Randomization:- The allocation of the treatment to the different experimental units by a
random process is known as randomization. •
 Local control:- The principal of making use of greater homogeneity in groups of experimental
units for reducing experimental error.
IMPORTANCE OF EXPERIMENTAL DESIGN :

7. CRD ( COMPLETELY RANDOMIZED DESIGN )
It is a single factor design.
The design which is used when the experimental material is limited and experimental units
homogeneous .
 The Completely Randomized Design(CRD) is the most simplest of all the design based on
randomization and replication. In CRD, all treatments are randomly allocated among all experimental
subjects. This allows every experimental unit; i.e.; plot, animal, soil sample etc., to have an equal
probability of receiving .
The principle of local control is not allow adopted in this design
The design is specially used for pot culture experiments .
Number of plots = number of replication +number of treatments

8. ADVANTAGES OF CRD :
CRD has several advantages it is easy to layout the design.
 There is complete flexibility in the number of treatments and number of replication which may very from
treatment to treatment.
The no. of replication need not to be same for each treatment.
The CRD provides maximum d.f. for the experiment of experimental

9. DISADVANTAGES OF CRD:-
It is difficult to find homogeneous experimental units in all respects and hence CRD
is seldom suitable field experiments as compared to other experimental designs.
It is less accurate than other desings .
It increase experimental errors .

10. ANOVA TABLE FOR CRD :

11. EXAMPLE OF CRD :
3 types of fertilizers A,Band C are used on 12 plots of cultivated land in order to test their effect on productivity.
Fertilizers are applied to each plot randomly . Details of productivity is given below . Test the hypothesis that
productivity of all three fertilizers are same.
plotProduction using Fertilizers A,B,C
A B C
1 3 10 5
2 4 7 4
3 6 8 5
4 4 6 5

12. Plot Production TOTAL
A B C
1 3 – (9) 10 (100) 5(25) 19
2 4-(16) 17(49) 4(16) 15
3 6 -( 36) 8(64) 5(25) 18
4 4 - ( 16) 6(36) 5(25) 15
TOTAL17 31 19 67 grand total
SUM Xij77 249 91 417
T2 289 961 361 1611

13. Coreection factor c.f = (GT)^2 /n
=(67)^2/ 12
=374.08
Total sum of square (TSS) =????????????��^2 – C.F
=417-374.08
=42.92
Treatment sum of square =
????????????
2
??????
−????????????
= 1611/4 -374.08
=28.67
Error sum of square = total ss – treatment s
= 42.92-28.67
=14.25
Source
Of
variation
d.fSum
Of
Square
Mean
square=
sum of
square/
d.f
Fc
St^2
/
se^2
F
table
decision
Treatment t-1
3-2=1
28.6714.335
9.324.26Null
Error n-t
12-
3=9
14.251.583
Is
Total n-1
12-
11=1
42.92
rejected

14. APPLICATION OF CRD :
Under conditions where the experimental material is homogenous and there is minimum variability among them
e.g. in physics, chemistry in chemical and in biological experiment in some green house studies.
In small experiments where there is a small number of d.f.
CRD is may be used in a chemical or baking experiment where the experimental units are the part of the
thoroughly mixed chemical or powder.
CONCLUSION :
 A completely randomized design relies on randomization to control for the effect of extraneous variables. CRDs
are for the studying the effect on the primary factor without the need to take other nuisance variables into
account.

15. RANDOMIZE BLOCK DESIGN :-
A randomise block design is an experimental design that groups experimental units into blocks and randomly
assigns treatments to the units with each block.
Purpose :- The purpose of a randomise block design is to reduce experimental error and obtain more precise
results.
When to use RBD:- A randomise block experiment should be considered when there is a unwanted variable
that could affect the outcome of the experiment .
RBD is also used when experimental materials is not homogenous ( heterogeneous).

16. ADVANTAGES OF RBD
Generally more precise than the CRD.
No restriction on the no. of treatment or replicates.
Some treatment may be replicated more items than others
Missing plots are easily estimated
Whole treatment or entire replicates may be deleted from the analysis.
 if experimental error is heterogeneous ,valid comparison can still be made.

17. DISADVANTAGES OF RBD :
Error DF is smaller than that for the CRD (problem with a small no. of treatment).
If there is a larger variation between experimental units within a blocks , a large error term may result ( this may
be due too many treatment)
 If there are missing data , a RCBD experiment may be less efficient than a CRD.

18. EXAMPLE OF RBD :
In given question, no. of replications (r=3) and the no of treatments (t=6)can be included in this design (RBD) .
R1 R2 R3
1 1.5 1.8 1.6
2 4.7 4.4 5.3
3 5.7 5.8 5.3
4 3.7 3.2 2.9
5 6.6 6.3 6
6 5.8 6.1 5.5
T
R
E
A
T
M
E
N
T
S
REPLICATION

19. R1 R1^2 R2 R2^2 R3 R3^2 TOTAL
1 1.5 2.25 1.83.24 1.6 2.56 4.9
2 4.7 22.09 4.419.365.3 28.09 14.4
3 5.7 32.49 5.833.645.3 28.09 16.8
4 3.7 13.69 3.210.242.9 8.41 9.8
5 6.6 43.56 6.339.696 36 18.9
6 5.8 33.64 6.137.215.5 30.25 17.9
TOTAL 28 ∑R1^2=
147.72
27.6∑R2^2
=143.3
8
26.6 ∑R3^2
=133.4
GRAND
TOTAL=
82.2
R E P L I C A T I O N
T
R
E
A
T
M
E
N
T

20. EXAMPLE OF RANDOM BLOCK DESIGN :-
Step1: -Set Hypothesis –
Ho ( Null Hypothesis ) : T1=T2=T3=T4=T5=T6
H1 ( Alternate Hypothesis) : T1≠T2 ≠ T3 ≠ T4 ≠ T5 ≠ T6
Step2 :-Correction Factor –
C.F. = (Grand Total )^2 / n (no. of experimental unit)
C.F. = (82.2)^2 / 18
= 375.38
Step3 :-Total Sum of Square ( TSS) –
TSS = ????????????��^2 – C.F
=(147.2+143.38+133.4)-375.38
=49.12

21. Step 4:- TrSS(treatment sum of square )
 =
????????????
2
??????
−????????????
=1269.62 / 3-375.38
=423.2-375.38
=47.82
Step 5:- RSS(replication sum of square )
=(R1^2+R2^2+R3^2) / t – C.F
=2253.32/6-375.38
=0.17
STEP 6:- ESS (error sum of square)
=TSS-TrSS-RSS
=49.12-47.82-0.17
=1.13

22. ANOVA TABLE FOR RBD :
SOURCE DEGREE OF
FREEDOM
SUM OF SQURE MEAN SQUARE F – VALUE
Replication r – 1
=3 -1=2
RSS =0.17 RMS=RSS / r-1
=0.17/2
=0.085

RMS/EMS
=0.085/0.13
=0.65
Treatments t -1=
6 – 1=5
TrSS=47.82 TrMS = TSS / t-1
=9.564
TrMS /EMS
=9.564/0.13
=73.5
Error
( r– 1) (t -1)=
2*5 =10
ESS =1.3 EMS =
ESS / (r – 1)( t -1)
=0.13
Total rt -1=
18 – 1 -= 17
TSS =49.12

23. RESULT :
Replication : F tab = 4.10
F cal =0.65
hence , Ftab> F cal
So we accept null hypothesis
Treatment : F tab =3.33
F cal =73.56
hence F tab < Fcal
So we reject null hypothesis .

24. APPLICATIONS OF RBD :
Randomized block design (RBD) is an experimental design that is used in many fields of science, including
agriculture, engineering, and medicine.
 It is used to reduce bias, errors, and variability in treatment conditions, and to improve the robustness of
statistical analyses.
CONCLUSION :
 Random block design (RBD) is powerful statistical design technique used to optimize experiments ,residues
variability and increase precision
 By dividing experimental units into blocks and randomly assigning treatments , RBD minimizes systematic errors
and ensures reliable results.

25. Thank you