Transcript Balanced Incomplete Block Designs

Lecture 9
• Last day: 3.2-3.5
• Today: Finish last day and start 3.6-3.8, 3.10-3.12
• Next day:
• Assignment #2: Chapter 2: 6, 15 (treat tape speed and laser power as
qualitative factors), 27, 30, 32, and 36….DUE Thursday
One-at-a-Time Experiments
• Have discussed the factorial layout for experimentation
– all level combinations
– m replicates
– performed in random order
• Another obvious strategy is call the “one-factor-at-a-time approach”
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identify the most important factor,
investigate this factor by itself, keeping other factors fixed,
decide on optimal level for this factor, and fix it at this level, and
move on to the next most important factor and repeat 2-3
Example:
• Suppose have 2 factors A and B, each with 2-levels (-1,+1)
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Comments
• Disadvantages of the on-factor-at-a-time approach
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less efficient than factorial experiments
interactions may cause misleading conclusions
conclusions are less general
may miss optimal settings
Assessing Effect Significance
• For replicated experiments, can use regression to determine important
effects
• Can also use a graphical procedure
• The graphical procedure can be used for replicated and replicated
factorial experiments
Normal and Half-Normal Probability Plots
• Graphical method for assessing which effects are important are based
on normal probability plots (a.k.a normal qq-plots)
• Let ˆ(1)  ˆ( 2)  ...  ˆ( I ) be the sorted (from smallest to largest) effect
estimates
i 1
• Plot ˆ( i ) versus  1 
 , where  represents the cumulative
 Iof the standard normal (N(0,1)) distribution
distribution function
Normal and Half-Normal Probability Plots
• That is, we plot the quantiles of our sample of effects versus the
corresponding quantiles of the standard normal
• If no effect is important then the sample of effects appear to be a
random sample from a normal distribution…we observe:
• Otherwise:
Normal and Half-Normal Probability Plots
• Why does this work?
Normal and Half-Normal Probability Plots
• Half-Normal Plots
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Example: Epitaxial Growth Layer Experiment
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Q u a n tile s
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