Factorial designs

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Factorial designs

• Why factorial designs?
• Effects of combinations of variables,
  interactions of variables
• Factorial nomenclature 2 X 2, 3 X 3 X 2
• Number of numbersnumber of factors
• Value of numbernumber of levels
• Multiply number of conditions or cells in design

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• 2 X 2
• 3 X 3 X 2
• Assignment to conditions
• Randomized groupcompletely randomized factorial
• Matched factorial designform groups based on
  matching and randomly assign to conditions

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The Purpose of Factorial Models

• Two or more variables at once
• Combinations of variables
• Main effects
• The effect of one independent variable, averaged
  over all levels of another independent variable
• The effect of one independent variable, ignoring
  the other independent variables

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• Interaction
• effect of one independent variable depends upon
  the levels of another independent variable
• the effects of one variable varies over the
  levels of another independent variable
• Main effects
• Model
• Stimulus
• Interaction

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• Three hypotheses
• Main effects
• Stimulus
• Model emotion
• InteractionStimulus X model emotion
• Actual interaction found
• Results from similar study

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Interactions

• Graphic representation
• Main effects conditioned by interaction

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Mood and Memory
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Factorial design analysis

• 2 X 2
• Three questions
• Two main effects
• Interaction
• Source table
• Source
• SS
• df
• MS
• F
• Significance

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Possible Patterns

• No effects

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Main effect no interaction
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Two main effects no interaction
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Interaction only
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Main effect and interaction
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Two main effects and interaction
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Interactions

• Interactions
• Antagonistic
• Synergistic
• Ceiling effect

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Higher Order Designs

• Extensions within a two way design
• More levels 2 X 3
• 3 X 3
• Higher order designs
• More factors
• 2 X 2 X 2
• Limitations
• Interpretation of higher order interactions
• Number of conditions and participants
• 3 X 3 X 3 X 3 81 cells

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Higher order interactions
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Within Subjects

• Repeated measures
• Withinsubjects factorial design
• Participants serve in all conditions
• 2 X 2
• 2 X 2 X 2 Aggressive/Prosocial stimuli X
  Similar/Dissimilar Target X Positive/Negative
  Target
• Limit on number of conditions
• Counterbalancing

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Mixed designs

• Between and within factors
• Subject variables

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Mixed Design Before/After X Treatment/Control
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Mixed Design Before/After X Treatment/Control