Factorial Designs
➔ cross two or more IV/factors to examine influence on the DV
➔ factor = any variable used to create experimental conditions
◆ IV = factors that have levels manipulated by researcher
◆ participant variable = factors that have levels based on come characteristic of the
participant
◆ contextual variables = factors that have levels based on the characteristic of the
context/situation
◆ moderators = factors that indicate when, or with whom, or in what context situation,
an IV most likely changes the DV
➔ crossing factorsmeans looking at various combinationsof factors to examine the impact of
the DV
◆ ketchup and fries, ketchup and pancakes, syrup and fries, syrup and pancakes
◆ use a punnett square design for crossing
➔ factorial designs examineinteractions
◆ when one factor changes the degree to which another factor influences the DV
● X causing Y depends on whether M is true
● X causes Y when combined with M
● X works best when combined with M
➔ factors of a factorial design
◆ IV
◆ participant variables
◆ contextual variables
➔ why use factorial design
◆ isolate causal mechanism and rule out possible confounds when theory testing
◆ examine multiple treatments at the same time
◆ examine generalizability of causal effects across diff groups, time points, contexts, or
settings
➔ 2 x 2 factorial designs
◆ 2 factors (i.e. condiments and food)
◆ each factor has 2 levels
● condiments = ketchup and syrup
● food = fries and pancakes
◆ total of 4 conditions (multiply the factors by the levels
➔ factorial design notation
◆ # x # x # ; # = variable
● in this design there are 3 variables
◆ # = 3
● indicates how many levels of that variable
● 3 x 4
○ first variable has 3 levels
○ second variable has 4 levels
, ◆ the numbers multiplied together indicated number of conditions (aka the number of
cells)
● 2 x 2 = 4 conditions
● 2 x 2 x 2 = 8 conditions
Conceptualizing Factorial Designs
➔ a major strength of a factorial design is that it allows experimenter to examine 3 diff effects
◆ main effect of factor 1 (does it have an effect on the DV)
◆ main effect of factor 2 (does it have an effect on the DV)
◆ interaction between factor 1 and factor 2 (does the direction or size of the effect for
factor 1 stay the same across all levels of factor 2 [no interaction] or differ across the
levels [interaction effect])
➔ understanding effects
◆ cell means = means of each experimental condition
● ketchup, fries = cell mean
● ketchup, pancakes = cell mean
● syrup, fries = cell mean
● syrup, pancakes = cell mean
◆ marginal means = the means of a given level of an IV averaged across conditions
● [(ketchup,fries cell mean) + (ketchup, pancake cell mean)] / 2 = marginal mean
◆ grand mean = the overall mean averaged across all the conditions
● add all the cell means and divide by number of cell means
◆ difference = cell mean A - cell mean B
● shows the interaction effect
➔ interpreting results
◆ null effect: no main effect and no interaction
- doesn’t matter what condiment is on what food
◆ one main effect: one IV affects the DV; the other does not
- pancakes are good with both ketchup and syrup
➔ cross two or more IV/factors to examine influence on the DV
➔ factor = any variable used to create experimental conditions
◆ IV = factors that have levels manipulated by researcher
◆ participant variable = factors that have levels based on come characteristic of the
participant
◆ contextual variables = factors that have levels based on the characteristic of the
context/situation
◆ moderators = factors that indicate when, or with whom, or in what context situation,
an IV most likely changes the DV
➔ crossing factorsmeans looking at various combinationsof factors to examine the impact of
the DV
◆ ketchup and fries, ketchup and pancakes, syrup and fries, syrup and pancakes
◆ use a punnett square design for crossing
➔ factorial designs examineinteractions
◆ when one factor changes the degree to which another factor influences the DV
● X causing Y depends on whether M is true
● X causes Y when combined with M
● X works best when combined with M
➔ factors of a factorial design
◆ IV
◆ participant variables
◆ contextual variables
➔ why use factorial design
◆ isolate causal mechanism and rule out possible confounds when theory testing
◆ examine multiple treatments at the same time
◆ examine generalizability of causal effects across diff groups, time points, contexts, or
settings
➔ 2 x 2 factorial designs
◆ 2 factors (i.e. condiments and food)
◆ each factor has 2 levels
● condiments = ketchup and syrup
● food = fries and pancakes
◆ total of 4 conditions (multiply the factors by the levels
➔ factorial design notation
◆ # x # x # ; # = variable
● in this design there are 3 variables
◆ # = 3
● indicates how many levels of that variable
● 3 x 4
○ first variable has 3 levels
○ second variable has 4 levels
, ◆ the numbers multiplied together indicated number of conditions (aka the number of
cells)
● 2 x 2 = 4 conditions
● 2 x 2 x 2 = 8 conditions
Conceptualizing Factorial Designs
➔ a major strength of a factorial design is that it allows experimenter to examine 3 diff effects
◆ main effect of factor 1 (does it have an effect on the DV)
◆ main effect of factor 2 (does it have an effect on the DV)
◆ interaction between factor 1 and factor 2 (does the direction or size of the effect for
factor 1 stay the same across all levels of factor 2 [no interaction] or differ across the
levels [interaction effect])
➔ understanding effects
◆ cell means = means of each experimental condition
● ketchup, fries = cell mean
● ketchup, pancakes = cell mean
● syrup, fries = cell mean
● syrup, pancakes = cell mean
◆ marginal means = the means of a given level of an IV averaged across conditions
● [(ketchup,fries cell mean) + (ketchup, pancake cell mean)] / 2 = marginal mean
◆ grand mean = the overall mean averaged across all the conditions
● add all the cell means and divide by number of cell means
◆ difference = cell mean A - cell mean B
● shows the interaction effect
➔ interpreting results
◆ null effect: no main effect and no interaction
- doesn’t matter what condiment is on what food
◆ one main effect: one IV affects the DV; the other does not
- pancakes are good with both ketchup and syrup
