Factorial Anova

Factor

An independent variable, so between subjects anova will have ONE factor.

Level

These are how many conditions each IV has; so if a factor is drug dose, the levels could be 5mg, 10mg, 15mg

Factorial design

A design where every level of every factor is paired with every level of every other factor. 

Interaction

The effect of one IV (factor) on the DV depending on the level of another IV (factor).

Parallel lines in the interaction

No interaction.

Main effect

The effect of one of the independent variables (one factor) averaged across the levels of another IV (factor)

Simple effect

The effect of one of the IVs (factors) at one level of another IV (factor)

Step 1

Source table which includes: Top row same as other anovas (SS, df, mean SS, F)

• Side row has the 2 factors, interaction, error and total

Step 2

Degrees of freedom:

• group: k-1 (DO FOR BOTH FACTORS/IVs)

• Interaction = group1 df x group 2 df

• Error = df(total) - group and interaction terms (N - # of cells)

• Total = N - 1

Step 3

Total SS: Sum of x-xhat squared for all numbers. Same as regulr ANOVA

Step 4

Group SS for the factors (finding a main effect)

• Do SSgroup = Sum of nj (xhat - grand mean)2

  • Similar to the equation used for one-way anovas again.

SS for each factor; need the means for each level of the factor.

• EX. self efficacy got the mean for LOW SE and HIGH SE

• Do the equation for each level + then add the answers together

Step 5

SS for interaction term.

First calculate SS cells, take the mean of one level of one factor. Do this for each individual level in each factor.

• Subtract each cell mean from the grandmean squared, multiple by number of people in each cell.

• Take the sum from each combination to get SS cells. 

SS cells - SS (factor 1)- SS (factor 2)

SScells

Sum of squares associated with the cell means.

Step 6

Get Mean SS:

• Just divide the DF from SS

Step 7

Calculate the F’s

• Divide each factor + the interaction mean SS by the error MS