MANE 6313
Week 7, Module D
Student Learning Outcome
- Select an appropriate experimental design with one or more factors,
- Select an appropriate model with one or more factors,
- Evaluate statistical analyses of experimental designs,
- Assess the model adequacy of any experimental design, and
- Interpret model results.
Module Learning Outcome
Describe single replicate of \(2^k\) factorial designs
Single Replicate of \(2^k\)
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Revisiting. Main problem is no estimate of error
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Very common occurrence because replicated experiments are expensive.
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Two approaches to analyzing an unreplicated \(2^k\) design
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Scarcity of effect principles assumes that higher order interactions do not exist. These effects are combined to estimate the SS(error).
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Normal probability plot approach
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Probability Plot Approach
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Recommended by Daniel (1959)
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Generate a normal probability plot for the effect estimates
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For non-significant effect, they will have zero mean and variance \(\sigma^2\). Thus, they will graph as a straight line on normal probability plot.
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Significant effects will have a non-zero mean and lie along a straight line in the normal probability plot
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Half-normal probability plot creates normal probability plot of absolute values of effect estimates
Design Projection
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Hopefully some variables can be discarded from the initial model.
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Whenever a variable is removed from an unreplicated design the resulting design (in fewer variables) is replicated.
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Very useful property that we will use later in the course
Problem 6.32 (9th Edition)
Problem 6.32, Data Table
Problem 6.32, Data Frame
Problem 6.32, Analysis of Variance (full model)
Problem 6.32, Half-Normal Plot
Problem 6.32, Initial Model
Diagnostics
- Residual analysis to confirm model assumptions should be performed
- For this problem, pay attention to the Factor B versus residuals plot