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Analysis of Data from Designed Experiments

Response Surface Design

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Example: An experiment was conducted at Division of Agronomy, Indian Agricultural Research Institute, New Delhi to obtain the optimum combination of Nitrogen (4 levels: 0, 50, 100, 150 kg/ha) and Sulphur (4 levels: 0, 20, 40, 60 kg/ha) for maximizing the yield of paddy crop. The plot size used was 4 2.2 m2.The experiment was conducted using a RCB design in 3 replications. The analysis of variance of the data revealed that replications are not significantly different, i.e. the replication mean square was small in comparison to error mean square. The main objective of the experiment was to obtain the optimum combination of nitrogen and sulphur that maximizes the yield. The treatment combinations tried and average yield of paddy in kg/ha are:

                                                             

Nitrogen

Sulphur

Yield

 

Nitrogen

Sulphur

Yield

0

0

4121.21

100

0

6761.36

0

20

4678.03

100

20

6916.67

0

40

4742.42

100

40

6852.27

0

60

4727.27

100

60

6810.61

50

0

6083.33

150

0

6174.24

50

20

6041.67

150

20

7022.73

50

40

6223.49

150

40

7003.79

50

60

6715.91

150

60

6943.18

MS-EXCEL DATA FILE  

1. Fit a second order response surface using the above data.

2. Obtain the co-ordinates of the stationary point.

3. Also find the nature of the stationary point.  

 

 

 

Analysis Using SAS                                                                               Analysis Using SPSS

 

 

 

  

 

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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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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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Other Designed Experiments
    
(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 Resources Server (www.iasri.res.in/design)