Week 5 Lecture 5 - factorial ANOVAS (specifically 2-way independent ANOVA) Flashcards
What is the criteria for a Factorial ANOVA?
- more than 1 IV
- at least 2 levels in each
What do factorial ANOVAS explore?
explore effects of each IV and interactions between IVs
What are the 3 types of factorial ANOVA?
- all IVs are between-subjects (independent)
- all IVs are within subjects (repeated measures)
- mix of between-subjects and within subjects (mixed)
What does a 422 ANOVA mean?
- 3 IVs
- 1st IV has 4 levels
- other 2 both have 2 levels
What 2 things does a 2-way ANOVA tell us?
- main effects
- interaction
How many main effects are there for a 2-way ANOVA?
2
How many interactions are there for a 2-way ANOVA?
1
Do factorial ANOVAs control for familywise error?
yes
How many f stats are there in a factorial ANOVA?
- 3 (one for each effect = 2 main effects and 1 interaction)
How do you determine whether you can reject the null hypothesis in a factorial ANOVA?
- consider whether you can reject each for each effect and interaction
What makes up the variance between IV levels in a factorial ANOVA?
- IV 1
- IV 2
- interaction
What makes up the variance within IV levels in a factorial ANOVA?
- error (inc. individual differences and experimental error)
- this stay the same for the whole ANOVA
With more IVs;
- does it get harder or easier to find significant results?
- is there more or less chance of a type two error?
- harder to find significant results
- more chance of a type 2 error
What is a significant interaction?
effects of manipulating 1 IV depends on the level of the other IV
What are cell means?
means for each condition
What are marginal mean?
average for an IV level e.g., male
ignore other IVs
What is the overall mean?
average mean overall
What are the assumptions for a 2 way individual ANOVA?
- normality –> within each condition
- homogeneity of variance –> check with Leven’s test but don’t have a correction for this
- equivalent sample size
- independence of observations
Is there a non-parametric equivalent for a Factorial ANOVA?
no but it is normally quite robust as a test
How do you finds to dofs for a main effect?
- m = IV looking at
- r = error row
Do you report partial eta^2?
yes –> find on SPSS
What is the difference between classical eta^2 and partial eta^2?
classical eta^2 = proportion of the total variance attributed to the factor
partial eta^2 = only takes into account the variance for 1 IV at a time rather than the total variance
What post hoc test is used for a 2-way independent ANOVA?
- Tukey HSD
When are post hoc tests relevant to report?
- when main effect of IV is significant and the IV has more than 2 levels
Do you report Cohen’s d for post hoc tests in factorial ANOVAS?
no
How do you report the interaction effects?
find IV1 * IV 2 row
report F stat as normal including partial eta^2
When do we consider simple effects?
when there is a presence of an interaction
What do simple effects use?
profile plots on SPSS
What are simple effects?
the effect of an IV at a single level of another IV
- comparison of all means (conditions)
How do you calculate simple effects?
conduct t-tests to determine if interactions between different conditions are significant
Do you need to run simple effects t-tests with a correction for multiple comparisons?
yes use Bonferroni correction
How do you calculate Bonferroni’s?
- divide required alpha level by number of comparisons
e.g., a/c
e.g., if there were 4 comparisons: 0.05/4 = 0.013
What are 2 key things to remember when conducting simple effects t-tests?
- remember to check Levene’s for each
- all of the t-tests have to be follow up with Cohen’s d
