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Analysis of Data from Designed Experiments

Factorial RCB Design 

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Example: An experiment was conducted at Crop Research Center, G.B.P.U.A.T., Pantnagar, Uttar Pradesh on bengal gram in rabi season 2003 using a  factoria   experiment  with  three  factors  viz., Farmyard Manure (2 levels:0 and 50 q/ha),   Phosphorus (3 levels:0, 20 and 40 kg/ha) and Phosphorus Solublizing Bacteria (2 levels: control and 20 gm/kg of seed as seed inoculation).  The main  objective of  the  experiment was to study the  effect of   Farmyard  Manure  (FYM),   Phosphorus (P) and  Phosphate  Solublizing  Bacteria (PSB)  on   productivity of  bengal  gram.  The experiment was conducted in a randomized complete block  design in 4  replications with 12 plots per replication of net plot size as 5.001.80m2. The yield (in kg/plot) are given as below:

Yield in kg/plot 

     

Replication 1

Replication 2

FYM

P

PSB

Yield

FYM

P

PSB

Yield

1

1

1

0.70

1

1

1

0.98

1

1

2

1.13

1

1

2

1.13

1

2

1

1.23

1

2

1

1.18

1

2

2

1.25

1

2

2

1.13

1

3

1

1.25

1

3

1

1.26

1

3

2

1.25

1

3

2

1.25

2

1

1

0.83

2

1

1

0.93

2

1

2

1.23

2

1

2

0.88

2

2

1

1.18

2

2

1

1.50

2

2

2

0.88

2

2

2

1.30

2

3

1

1.63

2

3

1

1.38

2

3

2

1.48

2

3

2

1.43

 

Replication 3

Replication 4

FYM

P

PSB

Yield

FYM

P

PSB

Yield

1

1

1

0.90

1

1

1

0.73

1

1

2

1.10

1

1

2

1.25

1

2

1

1.10

1

2

1

1.43

1

2

2

0.88

1

2

2

1.25

1

3

1

1.35

1

3

1

1.10

1

3

2

1.35

1

3

2

1.75

2

1

1

1.10

2

1

1

0.98

2

1

2

1.03

2

1

2

1.38

2

2

1

1.30

2

2

1

1.35

2

2

2

0.88

2

2

2

1.43

2

3

1

1.38

2

3

1

1.30

2

3

2

1.43

2

3

2

1.50

 

Here levels of different factors have been coded as

Factor

Original Data

Coded Level

Farmyard Manure

0 q/ha

1

50 q/ha

2

Phosphorus

0 kg/ha

1

20 kg/ha

2

40 kg/ha

3

Phosphate Solublizing Bacteria

0 gm/ha

1

20 gm/ha

2

MS-EXCEL DATA FILE

(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 farmyard manure, phosphorus, phosphorus solublizing bacteria and their 2-factor and 3-factor interactions.

2.      Identify the best levels of farmyard manure, phosphorus and phosphorus solublizing bacteria and combinations of two factors.

3.      Perform the analysis of variance for testing the significance of treatment combinations and identify the best treatment combination.

4.      Compare the treatment combinations with and without farmyard manure.

5.      Compare the treatments with and without phosphorus solublizing bacteria.

 

 

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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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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)