Two Multiple Level IVs and Continuous DV Flashcards
Factorial ANOVA is the general term for an ANOVA with…
More than one independent variable
2 x 2 factorial ANOVA
2 independent variables with 2 levels each
2 x 3 x 3 ANOVA
3 independent variables, one of them has 2 levels and two of them have 3 levels
Additive effect
AKA main effect
This occurs when the impact of one IV is completely separate of the other IV
Non-additive effect
AKA interaction
This occurs when the impact of one IV is NOT completely separate of the other IV
In a one-way ANOVA we have one omnibus F-test whereas in a two-way factorial ANOVA we will have THREE omnibus F-tests. These will test…
- The main effect of IV1 (effect of IV1 collapsing across IV2)
- The main effect of IV2 (effect of IV2 collapsing across IV1)
- Interaction effect of IV1 with IV2 (IV1 x IV2)
Interactions indicate that…
the effect of one IV is not the same (differs) across levels of the second IV
What is the null hypothesis of a main effect of factor (IV) A, the null hypothesis of a main effect of factor (IV) B, and the null hypothesis of an interaction?
Main effect of factor A: H0 = muA1 = muA2
Main effect of factor B: H0 = muB1 = muB2
Interaction: H0 = No interaction is present. The effect of each factor is independent of the other factor
In a factorial ANOVA there will be an F-test associated with each of the three hypotheses. These F-tests will have the same structure as one-way ANOVA F-tests but there is one primary difference. What is it?
The between treatment variance (numerator) changes across the three tests because the total variability is further divided into three components:
- Factor A between treatment variance
- Factor B between treatment variance
- Factor A x B between treatment variance
When are follow-up tests required for 2 x 2 factorial ANOVAs?
When the interaction is significant
What type of follow-up tests are most commonly used for significant interactions?
Planned follow-up tests (i.e., simple effect analysis)
A simple effect is…
the effect of one IV at a specific level of the other IV
Computing the simple effects allows us to solve what issue?
An interaction indicates that the simple effect of one IV differs across levels of the other IV
BUT
It does not tell us what this simple effect is and so computing a simple effect analysis will help solve this issue
When a simple effect involves more than two levels further follow-up tests are required (i.e., in a 2x3 if we examine the simple effect of the second IV at each level of the first IV our simple effects will be omnibus tests). What type of follow-up analyses can we conduct?
Planned contrasts
SS within reflects…
the error term of a two-way factorial ANOVA
SS between reflects…
the variability in scores attributable to all our treatment effects (A, B, AxB) combined
