 |
Analysis of Data from Designed Experiments |
 |
|
Partially Confounded Factorial Experiment |
Example: An experiment was conducted with 3 factors viz. Varieties (V)(3 levels: karan-3, karan-18 and karan-15), Nitrogen (N)(3 levels: 0, 40 and 80 kg/ha) and Phosphorus(P) (3 levels: 0, 30 and 60 kg/ha) at R.B.S. College, Agra, Uttar Pradesh Centre on Barley in 1979 rabi season. The experiment was conducted to find out the optimum doses of nitrogen and phosphorus on the yield of different varieties of barley using a 3´3´3 partially confounded design in 9 plots per block in 2 replications. The plot size used was 10.00×1.61m2. The yield (in kg/plot) is:
|
REPLICATION 1 (Confounded Interaction: ABC2 i.e. VNP2) |
|||||||||||
|
BLOCK 1 |
BLOCK 2 |
BLOCK 3 |
|||||||||
|
V |
N |
P |
Yield |
V |
N |
P |
Yield |
V |
N |
P |
Yield |
|
2 |
1 |
2 |
0.50 |
2 |
1 |
1 |
0.49 |
2 |
1 |
3 |
0.60 |
|
1 |
2 |
2 |
0.97 |
1 |
2 |
1 |
0.97 |
1 |
2 |
3 |
1.10 |
|
2 |
2 |
3 |
0.75 |
2 |
2 |
2 |
0.98 |
2 |
2 |
1 |
0.70 |
|
3 |
1 |
3 |
1.21 |
3 |
1 |
2 |
0.81 |
3 |
1 |
1 |
0.74 |
|
1 |
3 |
3 |
1.23 |
1 |
3 |
2 |
1.13 |
1 |
3 |
1 |
1.08 |
|
3 |
2 |
1 |
0.98 |
3 |
2 |
3 |
1.67 |
3 |
2 |
2 |
1.40 |
|
2 |
3 |
1 |
1.10 |
2 |
3 |
3 |
1.40 |
2 |
3 |
2 |
1.35 |
|
3 |
3 |
2 |
1.00 |
3 |
3 |
1 |
1.00 |
3 |
3 |
3 |
2.00 |
|
1 |
1 |
1 |
0.50 |
1 |
1 |
3 |
0.73 |
1 |
1 |
2 |
0.60 |
|
REPLICATION 2 (Confounded Interaction: ABC, i.e. VNP) |
|||||||||||
|
BLOCK 1 |
BLOCK 2 |
BLOCK 3 |
|||||||||
|
V |
N |
P |
Yield |
V |
N |
P |
Yield |
V |
N |
P |
Yield |
|
1 |
1 |
1 |
0.48 |
2 |
1 |
2 |
0.50 |
1 |
2 |
1 |
0.87 |
|
1 |
2 |
3 |
1.25 |
2 |
3 |
3 |
1.45 |
1 |
1 |
2 |
0.65 |
|
2 |
3 |
1 |
0.93 |
1 |
3 |
1 |
1.32 |
3 |
1 |
3 |
1.30 |
|
3 |
3 |
3 |
2.00 |
1 |
1 |
3 |
0.85 |
1 |
3 |
3 |
1.55 |
|
1 |
3 |
2 |
1.35 |
2 |
2 |
1 |
0.70 |
2 |
1 |
1 |
0.45 |
|
3 |
2 |
1 |
1.30 |
3 |
2 |
3 |
1.92 |
3 |
2 |
2 |
1.85 |
|
2 |
1 |
3 |
0.64 |
3 |
3 |
2 |
2.00 |
3 |
3 |
1 |
2.00 |
|
2 |
2 |
2 |
0.85 |
3 |
1 |
1 |
1.07 |
2 |
2 |
3 |
1.25 |
|
3 |
1 |
2 |
1.16 |
1 |
2 |
2 |
1.00 |
2 |
3 |
2 |
1.40 |
Here
levels of different factors have been coded as
|
Factor |
Original
Level |
Coded
Level |
|
Variety |
Karan-3 |
1 |
|
Karan-18 |
2 |
|
|
Karan-15 |
3 |
|
|
Nitrogen |
0
kg/ha |
1 |
|
40
kg/ha |
2 |
|
|
80
kg/ha |
3 |
|
|
Phosphorus |
0
kg/ha |
1 |
|
30
kg/ha |
2 |
|
|
60
kg/ha |
3 |
(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 varieties, nitrogen and phosphorus and their 2-factor and 3-factor interactions.
2. Identify the best levels of varieties, nitrogen and phosphorus and combinations of two factors.
3. Perform the analysis of variance for testing the significance of treatment combinations and identify the best treatment combination.
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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for analysis of data from designed experiments:
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