lecture 15 -- ANOVA for factorial designs

when do we need an ANOVA?

1. hypothesis testing with a single IV with more than 2 levels

2. hypothesis testing with 2 or more IVs

• complex design testing!

types of ANOVAs - ways

• how many factors?

• single factor, multilevel

  • one way

• factorial design with two IVs

  • two way

• factorial design with three IVs

  • three way

types of ANOVAs - bn or wn? both?

• if all between

  • randomized ANOVA

• if all within

  • repeated measures ANOVA

• combo of them

  • mixed ANOVA

types of ANOVAs — DVs testing?

• one DV

  • univariate ANOVA

• more than one

  • multivariate ANOVA

  • or MANOVA

2×3 all between subjects variables + one DV

two way randomized univariate ANOVA

3×3×2 combo of bn and wn and 3 DVs

• 3 way mixed MANOVA

4×2 all within sub, one DV

• 2 way repeated measures univariate ANOVA

ANCOVA

• analysis of covariance

• used when you have one DV

  • a categorical IV

  • a continuous IV (the covariate)

what is main effect?

• effect of a single IV

• how many main effects in a 2×2

  • 2

factors vs conditions

• factor = any one IV

• conditions = cells in the matrix

interactions

• the effect of one IV depends on the other IV

• do adolescent rats prefer THC more than adult rats?

possible outcomes of 2×2

•Main effect for IV 1

•Main effect for IV 2

•Main effects for both IVs, no interaction

•Main effect for IV 1 plus an interaction

•Main effect for IV 2 plus an interaction

•Main effect for both IVs plus an interaction

•No main effects, but an interaction

•No main effects, no interaction

where is the dv?

• always on the y-axis

how many main effects and interactions are possible?

2x2

3×3

2×3

2×2×2

• 2 ME, 1 interaction

• 2 ME, 1 interaction

• 2 ME, 1 interaction

• 3 ME, four interactions