8. Factorial ANOVA Flashcards
When would you use a factorial ANOVA?
When you have more than 1 categorical IV and one numerical DV
What are the 3 types of factorial designs?
Between subjects Within subjects (repeated measures) Mixed model (both)
What are the 2 types of factors?
Fixed (sex)
Random
What can’t you do with a fixed factor model?
Generalise results to other levels (e.g. can only speak about the types of rivals you used)
What is an example of a random factor?
Randomly selecting different class times from a set of possibilities
How are factorial designs labelled?
Number of factors by number of levels
e.g. sex (2) and rival (4)
= 2 x 4 design
What are the 3 effects that can be examined in a factorial design?
Main
Interaction
Simple
What is the main effect?
The separate effect of each independent variable
What is an interaction effect?
When the effects of one independent variable are dependent on the levels of another independent variable = moderated
How is an interaction effect represented in a line graph?
Straight lines that are NOT parallel
If the line graph has the two lines intersect each other in a perfect cross what does this mean?
No main effects - all interaction effects
When are simple effects examined in an ANOVA?
When there’s a statistically sig. interaction effect
How do you compute simple effects?
Using a syntax with 2 families of simple effects:
IV1 e.g. 4 x rival type: m v. f
IV2 e.g. 12x male with each pairwise of rivals and female with each
In a two-way independent groups ANOVA ho many parts make up SSB?
SS1 = Main effect IV1 SS2 = Main effect IV2 SS1*2 = Interaction
Total variance in the SPSS output is given as?
Corrected Total’s Type II Sum of Squares
in between subjects box
When we don’t have equal sample sizes in the groups during a factorial ANOVA what does the Model Variance account for?
The 3 effects (2 x main effect and 1 x interaction effect) simultaneously
(if equal size = sum of 3 effects)
When the F value is not sig. on one of the variables in an ANOVA, what does this mean?
There is no difference between the groups/ levels of that variable on the DV
e.g. IV: SEX = no difference between males and females on their ratings of jealousy
What is reported from a factorial ANOVA for effect size?
R Sq Adj or Partial Eta Sq
Converted to a %
What is observed power?
The likelihood of finding a sig. difference between groups in that sample size
Why would you look at observed power?
If non sig. F = gives explanation
What do you report when writing our ANOVA results?
Sig./Non Sig. effect for IV, F(x,x) = x, p = x (tailed),
eta sq = x (effect size),
obs. power = x
What do you do if you get a sig. main effect vs. a sig. interaction effect (on a variable with more than 2 levels)?
Sig. Main Effect = Contrasts or Pairwise Comparisons
Sig. Interaction = Simple Effects
How do you obtain the effect size for simple effects?
Syntax
What is the only assumption common to all three factorial designs (independent groups, repeated measures and mixed model)?
Scores on the dependent variable must be distributed normally within groups
What are the assumptions for an Independent groups factorial ANOVA?
Normality
Homogeneity of Variance
Independence
Proportionality
How is Independence tested in an Independent Groups Factorial ANOVA?
Chi Square test on IV’s
should be non sig.
What is proportionality?
All cell sizes equal or proportional
How is proportionality tested?
By checking the number of participants in each cell.
Ratio of males to females must be the same in each rival
How many times do you need to check normality in a factorial ANOVA?
Once for each cell
What two conditions need to be met to achieve Independence?
Participants not in more than 1 group
The IVs must be unrelated (Chi Squared non sig.)
How can the strength of the association between the IVs be tested (other than Chi Squared)?
Phi co-efficient (2 x 2 design)
Contingency co-efficient Cramer’s V
How many Chi Squares must be run to check for Independence?
Once for each pair of variables
If the assumption of proportionality is not met, what should you use?
Type II SS in SPSS
If normality is violated in a factorial ANOVA?
Transformation
Bootstrap
When is the violation of the assumption of the homogeneity of variance a problem in a factorial ANOVA?
When the largest group variance is more than 4 x the smallest
Different Groups skewed in different directions on the DV
What should you do if the assumption of Independence is violated?
Don’t use an ANOVA
Dummy code variables and use in a regression
When is the harmonic mean used?
When proportionality is violated to calculate equally weighted means
When would you use SS Type I?
Non-experimental research (sample sizes reflect importance of cells).
Effects have unequal priority.
When would you use SS Type II?
Non-experimental research (sample sizes reflect importance of cells).
Main effects have equal priority.
When would you use SS Type III?
Experiments designed to be equal
All cells equally important.
When would you use SS Type IV?
Experiments designed to be equal
Missing cells in the design.
