MANE 6313

Week 8, Module B

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 new block generation technique.

Resources for the Week 8, Module B micro-lecture are:

• Week 8, Module B Micro-lecture
• Week 8, Module B Marked Notes

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Designing a Blocked Experiment

• Define a linear combination

\[ L=\alpha_1x_1+\alpha_2x_2+\cdots+\alpha_kx_k \]

• We say that \(L\) is the defining contrast

• Represent the treatment levels (\(x_i\)) as 0 (low level) and 1 (high level) and \(\alpha_i\) = 0 or 1

• Choose an effect to confound with blocks

• Calculate the quantity \(L\mbox{ mod } 2\) for each effect

• Examine a \(2^3\) example in two blocks

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Two Block Example

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Reconciling the Two Block Generation Methods

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Summary

• Two techniques have been presented to design experiments in two blocks

• The block that contains \((1)\) is the principal block

• If you can replicate the experiment, use partial confounding to improve your design. For each replicate, select a different effect to generate the blocks. Thus, some information is available for each variable (more difficult to correctly design and analyze).