Factorial ANOVA Flashcards
Define
Factorial ANOVA
an Analysis of Variance test with more than one independent variable, or “factor“
Define
Main effects
the effect of an independent variable on a dependent variable averaged across the levels of any other independent variables
Define
Interaction effects
when the effect of one variable depends on the value of another variable
Define
Orthogonal
statistically independent
Definition
an Analysis of Variance test with more than one independent variable, or “factor“
Factorial ANOVA
Definition
the effect of an independent variable on a dependent variable averaged across the levels of any other independent variables
Main effects
Definition
when the effect of one variable depends on the value of another variable
Interaction effects
Definition
statistically independent
Orthogonal
Factorial ANOVAs can be independent-measures, repeated-measures and what?
Mixed-model
What does a 2 x 3 ANOVA mean?
Factor A has 2 levels (i.e. biological sex)
Factor B has 3 levels (i.e. SES)
What does a factorial ANOVA tells us?
Examines the effects of each factor (IV) on its own, as well as the combined effects of the factors…
A main effect is the effect of one factor (IV) on its own.
An interaction examines two or more factors at the same time – that is, their combined effect, which may not be predictable based on the effects of either factor on their own.
Thus, factorial ANOVAs produce multiple F ratios – one for each main effect and interaction term
How many F-ratios will be in a two-, three- and four-way ANOVA?
Two-way: 3
Three-way: 7
Four-way: 15
What do the three F-ratios of the two-way ANOVA represent?
Main effect of A
Main effect of B
A x B interaction
What is a main effect?
Mains effects are the mean differences across levels of one factor, collapsing (averaging, or sometimes called marginalizing) the other factor(s).
Effectively main effects examine one factor’s effects, ignoring other factors
What is a marginal effect?
The average for everyone in that given factor
When does an interaction occur?
An interaction between two factors occurs whenever the mean differences between individual treatment conditions, or cells, are different from what would be predicted from the overall main effects of the factors
Based on this graph, what can we conclude?
NO EFFECT OF A, NO EFFECT OF B, NO INTERACTION EFFECT
Based on this graph, what can we conclude?
MAIN EFFECT OF A, NO EFFECT OF B, NO INTERACTION EFFECT
Based on this graph, what can we conclude?
MAIN EFFECT OF A, MAIN EFFECT OF B, NO INTERACTION EFFECT
Based on this graph, what can we conclude?
NO EFFECT OF A, NO EFFECT OF B, INTERACTION EFFECT
Based on this graph, what can we conclude?
MAIN EFFECT OF A, NO EFFECT OF B, INTERACTION EFFECT
The variability accounted for by the model (SSM) is due what?
The variability accounted for by the model (SSM) is due to differences between the groups (e.g., the treatment effect)
What needs to be considered when choosing contrasts?
- Use control group as reference point
- Only 2 pieces
- Independence
What are the basic guidelines for contrasts?
- Choose sensible comparisons
- Groups coded with positive weights will be compared against groups coded with negative weights
- The sum of weights for a comparison should be zero
- If a group is not involved in a comparison, automatically assign it a weight of zero
- For a given contrast, the weights assigned to the group(s) in one chunk of variation should be equal to the number of groups in the opposite chunk of variation.
True or False:
Orthogonal contrasts are not required?
True
But they do facilitate interpretation
When are two contrasts considered orthogonal?
When the products of their weights sum to zero
