2 way

⭐ when to use factorial ANOVA

when there are two independent variables

⭐ factorial design

a design with more than one independent variable

⭐ what does 2 x 2 mean

2 levels of IV1 and 2 levels of IV2

⭐ number of F tests in a 2-way ANOVA

3 (main effect of IV1, main effect of IV2, interaction)

⭐ main effect

effect of one independent variable on the dependent variable ignoring the other IV

⭐ number of main effects in 2-way ANOVA

2 (one for each IV)

⭐ interaction

when the effect of one IV changes depending on the level of another IV

⭐ what interaction means conceptually

the effect of one IV is different across levels of the other IV

⭐ do IVs affect each other

no, IVs do not affect each other, only the DV

⭐ where interactions occur

between independent variables

⭐ MSw

SSwithin divided by dfwithin

⭐ SSwithin meaning

variability within each cell

⭐ cause of SSwithin

everything except the independent variables because individuals within each group are treated the same

⭐ why SSwithin exists

individuals differ even when treated the same within a cell

⭐ SSbetween in factorial ANOVA

variability due to IV1, IV2, and their interaction

⭐ F statistic in ANOVA

MSbetween divided by MSwithin

⭐ df for main effects

number of levels minus 1

⭐ df for interaction

product of the dfs of each IV

⭐ dfwithin

N minus number of cells

⭐ cell definition

a unique combination of levels of both independent variables

⭐ main effect comparison

based on differences between row or column means

⭐ interpreting main effect

compare averages across levels of one IV

⭐ what to do if main effect is significant

describe the pattern of means

⭐ how to explain interaction

describe how the effect of one IV differs at each level of the other IV

⭐ what happens if interaction is significant

interaction takes priority in interpretation

⭐ why interaction takes priority

it explains differences that main effects may hide

⭐ crossover interaction

when lines cross and effects reverse direction

⭐ non-parallel lines

indicate likely interaction

⭐ parallel lines

indicate no interaction

⭐ strength of interaction indicator

less parallel lines means more likely interaction

⭐ interaction without main effects

possible

⭐ main effects without interaction

possible

⭐ purpose of factorial ANOVA

test multiple IVs and their interaction at the same time

⭐ Tukey use in factorial ANOVA

only for significant main effects with more than 2 levels

⭐ Tukey for interaction

do not use Tukey for interaction

⭐ how to analyze interaction instead of Tukey

examine pattern of cell means

⭐ partial eta squared

effect size for factorial ANOVA

⭐ when to calculate partial eta squared

only when the effect is significant

⭐ partial eta squared formula for IV A

SS for A divided by (SS for A plus SSwithin)

⭐ partial eta squared formula for IV B

SS for B divided by (SS for B plus SSwithin)

⭐ partial eta squared formula for interaction

SS for interaction divided by (SS for interaction plus SSwithin)

⭐ meaning of partial eta squared

proportion of variance explained by that effect

⭐ effect size cutoffs

small = .01, medium = .06, large = .14

⭐ error variance in factorial ANOVA

SSwithin

⭐ why within-cell variance is error

IVs are constant within each cell

⭐ what must be reported if F is significant

pattern of means and interpretation

⭐ what not to do for interaction in this course

do not run Tukey for interaction

⭐ goal when explaining interaction

clearly show how effects differ across conditions