Factorial ANOVAs Flashcards
what do ANOVAs help us to reduce?
type 1 errors (based on the use of multiple comparisons -> we want to avoid family wise error)
what is a Factorial Independent ANOVA?
has multiple independent variables
* different participants in all conditions
*one dependent/outcome variable
* you still need to run one ANOVA per dependent variable
what is a factorial design?
when you have several independent variables
what is a two-way factorial anova?
when there are two independent variables
i.e.
IV1: democratic status (4 levels)
IV2: GDP (3 levels)
DV: happiness score
what is a three-way factorial anova?
when there are three independent variables
what does a factorial design allow you to do?
allows you to look at interaction effects between variables
* the effect of one IV may depend on the level of another IV
what are the assumptions of a factorial anova?
- independence (each participant contributes one data point)
- normality (K-S, Shapiro Wilk and observe your graphs)
- homogeneity of variance (Levene’s Test and observe your graphs Q-Q Plots)
what should you do when assumptions are violated?
non-parametric alternative
how to structure your data (for a two-way factorial ANOVA)
IV1 (Coded)
IV2 (Coded)
DV
How to inspect your data for a One-Way Factorial ANOVA?
- drag the type of graph you need (multiple line graphs)
- drag one IV to the x-axis -> choose the one with the most levels first
- drag the second IV to set colour
- drag the DV to the y-axis
- Element Properties -> Error Bars -> SE +/- 1
- Click OK to generate your graph
Running the Factorial ANOVA
Analyse > General Linear Model > Univariate
* use this option for any factorial independent ANOVA (two-way, three-way etc.)
* Drag IVs to fixed factors box
* Drag DV to to dependent variable box
* Click Plots
â—‹ Plot Window allows you to draw a graph
â—‹ Drag IV with most levels to Horizontal axis
â—‹ Drag IV with fewest levels to separate lines
â—‹ Click Add > Continue
* Click Post-Hoc Tests (options same as ones in One-Way ANOVA)
â—‹ Post Hoc Window - Drag IVs to post-hoc box (select appropriate test(s))
* Click Options
â—‹ Drag your IVs and the interaction across to the Display means box
* Display
â—‹ Descriptive statistics, estimates of effect size, homogeneity tests
How should you interpret the output?
- Descriptive statistics box/table
- Levene’s Test of Equality of Error Variances
- Tests of Between-Subjects Effects
- Write up your results
descriptive statistics box/table
- check sample sizes are what you expected
Levene’s Test of Equality of Error Variances
homogeneity test -> we want Levene’s to be non-significant so we can assume equal variance
Test of Between-Subjects Effect
- main ANOVA summary table
- highlights main effects of your IVs -> interaction effect between the IVs
- Partial Eta Squared
what is Partial Eta Squared?
Effect Size
Writing up your results:
- Descriptive for graphs
- Results of assumptions tests
- Test statistics (F)
- Degrees of Freedom (model, error)
- P Value
- Effect Size (n2)
(if there’s a significant main effect, the graph should technically show us)
how do we know if there’s a significant interaction?
if there isn’t then two variables do not influence one another -> main effect of IV1 is not influenced by the level of IV2