Randomized Complete Block Designs Be careful about the

Randomized Complete Block Designs Be careful about the text treatment of this 1

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. 2

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. 3

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. 4

Blocking and Inference Blocks Fixed- Inference is only to the experimental units/conditions under which the Experiment is run, i. e. to these Blocks Random- Inference is to the experimental units/conditions for which these Blocks are representative (whatever that might reasonably be concluded to be). 5

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. 6

Consider Problem 5. 21 with Day Fixed 7

Correct F-tests for Fixed Effects are by their Interaction with Day Random 8

EMS Day Random and number of Days=d 9

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. 10

What happens if we include Day in the Model but not the Day Interaction terms? (Author suggests this) 11

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. 12