Practical on Design of Experiments: CRD, RBD, LSD and Factorial Experiments.


Shikshan Prasarak Santha’s

PADMABHUSHAN VASANTRAODADA PATIL MAHAVIDHYALAYA, KAVATHEMAHANKAL.

DEPARTMENT OF STATISTICS

B. Sc.-III: Practical – VI

Expt. No.:- 1                                                                          Date:

Title:  Analysis of CRD and RBD, Efficiency of RBD over CRD.

Q.1 Analyze the data and test the significance of treatment effect. Which treatment differs significantly?

Treatment

Observations

T1

10,50,30,41,52

T2

98,60,70,45,63,65

T3

48,58,39,70,55,78,65

T4

30,45,33,20

T5

48,39,51,50,36,77

 

 

 

                

Q.2. Given following observations for varieties V1, V2, V3 and V4. Identify the design and Carryout analysis of variance, write your conclusion.

 

V1    320

V4     340

V2    398

V4    360

V3     350

V2    322

V2     455

V3    417

V1    420

V4     388

V3    400

V3     353

V2    334

V3    331

V4     358

V4    370

V4     340

V2    375

V4    320

V3     325

V1    430

V1     350

V3    378

V4    378

V2     328

    

 

 

Q.3. Analyze the following RBD. Also compare the treatments T1 and T2.

 

Treatments

Blocks

I

II

III

IV

T1

19

25

22.5

25.5

T2

26

28

27

33

T3

20.5

28.5

21.5

25.5

  

Q.4. Analyze the data and state your conclusion. Also test whether A and D differ   significantly.


Block

Treatments

I

A   24.7

B   27.7

C     20.6

E   16.2

D   16.2

F   24.9

II

C   22.9

B  28.8

A   27.3

D   15

F    17

E   22.5

III

F   26.3

D   19.6

A   38.5

C   36.8

B    39.5

E   15.4

IV

E   17.7

B    31

A    8.5

D    14.1

C    4.9

F    22.6

 




***

 

         




 RBD




***

Shikshan Prasarak Santha’s

 PADMABHUSHAN VASANTRAODADA PATIL MAHAVIDHYALAYA, KAVATHEMAHANKAL.

DEPARTMNT OF STATISTICS

B.Sc.-III: Practical – VI

Expt. No.:- 2                                                                          Date:

Title: Analysis of LSD and efficiency of LSD over CRD and RBD.


Q.1. Layout given bellow represents LSD with four treatment A, B, C, and D each replicated four times. Analyze the design.


 

I

II

III

IV

Total

I

A  120

B  112

C  110

D  109

451

II

B  115

A  118

D  102

C  105

440

III

C  105

D  90

A  121

B  109

425

IV

D  108

C  115

B  120

A  120

463

Total

448

435

453

443

1779

                      

 

 

   

Q.2. Complete the ANOVA table for 4*4 LSD and state your conclusion.

S.V.

d. f.

S.S.

M.S.S.

F cal

Treatment

3

……..

186.94

……….

Row

3

318.76

……….

……….

Column

3

………

……….

……….

Error

6

……...

25.87

 

Total

15

1755.21

 

 

 

Q.3 Complete the following table for the analysis of variance of LSD and find the efficiency of LSD  with respect to RBD and CRD.

 

S.V.

d.f

S.S

M.S.S.

F

Rows

…….

36

………

2

Columns

…….

…….

18

…….

Treatment

……..

……..

30

……..

Error

6

…….

6

……..

Total

……..

 

 

 

 Q.4 Find the efficiency of given 5*5 LSD over CRD and RBD from following data.

  

S.V.

S.S.

D.F.

Rows

330

4

Between column

68

4

Error

150

12

total

676

 

   

 

 

***

Theory/Statistical formulae:



ANOVA Table:

Solutions: 

***
 

Shikshan Prasarak Santha’s

PADMABHUSHAN VASANTRAODADA PATIL MAHAVIDHYALAYA, KAVATHEMAHANKAL.

DEPARTMENT OF STATISTICS

B.Sc.-III: Practical – VI

Expt. No.:- 3                                                                          Date:

Title:  Missing plot technique for RBD and LSD with single missing observations.


1.      In the following RBD observation on one lot is missing. Estimate the missing value and then carryout the analysis.


Treatments

Blocks

1

2

3

1

9

8.5

8

2

7.5

9.8

7.5

3

10

-------

6.9

4

9.3

8.68

7.98

        

 

 

 

   

2.      An experiment was carry out on wheat with 3 treatments in our RBD.  The  plant and yield/plot in kg. are given below with one missing value . Estimate the missing value and then carryout the analysis.


I

II

III

IV

A-8

C-10

A-6

B-10

C-12

B-

B-9

A-8

B-10

A-8

C-10

C-9

    

 

 

  3.      In following 4*4 LSD the yield of one plot is missing .Estimate this and analyze the data.


A-120

B-98

C-46

D-78

B-50

A-95

D-

C-100

C-85

D-90

B-100

A-79

D-75

C-66

A-88

B-108

  

 

   

4.      Estimate the missing value in 4*4 LSD and carry out the analysis of following.


Day No.

I

II

III

IV

1

B-47

A-90

C-79

D-59

2

D-46

C-74

B-63

A-69

3

A-62

B-

D-58

C-66

4

C-76

D-63

A-87

B-59

 

 


***




***

Shikshan Prasarak Santha’s

PADMABHUSHAN VASANTRAODADA PATIL MAHAVIDHYALAYA, KAVATHEMAHANKAL.

DEPARTMENT OF STATISTICS

B.Sc-III: Practical – VI

Expt. No.:- 6                                                                          Date:

Title:  Analysis of 22 and 23 factorial experiment.

Q.1 Analyze the 22 factorial experiment given below and state your conclusion.


Q.2 Analyze the  22 factorial experiments  given below and state your conclusion.


Block

1

a

b

ab

1

64

25

30

8

2

75

14

50

33

3

76

12

41

17

4

25

33

25

10

 

 

 

 Q.3 Analyze the 23 factorial experiments given below and state your conclusion.


Block

treatments

I

(npk)

49.3

(1)

47.2

(k)

45.3

(np)

63.4

(p)

44.7

(n)

62.7

(nk)

57.9

(pk)

50.6

II

(p)

56.6

(nk)

50.2

(k)

55.8

(np)

52.3

(1)

51

(npk)

60

(pk)

49

(n)

60.3

III

(p)

63.3

(npk)

56.8

(nk)

51.1

(1)

51.1

(n)

70.2

(k)

55.3

(pk)

55.2

(np)

59.8

IV

(1)

42.3

(np)

38.2

(npk)

58.5

(n)

61

(nk)

60.3

(pk)

48.5

(p)

42.3

(k)

52.1

 

 Q.4 Analyze the 23 factorial experiments given below and state your conclusion.

 

Factor combination

Replication

I

II

III

IV

1

28

24

27

23

A

42

39

32

40

B

31

28

27

33

C

38

33

35

41

AB

37

34

33

32

BC

30

42

36

34

AC

23

41

27

38

ABC

47

32

37

43

 

 

 

 

 

 ***

 Shikshan Prasarak Santha’s

PADMABHUSHAN VASANTRAODADA PATIL MAHAVIDHYALAYA, KAVATHEMAHANKAL.

DEPARTMENT OF STATISTICS

B.Sc-III: Practical – VI

Expt. No.:- 7                                                                          Date:

Title:  Partial and total confounding

Q.1.The following table gives the plan and yield of an experiment involving 3 factors  n, p and k each at two levels arranged in 6 blocks of 4 plots each.

Replicate-I

Replicate-II

Replicate-III

Block 1

Block-2

Block-3

Block-4

Block-5

Block-6

pk

19

npk

31

n

15

pk

5

p

13

np

17

(1)

15

n

27

npk

17

np

21

k

15

pk

11

nk

19

k 

23

p

11

nk

13

n

17

(1)

11

np

29

p

17

k

13

(1)

9

npk

21

nk

15

 

 

 

 

 

 

 

 Q2. For the following 23 partial confounding design carry out complete analysis.

Block

Replicate II

I

(abc)

(a)

(b)

(c)

29

40

25

40

II

(1)

(ab)

(ac)

(bc)

50

35

30

48

Block

Replicate I

I

(a)

(bc)

(abc)

(1)

35

40

25

31

II

(ac)

(b)

(c)

(ab)

60

50

30

40

Block

Replicate III

I

(ac)

(abc)

(1)

(b)

60

45

40

26

II

(ab)

(bc)

(a)

(c)

35

45

30

40

        

 

 

 

 

       

 


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***
Expt. No. 6

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