MANE 6313
Week 4, Module E
Student Learning Outcome
Analyze simple comparative experiments and experiments with a single factor.
Module Learning Outcome
Interpret multiple comparisons of treatments and treatments to a control.
Resources for the Week 4, Module E micro-lecture are:
Contrasts
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A hypothesis from a linear combination of the parameters \(C=\sum_{i=1}^ac_iy_{i.}\) with the constraint that \(\sum_{i=1}^ac_i=0\)
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Can be extended to multiple comparisons using orthogonal contrasts
Multiple Comparisons
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Used to test \(H_0:\mu_i=\mu_j\) for all \(i\neq j\)
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Only used if \(H_0\) is rejected
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There are four methods presented in the textbook
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LSD method
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Duncan's multiple range test
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Newman-Keuls test
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Tukey's test
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All methods control family-wise error rate not individual error rate
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Read the section on "which method do I use?"
Tukey Multiple Comparison Example
Comparison to a Control - Dunnett's Test
- In many experiments, one of the treatments is a control and the analysis is interested in comparing the other treatments to the control
Minitab Demonstration
- Multiple comparisons for mortar problem
- Dunnett's procedure for problem 12.10