Factorial Designs

• More than one independent variable
• More complex designs
• Each level of one independent variable is paired with every level of every other independent variable

An example of a factorial design:

	Drug B - 20 mg	Drug B 100 mg
Drug A - 20 mg	10	20
Drug A - 100 mg	20	30

Can this be a between or a within or a mixed design?
 
 
 
 
 

Other Examples of Factorial Designs

• cognitive dissonance: choice X pay
• memory: age X domain

What you can find in the data

• Main Effects
• The separate effects of each independent variable (averaging over the other variables)
• e.g., drug A tends to make you sleepy, same for drug B
• Interactions
• The effect of one independent variables changes as the level of another independent variables varies
•  e.g., two depressants together can actually be a stimulant
• The interaction is like a "free" experiment

What is the null hypothesis?

• There are many for a 2 X 2 design
• Main effect of factor A
• H_a0: mu_a1=mu_a2; H_a1: mu_a1<>mu_a2
• Main effect of factor B
• H_b0: mu_b1=mu_b2; H_a1: mu_b1<>mu_b2
• Interaction
• H_i0: mu_a1-mu_b1=mu_a2-mu_b2
• H_i1: mu_a1-mu_b1<>mu_a2-mu_b2

Graphs

Floor/Ceiling effects and interactions (see last panel)

• Is it really an interaction or an artifact?

Crossover Interaction

• Strongest form of an interaction
• See two panels up on left

Naming Designs

• 2 X 2
• two variables with two levels each
• 2 X 2 X 3
• three variables
• two levels, two levels, and three levels
• 12 groups
• Within/Between/Mixed

Three way interactions

• the level of one variable is affected differently by the levels of a second variable, but that effect is mediated by the level of the third variable.
• it gets tricky to interpret your data

Multiple Dependent Variables

• univariate vs. multivariate