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 2k factorial designs
Resources for the Week 7, Module D micro-lecture are:
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
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
Diagnostics
- The usual diagnostics (residual) analysis should be applied in an unreplicated design