 |
Analysis of Data from Designed Experiments |
 |
|
Balanced Confounded Factorial Experiment with Extra Treatment |
Example: An experiment was conducted at Ludhiana Centre of AICRP on Cropping Systems on Maize crop in 1998 kharif season using a balanced confounded design for factorial experiments with three factors viz., Nitrogen (N)(40, 80 and 120 kg/ha), Phosphorus(P) (0, 40 and 80 kg/ha) and Potassium(K)(0 and 40 kg/ha). These 18 treatment combinations were arranged in 3 blocks of size 6 each with 4 replications. To each of the blocks one control treatment was also added. Therefore, there were 7 plots per block and 21 experimental units in each replication. The yield (in kg/plot) is:
|
Replication
1 |
|||||||||||
|
BLOCK
1 |
BLOCK
2 |
BLOCK
3 |
|||||||||
|
N |
P |
K |
Yield |
N |
P |
K |
Yield |
N |
P |
K |
Yield |
|
40 |
0 |
0 |
7.79 |
40 |
0 |
40 |
6.12 |
80 |
0 |
0 |
6.25 |
|
120 |
80 |
0 |
10.30 |
120 |
0 |
0 |
8.44 |
120 |
0 |
40 |
7.78 |
|
40 |
80 |
40 |
10.08 |
120 |
80 |
40 |
11.44 |
40 |
40 |
40 |
6.66 |
|
120 |
40 |
40 |
11.66 |
80 |
40 |
40 |
9.13 |
80 |
80 |
40 |
9.42 |
|
80 |
0 |
40 |
9.13 |
80 |
80 |
0 |
9.40 |
40 |
80 |
0 |
6.50 |
|
80 |
40 |
0 |
10.56 |
40 |
40 |
0 |
6.85 |
120 |
40 |
0 |
11.82 |
|
0 |
0 |
0 |
4.75 |
0 |
0 |
0 |
4.22 |
0 |
0 |
0 |
2.82 |
|
Replication
2 |
|||||||||||
|
BLOCK
1 |
BLOCK
2 |
BLOCK
3 |
|||||||||
|
N |
P |
K |
Yield |
N |
P |
K |
Yield |
N |
P |
K |
Yield |
|
120 |
0 |
0 |
7.86 |
120 |
0 |
40 |
8.50 |
80 |
0 |
0 |
7.00 |
|
120 |
40 |
40 |
10.15 |
80 |
80 |
40 |
9.86 |
40 |
80 |
0 |
8.00 |
|
40 |
80 |
40 |
7.50 |
40 |
40 |
40 |
7.70 |
120 |
80 |
40 |
10.90 |
|
80 |
0 |
40 |
7.89 |
120 |
40 |
0 |
10.79 |
40 |
0 |
40 |
6.62 |
|
80 |
80 |
0 |
8.00 |
80 |
80 |
0 |
7.87 |
80 |
40 |
40 |
9.62 |
|
40 |
40 |
0 |
6.40 |
40 |
0 |
0 |
6.30 |
120 |
40 |
0 |
9.50 |
|
0 |
0 |
0 |
4.57 |
0 |
0 |
0 |
4.22 |
0 |
0 |
0 |
2.22 |
|
Replication
3 |
|||||||||||
|
BLOCK
1 |
BLOCK
2 |
BLOCK
3 |
|||||||||
|
N |
P |
K |
Yield |
N |
P |
K |
Yield |
N |
P |
K |
Yield |
|
80 |
80 |
0 |
10.00 |
120 |
0 |
40 |
9.00 |
80 |
40 |
0 |
7.20 |
|
120 |
80 |
40 |
10.86 |
40 |
80 |
40 |
8.80 |
120 |
0 |
0 |
8.36 |
|
40 |
40 |
40 |
7.58 |
80 |
40 |
40 |
9.53 |
40 |
0 |
40 |
6.05 |
|
80 |
0 |
40 |
6.35 |
120 |
80 |
0 |
10.56 |
80 |
80 |
40 |
10.45 |
|
120 |
40 |
0 |
9.40 |
40 |
40 |
0 |
7.07 |
120 |
40 |
40 |
10.10 |
|
40 |
0 |
0 |
5.94 |
80 |
0 |
0 |
6.00 |
40 |
80 |
0 |
7.50 |
|
0 |
0 |
0 |
3.26 |
0 |
0 |
0 |
2.64 |
0 |
0 |
0 |
3.50 |
|
Replication
4 |
|||||||||||
|
BLOCK
1 |
BLOCK
2 |
BLOCK
3 |
|||||||||
|
N |
P |
K |
Yield |
N |
P |
K |
Yield |
N |
P |
K |
Yield |
|
80 |
80 |
0 |
7.97 |
80 |
0 |
0 |
6.65 |
80 |
0 |
40 |
6.12 |
|
80 |
40 |
40 |
7.18 |
40 |
40 |
0 |
6.66 |
40 |
40 |
40 |
5.80 |
|
40 |
80 |
40 |
6.16 |
80 |
80 |
40 |
7.90 |
120 |
80 |
40 |
10.06 |
|
40 |
0 |
0 |
4.95 |
120 |
40 |
40 |
10.10 |
120 |
0 |
0 |
7.37 |
|
120 |
40 |
0 |
10.12 |
40 |
0 |
40 |
6.49 |
80 |
40 |
0 |
7.24 |
|
120 |
0 |
40 |
7.15 |
120 |
80 |
0 |
10.30 |
40 |
80 |
0 |
7.70 |
|
0 |
0 |
0 |
1.98 |
0 |
0 |
0 |
1.76 |
0 |
0 |
0 |
1.62 |
Here
levels of different factors have been coded as
|
Factor |
Original
Data |
Coded
Level |
|
Nitrogen |
40
kg/ha |
1 |
|
80
kg/ha |
2 |
|
|
120
kg/ha |
3 |
|
|
Phosphorus |
0
kg/ha |
1 |
|
40
kg/ha |
2 |
|
|
80
kg/ha |
3 |
|
|
Potassium |
0
kg/ha |
1 |
|
40
kg/ha |
2 |
(For performing the analysis using original levels,
change coded levels to original level throughout the steps
discussed in sequel).
1.
Perform the
analysis of variance of the data to test the significance of
the main effects of nitrogen, phosphorus and potassium and
their 2-factor and 3-factor interactions.
2.
Test the
significance of 19 treatment combinations and identify the
best treatment combination.
3.
Compare all the
18 treatment combinations with the control treatment.
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
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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 Resources Server (www.iasri.res.in/design)