 |
Analysis of Data from Designed Experiments |
 |
|
Balanced Confounded Factorial Experiment with Extra Treatment |
Analysis Using SPSS
Analysis Using SAS
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 |
|
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;
<<Back
Analysis Using SAS Analysis Using SPSS
Home Descriptive Statistics Tests of Significance Correlation and Regression Completely Randomised Design RCB Design
Incomplete Block Design Resolvable Block Design Augmented Design Latin Square Design Factorial RCB Design
Partially Confounded Design Factorial Experiment with Extra Treatments Split Plot Design Strip Plot Design
Response Surface Design Cross Over Design Analysis of Covariance Diagnostics and Remedial Measures
Principal Component Analysis Cluster Analysis Groups of Experiments Non-Linear Models
Copyright Disclaimer How to Quote this page Report Error Comments/suggestions
(Under Development)
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)