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SPSSMixed

# SPSSMixed - Mixed Analysis of Variance Models with SPSS...

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1 Mixed Analysis of Variance Models with SPSS Robert A.Yaffee, Ph.D. Statistics, Social Science, and Mapping Group Information Technology Services/Academic Computing Services Office location: 75 Third Avenue, Level C-3 Phone: 212-998-3402

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2 Outline 1. Classification of Effects 2. Random Effects 1. Two-Way Random Layout 2. Solutions and estimates 3. General linear model 1. Fixed Effects Models 1. The one-way layout 4. Mixed Model theory 1. Proper error terms 5. Two-way layout 6. Full-factorial model 1. Contrasts with interaction terms 2. Graphing Interactions
3 Outline-Cont’d Repeated Measures ANOVA Advantages of Mixed Models over GLM.

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4 Definition of Mixed Models by their component effects 1. Mixed Models contain both fixed and random effects 1. Fixed Effects : factors for which the only levels under consideration are contained in the coding of those effects 2. Random Effects: Factors for which the levels contained in the coding of those factors are a random sample of the total number of levels in the population for that factor.
5 Examples of Fixed and Random Effects 1. Fixed effect : 1. Sex where both male and female genders are included in the factor, sex. 2. Agegroup: Minor and Adult are both included in the factor of agegroup 1. Random effect: 1. Subject: the sample is a random sample of the target population

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6 Classification of effects 1. There are main effects: Linear Explanatory Factors 2. There are interaction effects: Joint effects over and above the component main effects.
7 Interactions are Crossed Effects Variable Y Variable X Level 1 Level 2 Level 3 Level 4 Level 1 Level 2 Level 3 X11 X12 X13 X14 X21 X22 X23 X24 X31 X32 X33 X34 All of the cells are filled Each level of X is crossed with each level of Y

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8 Classification of Effects- cont’d Hierarchical designs have nested effects. Nested effects are those with subjects within groups. An example would be patients nested within doctors and doctors nested within hospitals This could be expressed by patients(doctors) doctors(hospitals)
9 Hospital 1 Hospital 2 Doctor1 Doctor 2 Doctor 3 Doctor 4 Doctor 5 Pat 1 Pat 2 Pat 3 Pat 4 Pat 5 Pat 6 Pat 7 Pat 8 Nesting of patients within Doctors and Doctors within Hospitals

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10 Between and Within- Subject effects Such effects may sometimes be fixed or random. Their classification depends on the experimental design Between-subjects effects are those who are in one group or another but not in both. Experimental group is a fixed effect because the manager is considering only those groups in his experiment. One group is the experimental group and the other is the control group. Therefore, this grouping factor is a between- subject effect. Within-subject effects are experienced by subjects repeatedly over time. Trial is a random effect when there are several trials in the repeated measures design; all subjects experience all of the trials. Trial is therefore a within-subject effect.
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