Factorial ANOVA Flashcards
When do you use Between subjects 2 way ANOVA?
Wish to compare samples based on multiple categories with 2+ levels in each category
Qualities of 2 way ANOVA:
Two or more categorical IVs with 2+ levels. There is also one continuous variable
Fully crossed:
All possible combinations of factors represented
Between Subjects:
Different students in each possible combination
Within subjects:
Every person is in each possible combination
Mixed factorial ANOVA:
has a combination of between and within subjects. At least one IV has to be between and one has to be within
Name different design types:
- Between subjects (Independent)
Within subjects (repeated measures)
Mixed (split plot)
Pros of Factorial ANOVA:
Greater generalizability, more powerful, answers different research questions, can investigate interactions
Which is more powerful, one way or factorial ANOVA?
Factorial
What is an example of research questions in factorial ANOVA?
Is the mean of a DV significantly different among the levels of A averaged across levels of B? (main effect of A)
What are interactions?
Occur when the effect of one factor on the DV depends on the level of the second factor
What is the variance formula for factorial ANOVA?
Total = Factor A + Factor B + A*B + Within
Sources of Between Group variability?
1 for each factor(the main effect) and 1 for each interaction
What is the formula for df in Factors A and B?
(A) df: J-1 (J is the # of levels)
(B) df: K -1 )K is the # of levels)
What is the df formula for the interaction between A and B?
dfa*b: (K-1)(J-1)
What is the formula for dfw?
N - (J*K)
What is the df for the total sample?
Dft: N-1
How do you calculate the MS for factorial ANOVA?
SS/df
How do you calculate the f for factorial ANOVA?
MS/MSwithin
How many unique cells are in 3x4 factorial ANOVA?
12
What is the formula for calculating SS in a 2 way factorial ANOVA?
SStotal = SSa + SSb + SSab + SSwithin
What is the SStotal?
Variability of Y ignoring group membership
What is SSa?
Variability of Y explained by factor A
What is SSb?
The variability of Y explained by factor B
What is SSab?
Variability of Y explained by the interaction of AxB
What is SSwithin?
Variability of Y within each cell
When does a main effect occur?
When there is a difference between levels for one factor
When does an interaction occur?
When the effect of one factor on Y depends on the particular level of the other factor. AKA if the difference between levels of one factor is difference, depending on the other factor
What is eta-squared?
the amount of variance explained out of the total variance
What is partial eta squared?
The amount of variance explained out of only the variance attributed to that effect and the error variance
Can you have significant main effects if the interaction is non significant?
Yes
Can you have significant interaction if the two main effects are non-significant?
Yes
