7: 2 WAY REPEATED MEASURES ANOVA & 2 WAY MIXED ANOVA

Question 1

2-way repeated measures ANOVA: what contributes to variance

Answer 1

• the variance between IV levels does not include variance due to individual differences
• as a results we can subtract the variance due to individual differences from the variance within IV levels (i.e. error due to individual differences is removed from the error variance)
• also, because the same participants take part in each IV level, we can calculate the degree of error associated with each factor separately (so we can test each main effect and interaction against its own error term)

Question 2

2 way repeated measures ANOVA: F ratio

Answer 2

F = variance between IV levels / variance within
F = MSm / MSr

F(IV1) = variance due to manipulation of trial (+error) / variance due to error along (excl. individ diffs)

Question 3

2-way repeated measures ANOVA: means

Answer 3

cell means: mean scores for each condition

marginal means: mean scores for single IV levels (ignoring the other IV

Question 4

assumptions: 2 way repeated measures ANOVA

Answer 4

• normality: the distribution of difference scores under each IV level pair should be normally distributed (unlikely to be issue, we wont check)
• sphericity (homogeneity of covariance): the variance in difference scores under each IV level pair should be reasonably equivalent (Mauchly’s)
• equivalent sample size: sample size within each condition should be rouhgly equal

no parametric equivalent, if serious violation, attempt ‘fix’ or simplify design

Question 5

2 way repeated measures ANOVA: simple effects

Answer 5

a significant interaction suggests that the effect of the presence of critters (main IV) is dependent on the nature of the trial (secondary IV)

needs to be investigated with test of simple effects
- compare across the 2 levels of the main IV, separately for each level of the secondary IV
- if the main IV is a wihtin subjects IV, we use paired t-tests to compare the DV over its levels
- factor in the secondary IV, in this example 3 separate paired t tests
- these should only be conducted if a significant interaction is obtained

run cohens d for each test of simple effects

Question 6

2 way mixed ANOVA: locating model and residual variance

Answer 6

in a table titled “tests of between-subjects effects)
type III sub of squares a heading

Model variance for between subjects IV - IV name row

residual: error name row

Question 7

2 way mixed ANOVA: simple effects

Answer 7

a significant interaction suggests that the effect of intelligence on attractiveness ratings IS dependent on social interaction

needs to be investigated with test of simple effects:
* Used to compare the two levels of intelligence (the main IV), separately for each
level of social interaction (the secondary IV)
* Intelligence is a between-subjects IV, so we use independent t-tests to compare attractiveness ratings across the two levels of intelligence (high intelligence vs. low intelligence).
* We need to run two separate independent t-tests; one for each level of social
interaction (before chat and after chat)

if the main effect reversed, would use paired t-tests

cohens d