Transcript Latin and Graeco -Latin Squares.pptx

What we give up to do Exploratory Designs
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Hicks Tire Wear Example data
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Linear Model
Yijk    Ci  B j  Pk   ijk
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ANOVA with Main Effects
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It’s an orthogonal design so…
The Type III tests on top match the Type I tests below. Main Effects
Are not confounded with each other.
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We are primarily interested in Brand, but what
about interactions?
If we put in even one interaction, then there are no df for error and this
Interaction is completely confounded with Brand.
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Notice
 One cannot estimate and test Interaction terms since
we do not have enough d.f.
 Interaction terms are confounded with error and other
terms.
 As we shall see later with Fractional Factorials, they are
likely confounded with each other too.
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Brand is the only Fixed Effect for Inference
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Tukey HSD on Tire Wear LS Means
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Residuals vs. Predicted
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Normal Plot of Residuals
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Normality Test
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Hicks Graeco-Latin Square Example
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Basic ANOVA with Main Effects
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Only Time is close to significance so…
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Since this is a screening design…..
 Which variables might we investigate further?
 How might we collect more data?
 What about diagnostics on the model we fit?
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Residuals Vs. Predicted Plot
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Normality Plot
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Normality Test
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What happened with our Diagnostics?
 With Diagnostics we use Residuals as surrogates for
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Experimental Error in our Model
The Diagnostics are based on the assumption that our
Residuals are independently distributed
This assumption was never true in an absolute sense
However, if the df for Error is “large” relative to the
Model df, it is close enough to “true” so that our
Diagnostics make sense
Remember, these designs are meant to screen factors
for further study
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