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Analysis of Data from Designed Experiments |
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|
Factorial RCB Design |
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 5.00´1.80m2. 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 |
(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.
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:
Please see Module I of Electronic Book II: Advances in Data Analytical Techniques
available at Design Resources Server (www.iasri.res.in/design)