Factorial Designs. Time in Instruction 1 hour per week 4 hours per week SettingIn-classPull-out A...
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Transcript of Factorial Designs. Time in Instruction 1 hour per week 4 hours per week SettingIn-classPull-out A...
Time in InstructionTime in Instruction1 hour per week1 hour per week4 hours per week4 hours per week
SettingSettingIn-classIn-classPull-outPull-out
A Simple ExampleA Simple Example
R X11 OR X12 OR X21 OR X22 O
Factor 1:Level 1:Level 2:
Factor 2:Level 1:Level 2:
A Simple ExampleA Simple Example
Time in InstructionS
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1 hour/week 4 hours/weekIn
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A Simple ExampleA Simple Example
Time in InstructionS
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1 hour/week 4 hours/weekIn
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of factors
A Simple ExampleA Simple Example
Time in InstructionS
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A Simple ExampleA Simple Example
Time in InstructionS
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A 2(rows) x 2 (columns) design
A Simple ExampleA Simple Example
Time in InstructionS
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There are 4 (i.e., 2x2) groups.
A Simple ExampleA Simple Example
Group 2average
Group 4average
Group 1average
Group 3average
Time in InstructionS
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Usually, averages are in the cells.
Multiplicative NotationMultiplicative Notation
A 3 x 4 factorial design
The number of numbers tellsyou how many factors
there are.
Multiplicative NotationMultiplicative Notation
A 3 x 4 factorial design
The number of numbers tellsyou how many factors
there are.
There are 2 factors because there are 2
numbers.
Multiplicative NotationMultiplicative Notation
A 3 x 4 factorial design
The number values tell youhow many levels are in
each factor.
Multiplicative NotationMultiplicative Notation
A 3 x 4 factorial design
The number values tell youhow many levels are in
each factor.
Factor 1 has 3 levels.
Factor 2 has 4 levels.
The Null CaseThe Null Case
5 5
5 5
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5 5
1 hr 4 hrs
Out
In
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The lines in the graphsbelow overlap each
other.
A Main EffectA Main Effect
A consistent difference between levels A consistent difference between levels of a factorof a factor
For instance, we would say there’s a For instance, we would say there’s a main effect for setting if we find a main effect for setting if we find a statistical difference between the statistical difference between the averages for the in-class and pull-out averages for the in-class and pull-out groupsgroups
Main EffectsMain Effects
5 7
5 7
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Out
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Main Effect of Time
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Main EffectsMain Effects
5 5
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5
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Main Effect of Setting
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Main EffectsMain Effects
2
4
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5 7
7 9
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Main Effects of Time and Setting
An Interaction EffectAn Interaction Effect
When differences on one factor depend When differences on one factor depend on the level you are on on another on the level you are on on another factorfactor
An interaction is between factors (not An interaction is between factors (not levels)levels)
You know there’s an interaction when You know there’s an interaction when can’t talk about effect on one factor can’t talk about effect on one factor without mentioning the other factor without mentioning the other factor
Interaction EffectsInteraction Effects
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5 5
5 7
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The in-class, 4-hour perweek group differsfrom all the others.
Interaction EffectsInteraction Effects
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7 5
5 7
6
6
6 6
1 hr 4 hrs
Out
In
Time
Set
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g The 1-hour amount workswell with pull-outs whilethe 4 hour works as well
with in class.
Advantages of Factorial DesignsAdvantages of Factorial Designs
Offers great flexibility for exploring or Offers great flexibility for exploring or enhancing the “signal” (treatment)enhancing the “signal” (treatment)
Makes it possible to study interactionsMakes it possible to study interactions Combines multiple studies into oneCombines multiple studies into one