Chapter 21 Randomized Complete Block Designs Lecture 13 April 5 2006 Psych 791 Slide 1 of 32 Today s Class Overview Blocking Randomized Complete Block Designs Our example today will be from SAS http v8doc sas com sashtml stat chap17 sect4 htm Today s Class Blocking Model Fitting the Model ANOVA Table F test Model Fit Post Hoc More Than One Block More Than One Replication in Block More Than One Treatment Design Matrix Wrapping Up Slide 2 of 32 Blocking Slide 3 of 32 What is Blocking The idea of blocking for a variable is to control the levels of a factor that are not normally controlled This blocking variable will reduce the amount of experimental error variance in the model It will also increase the validity of your results For example if you have a design where one of the factor is gender and do not block for gender If the experimental groups do not have an equal number of males and females in them how do you know if the differences are due to the treatment or to gender The answer is you don t so block Overview Blocking What is Blocking Designing a Study Blocking Criteria Design continued Advantages to Blocking Disadvantages to Blocking Model Fitting the Model ANOVA Table F test Model Fit Post Hoc More Than One Block More Than One Replication in Block More Than One Treatment Design Matrix Wrapping Up Slide 4 of 32 Designing a Study This chapter deals with a specific design called a Randomized Complete Block Design Breaking this down Overview Blocking What is Blocking Designing a Study Blocking Criteria Block There is a blocking variable Complete Every experimental condition is contained within each blocking level Randomized Subjects are randomly assigned to an experimental condition within block Design continued Advantages to Blocking Disadvantages to Blocking Model Fitting the Model ANOVA Table F test Model Fit Post Hoc More Than One Block More Than One Replication in Block Let us suppose that gender is our blocking variable we determine our experimental conditions and then as we collect our subjects an equal amount from each gender we randomly assign them to a treatment group More Than One Treatment Design Matrix Wrapping Up Slide 5 of 32 Blocking Criteria The purpose of blocking is to sort subjects in groups where each are homogenous with respect to the response variable to make the differences between the groups as great as possible These are things that are not usually controlled but which you think may have an effect on the outcome variable There are two types of criteria for which to block Overview Blocking What is Blocking Designing a Study Blocking Criteria Design continued Advantages to Blocking Disadvantages to Blocking Model Fitting the Model ANOVA Table Characteristics of Subjects For persons age income intelligence education attitudes etc For something like region of the country population average income etc Characteristics of the Experiment observer time of processing machine measuring instrument batch etc F test Model Fit Post Hoc More Than One Block More Than One Replication in Block More Than One Treatment Design Matrix Wrapping Up Slide 6 of 32 Design continued The design of a blocking criteria really takes some pre thought It means that in advance you think that some variable might have an effect on the outcome response Usually it can be drawn from past research If something was shown to effect the response variable you can block for it in a sense control for that variable to be sure that your experimental factor is really effecting your response Overview Blocking What is Blocking Designing a Study Blocking Criteria Design continued Advantages to Blocking Disadvantages to Blocking Model Fitting the Model ANOVA Table F test Model Fit Post Hoc More Than One Block More Than One Replication in Block More Than One Treatment Design Matrix Wrapping Up Slide 7 of 32 Advantages to Blocking Overview It can provide more precise results It can accommodate any number of treatments or replications Do not need equal sample size of treatment level factors Analysis is simple really same as in previous chapters If a particular level of the blocking variable needs to be dropped it does not ruin the results Can deliberately induce variability by altering the levels of the blocking variable Blocking What is Blocking Designing a Study Blocking Criteria Design continued Advantages to Blocking Disadvantages to Blocking Model Fitting the Model ANOVA Table F test Model Fit Post Hoc More Than One Block More Than One Replication in Block More Than One Treatment Design Matrix Wrapping Up Slide 8 of 32 Disadvantages to Blocking If missing observations in a block analysis becomes complicated Degrees of freedom for model are reduced because you lose some for the blocking variable More assumptions Difficult to make inferences about blocking variable Overview Blocking What is Blocking Designing a Study Blocking Criteria Design continued Advantages to Blocking Disadvantages to Blocking Model Fitting the Model ANOVA Table F test Model Fit Post Hoc More Than One Block More Than One Replication in Block More Than One Treatment Design Matrix Wrapping Up Slide 9 of 32 Model for RCBD This is the model should look fairly similar Overview Yij i j ij Blocking Model Model for RCBD Where is a constant Model Notes Fitting the Model ANOVA Table F test i constant for the block row effects with i 0 P j constant for treatment effects with j 0 ij independent N 0 2 Model Fit Post Hoc P More Than One Block More Than One Replication in Block More Than One Treatment Design Matrix Wrapping Up Slide 10 of 32 Model Notes As you can see this model is the same as we used for the two factor design with no interaction term The only thing that changed is our greek letters so don t be fooled by the name differences We will NEVER fit a model with an interaction between a blocking variable and another variable The blocking effect is an essence a way to control the error variance So we take out the piece of the error variance associated with the variable so we can concentrate on the effect of the treatment Overview Blocking Model Model for RCBD Model Notes Fitting the Model ANOVA Table F test Model Fit Post Hoc More Than One Block More Than One Replication in Block More Than One Treatment Design Matrix Wrapping Up Slide 11 of 32 Fitting the Model Fitting the model is done in the same way as we did for the last chapter without the interaction term We define our parameters in terms of our s then we substitute in our Y Our