Randomized Complete Block DesignsBe careful about the text treatment of this

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.

Are Blocks Factors?Short answer: Sort of.Long answer: Blocks are an indication that

Experimental Units/Experimental Conditions vary from one run to the next. They are really nuisance parameters which we do not wish to confound with the Factors we are really interested in.

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.

More Examples……?.

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).

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.

Consider Problem 5.21 with Day Fixed

Correct F-tests for Fixed Effects are by their Interaction with Day with Day Random

EMS Day Random and number of Days=d

2 2

2 2

2 2

2 2

2 2

2 2

3 3

3 3

3

3

P PD P

T TD T

PT PTD PT

PD PD

TD TD

PTD PTD

MS d

MS d

MS d

MS

MS

MS

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.

What happens if we include Day in the Model but not the Day Interaction terms? (Author suggests this)

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.