
1 :

Mixed Designs:Between and Within Psy 420
Ainsworth 

2 :

Mixed Between and Within Designs Conceptualizing the Design
Types of Mixed Designs
Assumptions
Analysis
Deviation
Computation
Higher order mixed designs
Breaking down significant effects 

3 :

Conceptualizing the Design This is a very popular design because you are combining the benefits of each design
Requires that you have one between groups IV and one within subjects IV
Often called “Splitplot” designs, which comes from agriculture
In the simplest 2 x 2 design you would have 

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Conceptualizing the Design In the simplest 2 x 2 design you would have subjects randomly assigned to one of two groups, but each group would experience 2 conditions (measurements) 

5 :

Conceptualizing the Design Advantages
First, it allows generalization of the repeated measures over the randomized groups levels
Second, reduced error (although not as reduced as purely WS) due to the use of repeated measures
Disadvantages
The addition of each of their respective complexities 

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Conceptualizing the Design Types of Mixed Designs
Other than the mixture of any number of BG IVs and any number of WS IVs…
Pretest Posttest Mixed Design to control for testing effects


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Assumptions Normality of Sampling Distribution of the BG IVs
Applies to the case averages (averaged over the WS levels)
Homogeneity of Variance
Applies to every level or combination of levels of the BG IV(s) 

8 :

Assumptions Independence, Additivity, Sphericity
Independence applies to the BG error term
But each WS error term confounds random variability with the subjects by effects interaction
So we need to test for sphericity instead; the test is on the average variance/covariance matrix (over the levels of the BG IVs)


9 :

Assumptions Outliers
Look for them in each cell of the design
Missing data
Causes the same problems that they did in the BG and WS designs separately
Data points missing across the WS part can be estimated as discussed previously
Missing data in the randomized groups part causes nonorthogonality 


11 :

Sources of Variance SST=SSBG+SSWS
What are the sources of variance?
A
S/A
B
AB
BxS/A
T
Degrees of freedom? 

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Example – Books by Month Example:
Imagine if we designed the previous research study concerning reading different novels over time
But instead of having everyone read all of the books for three months we randomly assign subjects to three different books and have them read for three months 


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Sums of Squares  Deviation The total variability can be partitioned into A, B, AB, S/A, and B*S/A







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Sums of Squares  Computational What are the degrees of freedom?
And convert them into the formulas
A = a  1
S/A = a(s – 1) = as  a
B = b  1
AB = (a – 1)(b – 1)
BxS/A = a(b – 1)(s – 1)
T = abs – 1 or N  1





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Results – ANOVA summary table 

25 :

Higher order mixed designs 

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Breaking down significant effects Between Groups IV(s)
If you have a significant BG main effect(s) they need to be broken down to find which levels are different
The comparisons are done the same way as completely BG comparisons
The BG comparison error term is the same for all BG comparisons 

27 :

Breaking down significant effects Within Groups Variables
If a WG main effect is significant it also needs to be followed by comparisons
WG comparisons differ from BG variables in that a separate error term needs to be generated for each comparison
Instead of the Fcomp formula you would actually rearrange the data into a new data set


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Breaking down significant effects Example 

29 :

Breaking down significant effects 

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Breaking down significant effects Interactions
Purely BG interactions can be treated with simple effects, simple contrasts and interaction contrasts using the Fcomp formula, the same error term each time
Purely WG and mixed BG/WG interactions require a new error term for each simple effect, simple contrast and interaction contrast (leave it to SPSS) 
