experimental designs for research workers

1. 32 FACTORIAL
EXPERIMENT
Presented by-: Deepak
M.Sc. Agriculture(Agronomy)
Roll no.- 10006

2. FACTORIAL
Factorial experiments involve
simultaneously more than one factor
each at two or more levels. Several
factors affect simultaneously the
characteristic under study in factorial
experiments and the experimenter is
interested in the main effects and the
interaction effects among different
factors.

3. MAIN EFFECT
The main effect of a factor is
defined to be the change in
response produced by a change
in the level of a factor.
The main effect of A is the
difference between the average
response at A1 and A2.

4. INTERACTION EFFECT
In some experiments we may find that
the difference in response between
the levels of one factor is not the
same at all levels of the other factor.
When this occurs, there is an
interaction between the factors.

5. TYPES OF FACTORIAL
Based on number of factors:
A factorial experiment is two factor factorial
experiment, three factor factorial
experiment. A factorial experiment with five
varieties and three doses of nitrogen is a
two factor factorial experiment. An
experiment with three irrigation schedule,
five varieties and three doses of nitrogen is
a three factor factorial experiment.

6. Based on level of factors:
A factorial experiment is either symmetrical
or asymmetrical depending upon the
equality or inequality in levels of factors put
under experimentation. A factorial
experiment is symmetrical, if the no. of
levels for all the factors are same. For
example, a two factor factorial experiment
with five varieties and five different doses
of nitrogen, is a symmetrical factorial
experiment. On the other hand a two factor
factorial experiment with five varieties and
any no. of doses of nitrogen, is an
asymmetrical factorial experiment.

7. ADVANTAGES
 Factorial experiments give the opportunity to an
experimenter to combine the effects of more than one
factor at a time.
 Compared to single factor experiments factorial
experiments are effective because of the fact that the
interaction effects can be worked out from these
experiments which is not possible in single factor
experiments.
 Factorial experiments are not only time saving but also to
some extent cost saving also.

8. DISADVANTAGES
 If the no. of factors or the levels of the factors or both the
no. and levels of factors are more, then the no. of
treatment combinations will be more, resulting in
requirement of bigger experimental area and bigger block
size. As the block size increases, it is very difficult under
field condition to maintain homogeneity among the plots
within the block. Thus there is a possibility of increasing
the experimental error vis-a-vis decrease precision of
experiment.

9.  Statistical procedure and calculation of factorial
experiments are more complicated than single factor
experiments.
 As the no. of factors or the levels of the factor or both
increases the no. of effects, including the interaction
effects also increases. Sometimes it becomes very
difficult to extract the information from interactions
particularly the higher order interaction effects.
 Utmost care is needed to meticulously conduct the
experiment because the failure in one experiment may
result in loss of information greater compared to single
factor experiment.

10. 32 FACTORIAL
EXPERIMENT
 This is the three level experiment. It has two
factors, each at three levels. Let the levels of A be
denoted by a0, a1, a2 and the levels of B be
denoted by b0, b1, b2. Since every factor has three
levels, 2 d.f. will be attached with each factor.

11. 32 FACTORIAL RBD
EXPERIMENT
Variety R1 R2 R3
S1 S2 S3 S1 S2 S3 S1 S2 S3
V1 145 155 148 140 160 150 135 160 152
V2 160 162 155 152 168 152 148 165 158
V3 135 148 145 138 155 143 140 152 148

12.  Grand Total= 4069
 Correction Factor= GT2 = 40692 = 613213.370
3.3.3 27
 TSS = 4069-CF = 615257- 613213.370
= 2043.630
 RSS = 13532+ 13582+13582 - 613213.370
9
= 1.852

13. Yield (q/ha)
S1 S2 S3 Total Averag
e
V1
V2
V3
420
460
413
475
465
436
450
465
436
1345
1420
1304
149.44
157.78
144.89
Total
Averag
e
1293
143.67
1425
158.33
1351
150.11

14. TrSS = 4202+4752+4502+..+4552+4362– 613213
3
=1808.296
ErSS=TSS-TrSS-RSS=2043-1808-1.852=233.482
SS(variety)=13452+14202+13042-69413.370
9
=768.963
SS(spacing)=12932+14252+13512-69413.370
=972.741 9
SS(VS)= TrSS- SSv -SSs
=1808.296-768.963-972.741
=66.593

15. Table of Averages
Variety Yield(q/ha)
V2
V1
V3
157.78
149.44
144.89
Spacing
S2
S3
S1
158.33
150.11
143.67