Transcript Randomized Complete Block Designs.pptx

Be careful about the text treatment of this 
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What is Blocking?
Blocking is:
 A way to control for a source of Variation in an
Experiment.
 It may also refer to a Replication of the entire
Experiment.
 It is usually included in the ANOVA Model as a
term.
 Some people handle it in “different” ways.
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Are Blocks Factors?
 Short answer: Sometimes. We may block on Gender in
an experiment and in that case Gender is a factor.
 Long answer: Blocks are an indication that
Experimental Units/Experimental Conditions vary
from one run to the next. They are often nuisance
parameters which we do not wish to confound with the
Factors we are really interested in.
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Examples
 Hospitals- Patient populations and facilities vary.
 Farms- Soil type and Environment vary.
 Greenhouses- Environmental variation.
 Batch-Batches of material may vary from one
production run to the next.
 Basically any Replication of an entire Experiment done
at various times/places.
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Blocking and Inference
Blocks Fixed- Inference is only to the experimental
units/conditions under which the Experiment is run,
i.e. to these Blocks.
Blocks Random- Inference is to the experimental
units/conditions for which these Blocks are
representative (whatever that might reasonably be
concluded to be).
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Recall 5.21 with Day, Temperature and Pressure
We can think of the entire Experiment with
Temperature and Pressure as a Factorial Experiment,
with the entire Experiment replicated on two different
Days. In this case Day is Block.
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Consider Problem 5.21 with Day Fixed
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Correct F-tests for Fixed Effects are by their Interaction
with Day with Day Random
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EMS Day Random and number of Days=d
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MS P   2  3 PD
 3dP
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MST   2  3 TD
 3dT
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MS PT   2   PTD
 dPT
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MS PD   2  3 PD
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MSTD   2  3 TD
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MS PTD   2   PTD
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Allocation of effort
If fixed effects were marginally significant, the EMS
says to add Replications in more Blocks (Days).
Be careful since Replications has multiple meanings.
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What happens if we include Day in the Model but not
the Day Interaction terms? (Author suggests this)
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Why was Interaction no longer significant?
Answer: We inflated the Mean Square Error for
Temp*Pressure by pooling all of the Interaction terms
into Error!
Moral of Story: When deleting terms from the model
you can get misleading results.
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