Factorial designs: Main effects and interactions

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Factorial designsMain effects and interactions

• Psy 245 Research Methods

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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
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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 lt .001 while no
effect of colour was observed F(1, 9) lt 1, p gt
.5. No interaction between rate of presentation
and colour was found F(1, 9) lt 1, p gt .7.
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Slow-red Slow-blue Fast-red Fast-blue Sub1 87
.000 82.000 56.000 54.000 Sub2 82.000 79.000
57.000 59.000 Sub3 76.000 78.000 38.000 28.0
00 Sub4 75.000 76.000 45.000 46.000 Sub5 74.0
00 73.000 32.000 39.000 Sub6 72.000 77.000 4
2.000 50.000 Sub7 69.000 80.000 41.000 39.000
Sub8 75.000 73.000 38.000 25.000 Sub9 58.000
57.000 29.000 28.000 Sub10 76.000 65.000 59
.000 57.000
xSR 74.4
xSB 74.0
xFR 43.7
xFB 42.5
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xR ( xRS xRF ) / 2
xB ( xBS xBF ) / 2
xR (74.443.7) / 2 59.05
xB (7442.5) / 2 58.25
Performance levels in colour conditions,
regardless of rate of presentation, are similar
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xF ( xFR xFB ) / 2
xF (43.7 42.5) / 2 43.1
xS ( xSR xSB ) / 2
xS (74.4 74) / 2 74.2
Performance levels in rate of presentation
conditions, regardless of colour, are different
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Main effect of rate of presentation
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No main effect of A No main effect of B
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Main effect of A No main effect of B
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No main effect of A Main effect of B
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Main effect of A Main effect of B
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?
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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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Does the group of participants predict memory
performance ? Yes, to a certain extent but it
also depends on the task...
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Memoryperformance
Group ofparticipants(Ctrls/amnesics)
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Interaction
Independent variables influence the dependent
variables and not one another. Mathematically In
teraction 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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Interaction No main effect
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Main effect of A interaction
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Interaction main effect of B
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Main effect of A B interaction
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Practice
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Main effect of A, interaction Same data changed
factor illustrated on X-axis. Plotting the data
in different ways can help interpretation
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2 x 2 design so far What about 2x3? 3x3? 2x2x2?
2x2x2x2?
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2 x 3 design
Main effect of B
?1 lt ?2 Effect of B is not linear
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2 x 3 design
Main effect of A B
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Main effect of A B interaction
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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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Main effect of size No main effect of colour Main
effect of rate
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Size x Colour No Rate x Colour No Size x Rate
No
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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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2 x 2 x 2 For you to practice at home
C1
C2
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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
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Why the stats?
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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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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