PSY 2302 Ch. 9 & 10 Factorial ANOVA

a factorial ANOVA is different from other types because it can have two or more

independent variables

why would we want to use a factorial ANOVA?

- variables may interact with each other
i.e: different to have caffeine in day v.s night
i.e: the effect of caffeine might depend on time of time

a factorial design can be either

between subjects or within subjects or even mixed

what is a fully crossed or fully factorial design?

- all possible combinations
- 2x2 = each independent variable has two levels (i.e caffeine, no caffeine and day, night), 4 combination

what are the multiple types of effects?

- main effects of each independent variable
- interaction between them (?)

main effect

there is an effect but ignoring one of your IV

interaction effects

effect of one independent variable depending on the other independent variable
i.e: occurs between coffee/caffeine and time of day because quiz outcome is dependent on time of day (you do better with coffee in the morning, but not so well with coffee in the evening)

within subjects

each participant appears in each condition

repeated measures

all factors are within subjects
- each participant is tested under every possible combination of conditions in design

between subjects

participants are assigned to conditions so that each participant appears in only one condition

between subjects factors

independent variables in factorial design in which participants are assigned to conditions so that each participant only appears in only one condition

significant interaction

effect of one independent variable depends on the other
i.e: amount of coffee/caffeine had

how to calculate 2x2 ANOVA

if between subjects calculate sum of squares total, calculate each main effect

how to calculate interactions

- want to see how much additional variance can be explained by looking at our four groups as FOUR groups
- take mean of each condition, subtract each "combined" group score, and add back grand mean and then sum of squares interaction

if you have 3 independent variables you can have

3 different interactions
i.e: coffee x time of day x # of hrs of sleep/study y

what other type of factorial design can you have?

mixed (between and within) `

if you have an interaction it changes the meaning of your main effect which means

you can no longer just look at main effect
- is main effect CONSISTENT?

consistent main effect

there is an interaction but effect always happens

i.e: the outcome of a quiz depends on coffee and time of day but there is always a better outcome of quiz on coffee, time of day (and maybe # of hours spent studying)

i.e: exercise ALWAYS improves moods compared to control but affirmations only seem to help (depends) if you are not exercisingin

inconsistent main effect

can't say 1 IV is always different from IV 2 because IV2 fully depends on IV 1 since there is a consistent null main effect of IV 1

mixed designs

includes both between person and within person factors
i.e: assign people to exercise or no exercise throughout study BUT some mornings affirmations will be done and others mornings no affirmations