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WK4: FACTORIAL ANOVA: BETWEEN-SUBJECTS (Terms (Interaction (magnitude /…
WK4: FACTORIAL ANOVA: BETWEEN-SUBJECTS
Terms
Main Effect
(effect on IV in isolation + means combined not partitioned)
Decomposing
(breaking down 3x2 design into 2x2 to compare)
Interaction
(magnitude / direction of an effect on: IV = DV with another IV moderating it)
Interaction may be
more interesting
than main effect
Or even the
only effect of interest
Simple Main Effect Analysis
(check if can interpret main effect with confidence)
Observed Power
(Min .80 / 8% - lower chance to reject null hypo if higher value)
Partial Eta Squared
(look at that + F-value + P-value)
Guidelines to Note
Cohen's d
(.20, .50, .80)
Assumes Homogeneity of Variance
Simple Main Effect
Not Significant ME,
Significant IE
= Conclude with
IE
Significant ME
+ Not Significant IE = Conclude with
ME
:star:
Significant ME + Significant IE = do SME
:red_flag:If certain condition is met, significant main effect
can be interpreted
despite
presence of significant interaction
:star:
Condition:
Significant +
Same direction
= can interpret ME across all levels of IV
SPSS Steps and Output
Descriptive Statistics Output
Observe the bottom row
total
for one IV (e.g. Male, Female)
Conclude
based on the difference,
how much they vary.
Observe the
total mean for IV + IV
for each level (e.g. violent, non-violent)
Test of Between-Subject Effects
Look at Interaction Effect (IV * IV)
Look at Main Effect Significance > F-value
Interpreting bar / line graph for SME
(decomposed)
The
more parallel
the lines are to each other =
impact is similar
Slant-ness
indicates
bigger magnitude of mean diff
(levels of the IV)
Imagine a line and observe the
'slant-ness'
Ideally:
Lesser
level IVs should be on
separate line
, while
more levels on horizontal plot
Observe
effect size
(cohen's d)
:star:
Conducting Simple Main Effects
(independent sample t-test after split)
Look at independent samples t-test
Look at result, check
p-value significance
of each test
Split-file
based on IV you're interested in
Weight choices accordingly (are you more confident?)
Factorial ANOVA
2 IV
=
Two-way
Factorial,
3 IV
=
Three-way
Factorial
:!:
Not realistic
to expect 1 significant ME, 1 non-significant ME (IE doesn't = SME)
2x2, 2x3 designs (number
represents how many levels
are there in
each IV
) 2x2x3x2 design also possible.
:warning: Ideally looking for both main effects to have a
difference
, if not, an interaction can still exist.
Purpose
IVs must only be
between-subjects design
(Mixed-design covers within).
Information Provided
Main Effect
for each IV in isolation.
Interaction Effect
- examines the influence of the IV in combination (moderator effect)
aka. Understand Nature of Interaction
Test for mean differences where there are
2 or more IV
(test main effect and interaction hypotheses)
Exclusive to Factorial ANOVA
ME, IE and SME also present in
Mixed-design ANOVA
:star:
Can't Use Brown or Welch Test if sample size is unequal
Solution:
Adjust sample sizes to be equal based on the size of smallest group (cut data accordingly)
Alternative Solution:
:question: Is
largest variance
associated with
smallest
sample size or
larger sample size?
(overestimate > underestimate p-value)
:check: Smallest sample size = p-value will be
under-estimated, type 1 error
:green_cross: Larger sample size = do nothing (bettter
over-estimated,
as conservative)