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Analysis of Data from Designed Experiments

Balanced Confounded Factorial Experiment with Extra Treatment  

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To test the significance of 19 treatment combinations and identify the best treatment combination and to compare all the 18 treatment combinations with the control treatment requires analysis to be performed on treatment combinations. Therefore, 19 treatment combinations are recoded as:

 

N

P

K

Treatment
(Renumbered)

40

0

0

1

40

0

40

2

40

40

0

3

40

40

40

4

40

80

0

5

40

80

40

6

80

0

0

7

80

0

40

8

80

40

0

9

80

40

40

10

80

80

0

11

80

80

40

12

120

0

0

13

120

0

40

14

120

40

0

15

120

40

40

16

120

80

0

17

120

80

40

18

0

0

0

19

 

Using the procedure of block designs with factorial structure, the contrasts for main effects and interactions are:

 

N:

1

1

1

1

1

1

-1

-1

-1

-1

-1

-1

0

0

0

0

0

0

0

1

1

1

1

1

1

1

1

1

1

1

1

-2

-2

-2

-2

-2

-2

0

P:

1

1

-1

-1

0

0

1

1

-1

-1

0

0

1

1

-1

-1

0

0

0

1

1

1

1

-2

-2

1

1

1

1

-2

-2

1

1

1

1

-2

-2

0

K:

1

-1

1

-1

1

-1

1

-1

1

-1

1

-1

1

-1

1

-1

1

-1

0

NP:

1

1

-1

-1

0

0

-1

-1

1

1

0

0

0

0

0

0

0

0

0

1

1

1

1

-2

-2

-1

-1

-1

-1

2

2

0

0

0

0

0

0

0

1

1

-1

-1

0

0

1

1

-1

-1

0

0

-2

-2

2

2

0

0

0

1

1

1

1

-2

-2

1

1

1

1

-2

-2

-2

-2

-2

-2

4

4

0

NK:

1

-1

1

-1

1

-1

-1

1

-1

1

-1

1

0

0

0

0

0

0

0

1

-1

1

-1

1

-1

1

-1

1

-1

1

-1

-2

2

-2

2

-2

2

0

PK:

1

-1

-1

1

0

0

1

-1

-1

1

0

0

1

-1

-1

1

0

0

0

1

-1

1

-1

-2

2

1

-1

1

-1

-2

2

1

-1

1

-1

-2

2

0

NPK:

1

-1

-1

1

0

0

-1

1

1

-1

0

0

0

0

0

0

0

0

0

1

-1

1

-1

-2

2

-1

1

-1

1

2

-2

0

0

0

0

0

0

0

1

-1

-1

1

0

0

1

-1

-1

1

0

0

-2

2

2

-2

0

0

0

1

-1

1

-1

-2

2

1

-1

1

-1

-2

2

-2

2

-2

2

4

-4

0

Control vs rest

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

-18

 

The analysis of the data is performed using PROC GLM of SAS. The SAS commands are given in the sequel.

 

Data Input:

For performing analysis, input the data in the following format. 

{Here the replication is termed as rep, block as blk treatment as trt and the three factors as N, P and K. It may however, be noted that one can retain the same name or can code in any other fashion}.

 

Prepare a SAS data file using

 

Options linesize=72;

data ludh98k;  /*one can enter any other name for data*/

input rep blk N P K trt yield;   

cards;

1          1          40        0          0          1          7.79

1          1          120      80        0          17        10.30

1          1          40        80        40        6          10.08

1          1          120      40        40        16        11.66

1          1          80        0          40        8          9.13

1          1          80        40        0          9          10.56

1          1          0          0          0          19        4.75

1          2          40        0          40        2          6.12

1          2          120      0          0          13        8.44

1          2          120      80        40        18        11.44

1          2          80        40        40        10        9.13

1          2          80        80        0          11        9.40

1          2          40        40        0          3          6.85

1          2          0          0          0          19        4.22

1          3          80        0          0          7          6.25

1          3          120      0          40        14        7.78

1          3          40        40        40        4          6.66

1          3          80        80        40        12        9.42

1          3          40        80        0          5          6.50

1          3          120      40        0          15        11.82

1          3          0          0          0          19        2.82

2          1          120      0          0          13        7.86

2          1          120      40        40        16        10.15

2          1          40        80        40        6          7.50

2          1          80        0          40        8          7.89

2          1          80        80        0          11        8.00

2          1          40        40        0          3          6.40

2          1          0          0          0          19        4.57

2          2          120      0          40        14        8.50

2          2          80        80        40        12        9.86

2          2          40        40        40        4          7.70

2          2          120      80        0          17        10.79

2          2          80        40        0          9          7.87

2          2          40        0          0          1          6.30

2          2          0          0          0          19        4.22

2          3          80        0          0          7          7.00

2          3          40        80        0          5          8.00

2          3          120      80        40        18        10.90

2          3          40        0          40        2          6.62

2          3          80        40        40        10        9.62

2          3          120      40        0          15        9.50

2          3          0          0          0          19        2.22

3          1          80        80        0          11        10.00

3          1          120      80        40        18        10.86

3          1          40        40        40        4          7.58

3          1          80        0          40        8          6.35

3          1          120      40        0          15        9.40

3          1          40        0          0          1          5.94

3          1          0          0          0          19        3.26

3          2          120      0          40        14        9.00

3          2          40        80        40        6          8.80

3          2          80        40        40        10        9.53

3          2          120      80        0          17        10.56

3          2          40        40        0          3          7.07

3          2          80        0          0          7          6.00

3          2          0          0          0          19        2.64

3          3          80        40        0          9          7.20

3          3          120      0          0          13        8.36

3          3          40        0          40        2          6.05

3          3          80        80        40        12        10.45

3          3          120      40        40        16        10.10

3          3          40        80        0          5          7.50

3          3          0          0          0          19        3.50

4          1          80        80        0          11        7.97

4          1          80        40        40        10        7.18

4          1          40        80        40        6          6.16

4          1          40        0          0          1          4.95

4          1          120      40        0          15        10.12

4          1          120      0          40        14        7.15

4          1          0          0          0          19        1.98

4          2          80        0          0          7          6.65

4          2          40        40        0          3          6.66

4          2          80        80        40        12        7.90

4          2          120      40        40        16        10.10

4          2          40        0          40        2          6.49

4          2          120      80        0          17        10.30

4          2          0          0          0          19        1.76

4          3          80        0          40        8          6.12

4          3          40        40        40        4          5.80

4          3          120      80        40        18        10.06

4          3          120      0          0          13        7.37

4          3          80        40        0          9          7.24

4          3          40        80        0          5          7.70

4          3          0          0          0          19        1.62

;

 

/* Perform the analysis of the main effects and the interactions of the data, test the significance of 19 treatment combinations and identify the best treatment combination and to compare all the 18 treatment combinations with the control treatment using the following statements. */

 

proc glm;

class rep blk trt;

model yield = rep blk(rep) trt;

lsmeans trt/pdiff;

 

contrast 'N trt 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0 ,

                    trt 1 1 1 1 1 1 1 1 1 1 1 1 -2 -2 -2 -2 -2 -2 0 ;                                                     

contrast 'P'  trt 1 1 -1 -1 0 0 1 1 -1 -1 0 0 1 1 -1 -1 0 0 0 ,

                    trt 1 1 1 1 -2 -2 1 1 1 1 -2 -2 1 1 1 1 -2 -2 0;

                                                                                                                                               

Contrast 'K trt 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 0;

                                                                                                                                   

Contrast 'NP' trt 1 1 -1 -1 0 0 -1 -1 1 1 0 0 0 0 0 0 0 0 0,

                     trt 1 1 1 1 -2 -2 -1 -1 -1 -1 2 2 0 0 0 0 0 0 0,

                     trt 1 1 -1 -1 0 0 1 1 -1 -1 0 0 -2 -2 2 2 0 0 0,

                     Trt 1 1 1 -2 -2 1 1 1 1 -2 -2 -2 -2 -2 -2 4 4 0;

                                                                                                                                               

Contrast 'NK' trt 1 -1 1 -1 1 -1 -1 1 -1 1 -1 1 0 0 0 0 0 0 0,

                      trt 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 -2 2 -2 2 -2 2 0;

                                                                                                                                   

Contrast 'PK' trt 1 -1 -1 1 0 0 1 -1 -1 1 0 0 1 -1 -1 1 0 0 0,

                      trt 1 -1 1 -1 -2 2 1 -1 1 -1 -2 2 1 -1 1 -1 -2 2 0;

                                                                                                                                   

Contrast 'NPK' trt 1 -1 -1 1 0 0 -1 1 1 -1 0 0 0 0 0 0 0 0 0,

                        trt 1 -1 1 -1 -2 2 -1 1 -1 1 2 -2 0 0 0 0 0 0 0,

                        trt 1 -1 -1 1 0 0 1 -1 -1 1 0 0 -2 2 2 -2 0 0 0,

                        trt 1 -1 1 -1 -2 2 1 -1 1 -1 -2 2 -2 2 -2 2 4 -4 0;          

Contrast 'Control vs rest' trt 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 -18;

run;  

 

Data File

 

Result File

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For exposure on SAS, SPSS, 

MINITAB, SYSTAT and  

MS-EXCEL for analysis of 

data from designed experiments:

 

Please see Module I of Electronic Book II: Advances in Data Analytical Techniques

available at Design Resource Server  (www.iasri.res.in/design)