Multiple Independent Variables

factorial design

an experiment with two or more independent variables

factor

another name for an independent variable

condition

one level of an independent variable

cell

in a between subjects factorial design, a particular combination of the conditions of each independent variable

• ex. writing about negative experiences, thinking about positive experiences, writing about positive experiences, thinking about negative experiences

numbering notation

• number of numbers

• number values

• product of all numbers

number of numbers

total number of factors in design

• ex. 2 × 2 = 2 factors

• ex. 2 × 2 × 2 = 3 factors

number values

refer to the number of levels of each factor

• ex. 2 × 2 = 2 factors with 2 levels each

• ex. 2 × 3 = 2 factors, one with 2 levels and one with 3 levels

order of numbers makes no difference

product of all numbers

indicates the number of cells

• ex. 2 ×2 = 4 cells

• ex. 2 × 3 = 6 cells

main effect

the overall effect of one independent variable on the dependent variable

• ignores (averages across) the other independent variable)

• one main effect to test for each independent variable

marginal mean

the mean for one level of one independent variable

• typically a simple average across the levels of the other independent variable

interaction effect

a test of whether the effect of one independent variable depends on the level of the other independent variable

• a ‘difference of differences’

• remembers moderators

• in an experiment with 2 independent variables, just one possible interaction effect (but two ways to think about interaction effect)

moderators

an interaction effect is essentially a test of moderation

comparing main effects of valence

compare marginal means of negative valence and positive valence

marginal mean ex

marginal mean of negative valence —> combining writing and thinking cells of negative valence

marginal mean of positive valence —> combining writing and thinking cells of positive valence

marginal mean of writing —> combining negative and positive valence for writing

marginal mean for thinking —> combining negative and positive valence for thinking

interaction effect ex.

one perspective —> is the difference between negative writing and positive writing bigger/smaller/same as the difference between negative and positive thinking

second perspective —> is the difference between negative writing and neg thinking bigger/smaller/same as difference between positive writing and positive thinking

simple effect

a comparison between two cells (when you know you have an interaction?)

• 1. difference between people writing about pos and people writing about neg, difference between people thinking about pos and thinking about neg

• 2. difference between writing neg and thinking neg, difference between writing pos and thinking pos

crossover interaction

the effect of one independent variable on the dependent variables reverses across levels of the other independent variable

• simple effects in opposite directions

spreading interaction

the effect of one IV on the DV is stronger at one level of the other IV than it is at the other level

• simple effects are in the same direction OR only one simple effect

two options for testing effects in a factorial design

• factorial ANOVA

• contrast testing

factorial anova

a statistical test that provides an F statistic and p value for each main effect and interaction term

contrast testing

a series of t tests that individually test different patterns of means across cells

variations on factorial designs (between subjects)

independent groups factorial design, mixed factorial design

independent groups factorial design

both independent variables manipulated between subjects

• each cell has independent groups of randomly assigned participants

variations on factorial designs (within subjects)

repeated measures factorial design, mixed factorial design

repeated measures factorial design

both independent variables manipulated within subjects

• one sample experiences all cells

mixed factorial design

one independent variable is between subjects, one is within subjects

• ex. one group writes about both pos and neg, other group thinks about both pos and neg

• OR ex. one group writes and thinks about pos, one groups writes and thinks about neg

important note regarding main effects and interaction effects

if you find an interaction effect, the main effects are far less interesting and can be misleading

• interaction effects essentially tell you when the main effect is gonna happen (you have a main effect overall, but the interaction effect tells you that the interaction only occurs at a particular level of the independent variable)

three way interaction effect

the regular (2 way) interaction becomes two independent variables depends on the level of the third independent variable