Lecture 5 Flashcards
what are advantages of factorial designs over one-factor designs?
advantages of factorial designs
- more efficient
- information about A x B interaction
- in case of additivity: generalizability
what kind of effects can be investigated in a two factorial design?
- main effect of A
- main effect of B
- interaction A x B
- simple effect of A
> effect of A given B1
> effect of A given B2
- simple effect of B
> effect of B given A1
> effect of B given A2
factorial design:
> what is crossing
> what is nesting
crossing: each level of A co-occurs with each level of B
A x B
> A varies within subjects: participant is crossed with A:
P x A
nesting: each level of A co-occurs with at most one level of B, but not vice versa
A(B)
> A varies between subjects, participant is nested within A: P(A)
calculation of df with formulae: what can go wrong?
> solution?
calculation df:
> when groups are not equal size, formulae fail
> using the matrix approach to calculating DF always yields the right answer
what is the difference between a two factorial between subjects and within subjects design?
between subjects:
> P(AxB) participants nested within A x B is the error term for ALL effects
within subjects:
> participant is crossed with both A and B
> for each effect the error term is the interaction of that effect with P
> for A: P x A, for B: P x B etc
critical question: how variable is the effect of A, B and A x B across participants
two factorial within subject design
> calculation of df?
SSa?
SS pxa?
SSb?
SS pxb?
SS axb?
SS axbxp?
SStotal?
SSa: a-1
SS pxa: (n-1)(a-1)
SSb: b-1
SS pxb: (n-1)(b-1)
SS axb: (a-1)(b-1)
SS axbxp: (a-1)(b-1)(n-1)
SStotal: nab-1
within subjects two factorial
> testing effect against what?
> difference with between subject?
within subjects:
> testing each effect against own unique error term
> between subject test all effects against a general error term
