Introduction to 2^3 Factorial Experiment
lecture - 26
The 2^3 factorial experiment is the extension of 2^2 factorial experiment to three factors named A, B, C and each factor at two levels say a0, a1, b0, b1, c0, c1. In this experiment 3 factors each at two levels are analyzed.
The 2^3 factorial experiment is represented by the following linear statistical model:
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The standard form of 2^3 factors combinations are:
|
1 |
a |
b |
ab |
c |
ac |
bc |
abc |
Assume that the total response values are:
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The response values can be arranged in a
three-dimensional contingency table as:
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The sums of squares of total, blocks and treatment can be
computed as:
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The sums of squares A, B and interaction effect can also be
computed as:
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ANOVA Table:
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Where:
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|
Replicate |
a |
b |
c |
abc |
1 |
ab |
ac |
bc |
|
1 |
1.9 |
1.6 |
2.1 |
3.8 |
1.3 |
3.2 |
2.8 |
3.2 |
|
2 |
3.0 |
2.7 |
3.0 |
4.8 |
2.2 |
4.1 |
3.9 |
4.1 |
|
3 |
4.0 |
3.8 |
2.1 |
5.9 |
4.2 |
5.2 |
5.1 |
5.0 |
|
4 |
1.9 |
1.5 |
2.0 |
3.9 |
1.1 |
3.4 |
3.0 |
3.0 |
Write statistical model for the above stated
experiment and test the significance of factors effects and interaction
effects.
Solution: The statistical model of the above
experiment (2^3 Factorial Experiment
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vi.
Remarks:
The
effects pf factor A, B, C and their order interaction (ABC) are significant.
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Solution: The data look like from homogeneous experimental units. So, we are using CRD 2^2 factorial experiment.
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ANOVA
Table:
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vi.
Remarks:
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