factorial designs: main effects and interactions
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Factorial designs: Main effects and interactions. Psy 245 Research Methods. Objectives: By the end of this session, you should be able to: - define the concept of interaction - determine the relationship between variables from the results of statistical analyses - PowerPoint PPT PresentationTRANSCRIPT
Factorial designs:Main effects and interactions
Psy 245 Research Methods
Objectives:
By the end of this session, you should be able to:
- define the concept of interaction
- determine the relationship between variables from the results of statistical analyses
- differentiate main effects and interactions
Imaginary study:
- Looking at the effect of rate of presentation and colour of stimuli on memory for a sequence of consonants
“… Performance was weaker for the fast presentation rate than for the slow; F(1,9)=110.12, p < .001; while no effect of colour was observed; F(1, 9) < 1, p > .5. No interaction between rate of presentation and colour was found; F(1, 9) < 1, p > .7. ”
Slow-red Slow-blue Fast-red Fast-blue
Sub1 87.000 82.000 56.000 54.000Sub2 82.000 79.000 57.000 59.000Sub3 76.000 78.000 38.000 28.000Sub4 75.000 76.000 45.000 46.000Sub5 74.000 73.000 32.000 39.000Sub6 72.000 77.000 42.000 50.000Sub7 69.000 80.000 41.000 39.000Sub8 75.000 73.000 38.000 25.000Sub9 58.000 57.000 29.000 28.000Sub10 76.000 65.000 59.000 57.000
xSR= 74.4 xSB= 74.0 xFR= 43.7 xFB= 42.5
Slow FastRed 74.4 43.7Blue 74 42.5
xR* = ( xRS + xRF ) / 2
xB* = ( xBS + xBF ) / 2
xR* = (74.4+43.7) / 2 = 59.05
xB* = (74+42.5) / 2 = 58.25
Performance levels in colour conditions, regardless of rate of presentation, are similar
Slow FastRed 74.4 43.7Blue 74 42.5
xS* = ( xSR + xSB ) / 2
xF* = ( xFR + xFB ) / 2
Performance levels in rate of presentation conditions, regardless of colour, are different
xF* = (43.7 + 42.5) / 2 = 43.1
xS* = (74.4 + 74) / 2 = 74.2
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Red Blue
% c
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Slow
Fast
Main effect of rate of presentation
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Red Blue
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Slow
Fast
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Red & Blue
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Red Blue
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A1 A2
B1
B2
No main effect of ANo main effect of B
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A1 A2
B1
B2
Main effect of ANo main effect of B
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A1 A2
B1
B2
No main effect of AMain effect of B
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A1 A2
B1
B2
Main effect of AMain effect of B
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A1 A2
B1
B2
?
Interaction
Presence of an interaction: conclusions based on main effects alone do not fully describe the outcome of the factorial experiment
Interaction: The effect of one independent variable on the dependent variable changes at the different levels of the second independent variable
e.g.: Do control participants show better long-term memory than amnesic patients? For explicit memory tasks? For implicit memory tasks?
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Explicit Implicit
Mem
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Control
Amnesics
Does the group of participants predict memory performance ?Yes, to a certain extent… but it also depends on the task...
Memoryperformance Group of
participants(Ctrls/amnesics)
Task(explicit/implicit)
Interaction
Interaction
Independent variables influence the dependent variables and not one another.
Mathematically:Interaction is present when the differences between means representing the effect of a factor A at one level of B do not equal the corresponding differences at another level of factor B.
An interaction is present when one of the independent variables does not have a constant effect at all levels of the other independent variable.
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A1 A2
B1
B2
Interaction & No main effect
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A1 A2
B1
B2
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A
B1
B2
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A1 A2
B
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A1 A2
B1
B2
Main effect of A & interaction
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A1 A2
B1
B2
Interaction & main effect of B
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A1 A2
B1
B2
Main effect of A & B & interaction
Practice
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A1 A2
B1B2
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A1 A2
B1B2
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A1 A2
B1B2
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A1 A2
B1B2
A & B & interaction B
A A & B
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A1 A2
% p
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B1B2
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B1 B2
% p
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A1A2
Main effect of A, interaction
Same data; changed factor illustrated on X-axis.
Plotting the data in different ways can help interpretation
2 x 2 design so far…
What about 2x3? 3x3? 2x2x2? 2x2x2x2?
2 x 3 design
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A1 A2
B1
B2
B3
Main effect of B
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B1 B2 B31
2 1 < 2
Effect of Bis not linear
2
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A1 A2 A3
B1
B2
2 x 3 design
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B1 B2
A1A2A3
Main effect of A & B
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A1 A2 A3
B1B2B3
Main effect of A & B & interaction
3-way design: 2 x 2 x 2
E.g.: Looking at the effect of rate of presentation, colour and font size of the stimuli on memory for a sequence of consonants
Rate of presentation: Fast versus Slow
Colour: Red versus Blue
Size: small versus large
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Small-Red
Small-Blue
Large-Red
Large-Blue
Slow
Fast
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Small Large
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Red Blue
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Fast Slow
Main effect of sizeNo main effect of colourMain effect of rate
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Small Large
RedBlue
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Fast Slow
RedBlue
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Small Large
FastSlow
Size x Colour: NoRate x Colour: NoSize x Rate: No
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Fast Slow
RedBlue
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Fast Slow
RedBlue
Small Large
The relationship between colour and rate is not different for the small and large conditions:
No 3-way interaction
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B1 B2
A1A2
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B1 B2
A1A2
C1 C2
2 x 2 x 2 : For you to practice at home
3-way interaction
3 factors interact when the interaction of two of the factors is not the same at all the levels of the third variable
Y A
3-way Interaction
B
C
Why the stats?
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A1 A2
% p
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B1B2
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A1 A2
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B1B2
Same data !!! Always look at the Y-axis values!
What really tells you what effects are present is the statistic analysis
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A1 A2
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B1B2
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A1 A2
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B1B2
Statistical tests take variations of the DV into account
Only the statistical test can evaluate whether differences in your samples can be relatively safely generalised to
the population