SD5. Factorial ANOVA (independent)

What are factorial ANOVAs used for?

to test for differences when we have more than one IV - we can explore the effects of each IV and interactions between the IVs

What are the three broad factorial ANOVA designs?

(1) all IVs are between-subjects (2) all IVs are within-subjects (3) a mixture of between-subjects and within-subjects IVs (mixed)

What does a two way factorial ANOVA tell us?

the main effects and the interaction between the IVs

What are the three null hypotheses for in a two way factorial ANOVA?

the main IV, the secondary IV and the interaction between the two IVs

How do you calculate the F value for the main IV?

variance due to the manipulation of the main IV / variance due to error alone

How do you calculate the F value for the secondary IV?

variance due to the manipulation of the secondary IV/ variance due to error alone

How do you work out the F value for the interaction between the IVs?

variance due to main IV + secondary IV / variance due to error alone

What are interaction effects?

the combined effects of multiple IVs/factors on the DV

What does a significant interaction effect indicate?

that the effect of manipulating one IV depends on the level of another IV

When interpreting interactions on a diagram, how do you know when there is no interaction?

the lines are parallel

What are the assumptions for a two-way independent ANOVA?

normality, homogeneity of variance, equivalent sample size and independence of observation

What is the parametric equivalent for factorial ANOVA?

there is none - if data violate the assumptions we must attempt to fix the data or simplify the design

How do you calculate partial eta squared?

SSM / SSM + SSR

What is classical eta squared?

proportion of the total variance attributable to the factor

What is partial eta squared?

proportion of the total variance attributable to the factor, partialling out (excluding) variance due to other factors

When are post hoc tests relevant?

when main effect of IV is significant and IV has more than 2 levels

Is Cohen D reported alongside post hoc results for factorial ANOVA?

no

What are simple effects?

the effect of an IV at a single level of another IV - comparison of cell means (conditions)

When do we consider simple effects?

in the presence of an interaction

How do you determine whether simple effects are significant?

we conduct t-tests between individual cell means - only appropriate when interaction significant

How do we correct for multiple comparisons when doing simple effect tests?

Bonferroni correction: divide required alpha level (e.g 0.05) by the number of comparisons - we then use this as our significance level