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Analysis of Data from Designed Experiments |
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Randomized Complete Block Design |
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Example 2. In order to select suitable Tree species for Fuel, Fodder and Timber an experiment was conducted in a randomized complete block (RCB) design with ten different Tree species and four replications. In this experiment tree species are treatments. The plant height was recorded in cm. The details of the experiment are given below:
| Tree Specie Number | Spacing | Replications | |||
| 1 | 2 | 3 | 4 | ||
| 1 | 4 ´ 4 | 144.44 | 145.11 | 104.00 | 105.44 |
| 2 | 4 ´ 2 | 113.50 | 118.61 | 118.61 | 123.00 |
| 3 | 4 ´ 2 | 60.88 | 90.94 | 80.33 | 92.00 |
| 4 | 4 ´ 2 | 163.44 | 158.55 | 158.88 | 153.11 |
| 5 | 4 ´ 2 | 110.11 | 116.00 | 119.66 | 103.22 |
| 6 | 4 ´ 4 | 260.05 | 102.27 | 256.22 | 217.80 |
| 7 | 4 ´ 2 | 114.00 | 115.16 | 114.88 | 106.33 |
| 8 | 4 ´ 2 | 91.94 | 58.16 | 76.83 | 79.50 |
| 9 | 4 ´ 1 | 156.11 | 177.97 | 148.22 | 183.17 |
| 10 | 4 ´ 2 | 80.20 | 108.05 | 45.18 | 79.55 |
1. Perform the analysis of variance of the data to test whether there is any difference among the tree species so far as height of the tree is concerned.
2. Perform all possible pair wise treatment comparisons and identify the best treatment i.e. the tree species with maximum height. Identify the other treatments which are not significantly different from the best treatment.
3. The Tree species 1, 2, 3, 4, 10 are useful for fuel, fodder and timber and tree numbers 5, 6, 7, 8, 9 are useful for fuel and fodder only. The interest of the experimenter is to test a null hypothesis that the average effect of trees in group one (useful for fuel, fodder, and timber) is equal to the average effect of Trees in group two (useful for fuel and fodder).
4. Compare the effects of Tree species within each group.
5. The experimenter is also interested in testing the following null hypotheses:
i.The effect of Tree species 9 is equal to the average effect of Tree species 1,2,3,4,5,6,7,8,10.
ii.The effect of Tree species 9 is equal to the average effect of Tree species 1,2,3,4.
iii.The effect of Tree species 10 is equal to the average effect of Tree species 1,2,3,4.
iv.The effect of Tree species 9 is equal to the average effect of Tree species 5,6,7,8.
v.The
effect of Tree species 10 is equal to the average effect
of Tree species 5,6,7,8.
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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