factorial designs. time in instruction 1 hour per week 4 hours per week settingin-classpull-out a...
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Factorial DesignsFactorial Designs
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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A Simple ExampleA Simple Example
Time in InstructionS
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Factors:Major independent variables
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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t Levels:subdivisions
of factors
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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A 2(rows) x 2 (columns) design
A Simple ExampleA Simple Example
Time in InstructionS
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1 hour/week 4 hours/weekIn
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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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1 hour/week 4 hours/weekIn
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t
Usually, averages are in the cells.
Multiplicative NotationMultiplicative Notation
A 3 x 4 factorial design
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
5
5
5 5
1 hr 4 hrs
Out
In
Time
Set
tin
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1h
r
4h
rs
out
in
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t
in
1hr
4hrs
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
6
6
5 7
1 hr 4 hrs
Out
In
Time
Set
tin
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Main Effect of Time
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1h
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4h
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out
in
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in
1hr
4hrs
Main EffectsMain Effects
5 5
7 7
5
7
6 6
1 hr 4 hrs
Out
In
Time
Set
tin
g
Main Effect of Setting
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1h
r
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out
in
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in
1hr
4hrs
Main EffectsMain Effects
2
4
6
8
10
1h
r
4h
rs
out
in
2
4
6
8
10
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t
in
1hr
4hrs
5 7
7 9
6
8
6 8
1 hr 4 hrs
Out
In
Time
Set
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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
2345678
1h
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4h
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out
in
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in
1hr
4hrs
5 5
5 7
5
6
5 6
1 hr 4 hrs
Out
In
Time
Set
tin
g
The in-class, 4-hour perweek group differsfrom all the others.
Interaction EffectsInteraction Effects
2345678
1h
r
4h
rs
out
in
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t
in
1hr
4hrs
7 5
5 7
6
6
6 6
1 hr 4 hrs
Out
In
Time
Set
tin
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