SAS Programs and Output for Alternative Experimentals Designs. Section 13-8 in Howell (2010)
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1 SAS Programs and Output for Alternative Experimentals Designs. Section 13-8 in Howell (2010) In Statistical Methods for Psychology (7 th ed.) I discuss various alternative experimental designs involving random effects and nested variables. This document contains the printout from SAS for each of those designs, as well as links to data and SAS code. Some may complain that I did not use SAS Proc Mixed, but that would lead us into a different world, and I didn t think that you were eager to go there right now. Proc Mixed does have some major advantages. For example it does not require complete data and it can handle alternative covariance matrices, but neither of those is an issue for the designs used here. It is also very much more difficult to set up and interpret. SAS Output for Various Models. The Variable Names Change, But Not the Data These analyses A crossed design with a standard fixed model analysis of variance A crossed design with one random factor A nested design with Therapist nested within Gender The relevant data can be found at The SAS code can be found at SAS GLM does not handle random factors well when it comes to deriving error terms. So I have indicated that there are places where the main analysis table should be ignored and the correct analysis is given after that. (SAS probably would not agree with my characterization of their procedures.) Standard Fixed Model 14:21 Friday, March 5, Class Levels Values Condition Age Number of Observations Read 100
2 Dependent Variable: Recall Model <.0001 Error R-Square Coeff Var Root MSE Recall Mean Age <.0001 Condition <.0001 Condition*Age Crossed Design with Random Factor Ignore the first part of this printout because it tests the wrong hypotheses. 14:21 Friday, March 5, 2010 Class Levels Values Subj Case Letter Number of Observations Read 101
3 Dependent Variable: ResponseTime Model Error R-Square Coeff Var Root MSE ResponseTime Mean Case Letter Case*Letter Case*Letter(Subj) Source Case Letter Case*Letter Type III Expected Mean Square Var(Error) + 10 Var(Case*Letter) + Q(Case,Case*Letter(Subj)) Var(Error) + 10 Var(Case*Letter) + 20 Var(Letter) + Q(Case*Letter(Subj)) Var(Error) + 10 Var(Case*Letter) + Q(Case*Letter(Subj)) Case*Letter(Subj) Var(Error) + Q(Case*Letter(Subj)) The following are the correct tests Dependent Variable: ResponseTime Tests of Hypotheses Using the Type III MS for Case*Letter as an Error Term Case Tests of Hypotheses Using the Type III MS for Case*Letter(Subj) as an Error Term Letter <.0001 Case*Letter Therapist Nested Within Gender 14:21 Friday, March 5,
4 Class Levels Values Gender Therapist Number of Observations Read 101 Ignore this analysis and look at the next one Dependent Variable: Effect Model <.0001 Error R-Square Coeff Var Root MSE Effect Mean Gender <.0001 Therapist(Gender) <.0001 Procedure The GLM Source Gender Therapist(Gender) Type III Expected Mean Square Var(Error) + 10 Var(Therapist(Gender)) + Q(Gender) Var(Error) + 10 Var(Therapist(Gender)) Correct Analysis Tests of Hypotheses for Mixed Model Analysis of Variance Dependent Variable: Effect Gender
5 Error Error: MS(Therapist(Gender)) Therapist(Gender) <.0001 Error: MS(Error)
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