Analysis of Variance: Factorial Designs

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Analysis of Variance Factorial Designs

• April 17, 2003

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Lecture Outline

• An Example Water Maze Learning what does the
  mouse learn?
• Factorial ANOVA
• Logic
• Main Effects and Interactions
• Computation.
• Simple Effects

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Hmm

• T-Test  
• 1 IV, two Levels
• One-Way ANOVA
• 1 IV, 2 or more Levels
• Factorial ANOVA
• 2 or more IVs, 2 or more Levels 
• (IVs can be between or within)

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Notation

• 2 Way Factorial (2 IVs)
• 3 Way Factorial (3 IVs)
• 4 Way Factorial (4 IVs)
• or
• 2 X 2
• (2 IVs each with 2 levels)
• 3 X 4
• (2 IVs, one with 3 levels, one with 4 levels)
• 2 X 3 X 4
• (3 IVs, one with 2 levels, one with 3 levels,
  one with 4 levels)

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Studying memory in animals Spatial memory
Visible Platform
Water Maze
Hidden Platform
How do the mice solve this task?
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Studying memory in animals Spatial memory
Morris (1981)

• 4 groups of 10 mice were run in a factorial
  experiment.
• Fixed Location - Cue Present a visible platform
  remains in the same spatial location in the pool
  on every trial
• Random Location - Cue Present a visible
  platform is moved to a new spatial location in
  the pool on every trial
• Fixed Location No Cue Present a hidden
  platform remains in the same spatial location in
  the pool on every trial
• Random Location No Cue Present a hidden
  platform remains in the same spatial location in
  the pool on every trial

After Morris (1981)
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Studying memory in animals Spatial memory
Morris (1981)
After Morris (1981)
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Studying memory in animals Spatial memory
Morris (1981)
50
fixed
45
random
40
35
30
Time Spent in Quadrant
25
20
15
10
5
0
cue
no cue
Cue Preset?
After Morris (1981)
9
Studying memory in animals Spatial memory
Morris (1981)
After Morris (1981)
10
Studying memory in animals Spatial memory
Morris (1981)Main Effects and Interaction..
50
fixed
45
random
40
35
30
Time Spent in Quadrant
25
20
15
10
5
0
cue
no cue
Cue Preset?
After Morris (1981)
11
Studying memory in animals Spatial memory
Morris (1981)SPSS
   
   
12
Studying memory in animals Spatial memory
Morris (1981)
After Morris (1981)
13
Studying memory in animals Spatial memory
Morris (1981)Main Effects and Interaction..
50
fixed
45
random
40
35
30
Time Spent in Quadrant
25
20
15
10
5
0
cue
no cue
Cue Preset?
After Morris (1981)
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Between Subjects SS
15
Within Subjects SS
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Factorial SS
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Factorial SS
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Simple Effects

• The effect of one IV at one level of another IV

19
Studying memory in animals Spatial memory
Morris (1981)
After Morris (1981)
20
Studying memory in animals Spatial memory
Morris (1981)Main Effects and Interaction..
50
fixed
45
random
40
35
30
Time Spent in Quadrant
25
20
15
10
5
0
cue
no cue
Cue Preset?
After Morris (1981)