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Analysis of Data from Designed Experiments

Partially Confounded Factorial Experiment 

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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 333 partially confounded design in 9 plots per block in 2 replications. The plot size used was 10.001.61m2. 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

 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 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.

 

 

 

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Partially Confounded Design Factorial Experiment with Extra Treatments Split Plot Design   Strip Plot Design 

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Descriptive Statistics
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Completely Randomised Design
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Incomplete Block Design
Resolvable Block Design
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Partially Confounded Design
Factorial Experiment with Extra Treatments
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Analysis of Covariance
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Principal Component Analysis
Cluster Analysis
Groups of Experiments
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Other Designed Experiments
    
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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)