be careful about the text treatment of this 1. what is blocking? blocking is: a way to control for...
DESCRIPTION
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. 3TRANSCRIPT
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Randomized Complete Block DesignsBe 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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ExamplesHospitals- 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 InferenceBlocks 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
2 2
2 2
2 2
2 2
2 2
2 2
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P PD P
T TD T
PT PTD PT
PD PD
TD TD
PTD PTD
MS d
MS d
MS d
MS
MS
MS
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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.