Assumption involving in ANOVA,Uses of CRD,RBD,LSD in agriculture, Principle of Design of Experiment,Uniformity trial,Level of Significance

1. Sub: Experimental Designs
Akash Sahoo
M.Sc. Agronomy
Department of Agronomy

2. Treatment :
Various objects of comparison in a comparative
experiments are termed as treatment.
Treatment is what we want to compare in the
experiment.
Block :
In agricultural experiment most of the time we
divided the whole experimental field into relatively
homogeneous sub group.
Within the block – Homogeneous
Between the block - Heterogeneous

3. Experimental Unit :
• It is the smallest part of the experimental area to
which we apply the treatment.
• Experimental unit is the physical unit that receives a
particular treatment. for example: a plot in the field.
Principle of Design of Experiment :
There are three principle-
Replication:
Replication is the repeated application of treatment
in different blocks.
• Replication reduce experimental error.
• It reduces the variability of the experimental result
• In RBD block and replication is equal.

4. Randomization :
Randomization is the random application of
treatment in the experimental unit. In a randomized
experimental design objects or individuals are
randomly assigned to an experimental group.
• To reduce the biasness.
• Randomization ensures that each individuals will
have equal chance of being assigned to any
experimental unit.
Local Control :
Local control is the techniques of the experimental
error.
• To reduce the error by suitably modifying the
allocation of treatment to the experimental unit
• It is not used in CRD.

5. ANOVA (Analysis of Variance) :
It is a powerful statistical tool for test of
significance. The test of significance based on t-
distribution is an adequate procedure only for
testing the significance of difference between two
sample mean.
• Basic purpose of ANOVA is to test the
homogeneity of several means.
Assumption involving in ANOVA :
1.The effects are additive in nature
2. The observations are independent
3.The variable concerned must be normally
distributed

6. A C B D C
C D A C D
B E D B
• 5 Treatment : A,B,C,D and E
• A Repeated 2 times
• B Repeated 3 times Total 14 treatment
• C Repeated 4 times
• D Repeated 4 times
• E Repeated 1 Time
CRD

7. T1 T8 T4 T7
T5 T6 T5 T1
T8 T2 T7 T4
T6 T7 T1 T2
T3 T5 T8 T3
T7 T1 T2 T6
T4 T3 T6 T5
T2 T4 T3 T8
RBD: 8 treatments with 4 replication
R1 R2 R4
R3

8. • In ANOVA model, t-test is used for testing
two population mean.
• F-test is used for test the population
variences.
Level of Significance :
Probability of rejecting null hypothesis when it is
true is called level of significance.
This probability are generally taken as 0.001,
0.05, 0.01 or 0.1%, 1%, 5% etc. these are called
level of significance.

9. Region of Rejection :
Let x1,x2,x3,…xn are the n number
of point, say x̂ are present in the N-
dimensional sample space(ω). If any point
falls not in the sample space then it is called
region of rejecton.
Experimental Error :
A variation in response due to some
extraneous factor (inherent different among
the experimental unit ,error associated
during measurement etc.) is known as
experimental error.

10. Uniformity trial :
In experiments particularly in field
experiment in order to have an idea about
the condition of the proposed experimental
area a trial known as uniformity trial.
A short duration crop is grown under
uniform condition by dividing the whole
area into smallest unit to determine shape
and size, no. of plot in a block.
At the time of harvesting the entire
field divided into smallest unit of same size
and shape and the produced from each unit
recorded separately

11. Symmetrical factorial experiment :
A factorial experiment is symmetrical if the
number of levels for all the factors are same.
Example : a two factor factorial experiment
with five varieties and five different doses of
nitrogen is symmetrical factorial experiments.
Asymmetrical factorial experiment :
A factorial experiment is asymmetrical if the
number of levels for all factors are different.
Example : a two factor factorial experiment with
five varieties and any doses of nitrogen (but not
equals to five) is an asymmetrical factorial
experiment.

12. Subject CRD RBD LSD
Advantages • Number of replication may be
varied from treatment to
treatment.
• CRD provide maximum number
of degrees of freedom for the
estimation of experimental error.
• Increases the precision of
the experiment.
• Any replication can be
included in RBD.
• The statistical analysis is
simple and easy.
• Experimental error is
small for LSD compared
to CRD and RBD.
• LSD is more efficient
than CRD, RBD.
Limitations • CRD is less accurate than
other design.
• RBD may not be
suitable large number
of treatment.
• It is a versatile design.
• Layout is not as simple
as CRD, RBD.
• It requires mainly
square shaped plot .
Comparisons • Completely homogeneous
• All the treatment are completely
randomized in the experimental
units.
• Heterogeneous
• All the treatments are
randomize each block are
separately.
• Heterogeneous
• Randomization takes
place under the restriction
gap. Each treatment occur
once and only in each row
and each column.

13. Uses of CRD in Agriculture :
• CRD is applicable when the experimental material
is homogeneous. Example : homogeneous soil
condition in the field.
• Usually in the field , the soil will be
heterogeneous. Thus CRD is not preferable in field
conditions.
Uses of RBD in Agriculture :
• Number of replication is same for all treatment.
• Missing plots are easily estimated.

14. Formula
CRD :
SE(m) = √(MSE/ri)
SE(d) = √(2MSE/r)
RBD :
SE(m) = √(MSE/r)
SE(d) = √2 x S.E(m)
LSD :
CD = SE(d).t

15. Thank You