Factorial Design Flashcards
Designs which include multiple independent variables are known asβ¦
Factorial Design
For a design with 2 independant levels and 2 different croups only tested in 1 condition, what design would u use?
2π₯3 two-way, between-groups design.
What are the steps to analyse a two-way between-groups design?
1, State the null hypotheses (π»_0)
2, Partition the variability
3, Calculate the mean squares
4, Calculate the F-ratios
There are 3 null hypotheses for a two-way between-groups design
Means of different levels of the first IV (π¨) will be the same
Means of different levels of the second IV (π©) will be the same
Differences between means of π© at different levels of π¨ are the same (there is no interaction between π¨ and π©).
We want to disprove all of these
What is the No Interaction effect?
No interaction between conditions (π―_π Null is true)
So you form your new hypothesis as the DV does not affect how IV changed
If there is seen to be an Interaction Effect thenβ¦
π―_π Null is false
Total deviation is the sum of
within-groups design
and
between-groups deviations
πΜ _(π¨,π)
means the average accross all subject designs
πΜ _π»
is still the total (grand) mean of all scores
πΜ _(π¨π©,(π)(π)) ij
Low caffeine IV level 1
IV level 1
πΜ _(π¨π©,(π)(π)) ij
High caffeine IV level 2
IV level 3
πΜ _(π©,π)
mean score of IV level
across IV level 1
π_(π¨π©)
subjects single score they got (DV)
so basically, The between-group deviation for the effect of the interaction isβ¦
(π¦Μ
_π΄π΅βπ¦Μ
_π )β(π¦Μ
_π΄βπ¦Μ
_π )
β
(π¦Μ
_π΅βπ¦Μ
_π )=π¦Μ
_π΄π΅βπ¦Μ
_π΄βπ¦Μ
_π΅+π¦Μ
_π
total sum of squares for a one-way between-group design isβ¦
γππγ_π=γππγ_π΄+γππγ_π
Sums of squares associated with the two-way between-groups design are a bit more involvedβ¦
γππγ_π=γππγ_π΄+γππγ_π΅
(between groups)
+γ
ππγπ΄π΅+γππγ(π/π΄π΅)
(within groups)
sum of squares:
πΊπΊ_π¨π© refers to
the squared differences related to an interaction between π¨ and π© β are the effects of π¨ different at different levels of π©
πΊπΊ_(πΊ/π¨π©) refers to
refers to the residual error β whatβs left over after weβve accounted for π¨
To calculate F-Ratios, we need to calculateβ¦
the mean squares associated with:
Main effect of A
Main effect of B
Interaction between A and B
Error Term
How do we test
the effect of IV on DV
for individual IV 2 ?
For each level, perform:
F tests for simple main effects
Planned or post hoc comparisons (low vs high)
The significant interaction effect suggests
it might be difficult to interpret the main effects.
To do this, we need to analyse simple main effects
If all IVs are between groups
We use a
Between-groups design
If all IVs are collected from the same participants
We use a
Within-subjects or repeated-measures design
