Archive:Advanced ANOVA/Factorial ANOVA

Resource type: this resource contains a tutorial or tutorial notes.

Template:0%done Factorial ANOVA involves testing differences between group means based on two or more independent variables.

One of the keys to understanding Factorial ANOVA is being able to intepret interactions.

SPSS tip

To show the syntax in the output:

2 or more between subjects categorical/ordinal IVs
1 interval/ratio DV
e.g., what is the effect of Gender (2) and Degree Type (3) on Overall Satisfaction?

This would be a 2 x 3 Factorial ANOVA (or 2 x 3 Between-Subjects ANOVA)

Establish hypothesis/hypotheses
- Make sure you have separate hypotheses for:
  - Main effect for each IV
  - Interactions between IVs
  - Planned contrasts (if warranted)
Examine assumptions:
IVs (categorical; between-subjects) and DV (at least interval)
- The data in each cell is normally distributed
- Homogeneity of variance (the variance in each cell is similar)
- Cells are independent
Examine descriptive statistics, particularly the four moments (M, SD, Skewness, Kurtosis) overall, and also for each cell
Examine graphs
Conduct inferential test (ANOVA) and interpret significance of F scores
Conduct follow-up tests (planned contrasts or post-hoc tests) if F is significant
Interpret interactions
Calculate and interpret effect sizes
- Eta-square (omnibus - equivalent to R²)
- Standardised mean effect size (difference b/w two means)