agricultural ststistics

1. WELCOME

2. RANI LAKSHMI BAI CENTRAL AGRICULTURAL UNIVERSITY
JHANSI,UP
Subject:Experimental designs,ABB 512(2+1)
Topic: Cross over design.
Submitted to,
Dr. Shailendra Kumar,
Asst.Professor(Statstics),
RLBCAU,Jhansi.
Submitted by,
Harish J,
AG/PG/0020/19,
1st year M.sc Agriculture,
RLBCAU,Jhansi.

4. Design types of Controlled Experimental studies.
1. Parallel design
2. Crossover design
3. Time series design

5. • A type of design in which a treament applied to any
particular experimental unit does not remain the same
for the whole duration of the Experiments.
• It is also called as Switch over trials.
• In this design the whole duration of experiment is
divided into a number of fractions of time depending
upon the number of observations.
• Then a treatment is applied to an experimental unit for
a fraction of time of whole duration of the experiment.
Cross over design

6. • After lapse of the fraction of time ,this treatment is changed and
another treatment is applied for the second fraction of time of
the whole duration of the experiment.
• The process is continued till all the treatments are applied to that
particular unit,each treatment remaining in the unit for one
fraction of time.
• Each treatment is applied to each experimental unit once and
only once.
• In this Fractions of time in which the whole duration of the
experiment units and units of the experiment to which the
treatments are applied for a fraction of time serve as replications.
• The number of replications shall be an integral multiple of the
number of treatments.

8. Residual effect
• The effect of a treatment that continues even after the
application of the treatment is disconnected.
• Residual effect of a particular treatment in any experimental unit
influences the measurements of the effect of the succeding
treatment in the same experimental unit.
• It is necessary to eliminates or reduce this residual effect before
application of the next treatment.

9. • After the application of any one treatment is
discontinued,rest is given for a short period of time to
this experimental unit and succeding treatment is
applied after this rest period.
• During rest period no observation is recorded on the
effect of treatments.
• Rest period is like the border which in left all around the
experimental plot in field experiments to eliminate of the
adjacent plots.

10. Experiment: A random sample of 8 cows was taken to test the
effect of two types of ratios A and B on their milk yields,out of
these cows,4 cows were selected randomly.Each of these 4 cows so
selected were given rations A in their better lactation period and
ration B in their poorer lactation period .Each of the remaining 4
cows were given ration B in their better lactation period and ration
A in their poorer lactation period.The layout and average milk yield
per day(in kg) is given below:-
Example:
A random sample of 8 cows was taken to test the effect of two types of ratios A
and B on their milk yields,out of these cows,4 cows were selected randomly.Each
of these 4 cows so selected were given rations A in their better lactation period
and ration B in their poorer lactation period .Each of the remaining 4 cows were
given ration B in their better lactation period and ration A in their poorer lactation
period.The layout and average milk yield per day(in kg) is given below:-
Lactati
on
period
Cows Total
1 2 3 4 5 6 7 8
First
B
25
A
22
B
15
A
20
B
15
B
15
A
14
A
20 147
Second A
15
B
11
A
15
B
15
A
15
A
12
B
6
B
14 103
Total
40 34 30 35 30 27 20 34 250

11. Theory:
Null hypothesis:-H0:The two rations do not differ significally as regards their effect on
milk yield.
Alternate hypothesis:-H1:The 2 ratios are differ significantly as regards their effect on
milk yield.
Table and Calculation :
1. C.F =( Grand total)²/Total no. Observations
= (250)²÷16= 3906.25
2. TSS=Sum of squares of each observation- CF
=25²+23²+15²+.....+14²−3906.25=315.75
3. Sum of squares due to cows=X²+Y²+..../n(lactation period)-CF
=(40)²+(34)²+(30)²+.....+(34)²÷2-3906.25
= 8066÷2-3906.25= 126.75
4. Sum of squares due to Lactation period= X²+Y²∕r(No. of cows)−CF
=(147)²+(103)²÷8-3906.25=121
5. Sum of squares due to Ration=TA²+TB²/r-CF
= (134)²+(116)²÷8-3906.25=20.25

12. S.V df S.S M.S Cal F Tab F
Cow n-1= 7 126.75 18.10 2.27 (7,6)
4.21
Period K-1= 1 121 121 15.22 (1,6)
5.99
Ration K-1=1 20.25 20.25 2.59 (1,6)
5.99
Error (n-2)(K-
1)=6
47.75 7.95
Total nk-1=15
ANOVA TABLE
6. Sum of squares due to error=TSS-S.S(cows)-S.S(Lactation Period)-S.S(Rations)
=315.75-126.75-20.25
=47.75

13. Conclusion:
• There are 2 ratios do not differ significantly and hence there is no
significant difference among the ration and cow.
• There is significant difference in lactation period.

14. Advantages
• It is useful in case the effect of treatment varies with
time.
• Treatment effects over a short period of time can be
estimated in this design.
• This design controls fluctations due to time.
• We can use this design with any number of treatments
with the restriction that the number of replicates must
be integral multiple of the number of treatment.
• This design is almost similar to LSD but it can easily used
for small number of treatments (less than 5)in
which,LSD is not possible.

15. Disadvantages
• Time involved for a crossover design is longer than
other design types.
• More dropouts because time involved.
• Period effects
• Sequence effects
• Carryover effects

16. Applications
• Dairy husbandary
• Biological studies
• Psychological studies
• Education purpose
• Marketing research
• Clinical trials

17. THANK YOU