Ch. 14: Factorial ANOVA

What is the difference between a one way ANOVA and a factorial ANOVA?

One Way ANOVA:
Single factor experiments - one IV

Factorial ANOVA:
Factorial designs - two or more IV

What is a factorial notation?

A way to summarize the design of a study numerically.

What does a "2 x 2 design" mean?

The number of numbers = number of factors (IV)
-Two factors

Actual numbers = number of levels for each factor
-Each factor has two levels

What does a "2 x 3 design" mean?

Factors: 2
Levels: one factor has 2 levels and the other has 3

What does a "3 x 4 x 5 design" mean?

Factors: 3
Levels: one factor has 3 levels, one has 4, and one has 5

What are conditions? How do you get them?

Conditions: number of cells in the matrix

Multiple numbers in factorial design to get number of conditions

Ex:
2x2 design = 4 cells (conditions)
2x3 design = 6 cells
2x3x3 = 18 cells

What is the design in this example: We recruit younger and older adults to participate. Half of each group is given testosterone and half is given placebo shots.

Factors: 2- age & treatment

Levels:
Age = 2 (younger & older adults)
Treatment = 2 (testosterone & placebo)

2 x 2 design

What is the design in this example: Younger and older adults participate with 1/3 given testosterone, 1/3 given placebo, and 1/3 given nothing

Factors: 2- age & treatment

Levels:
Age = 2 (younger & older adults)
Treatment = 3 (testosterone, placebo, & nothing)

2 x 3 design

What is the design in this example: Students are asked to point to 3 unseen locations: one near campus, one a nearby city, and one a distant city. All participants are in a windowless room. Half use a compass, half do not.

Factors: 2 - locations & compass

Levels:
Locations = 3 (near campus, nearby city, & distant city)
Compass = 2 (has it & doesn't have it)

3 x 2 design

What are the two types of outcomes in factorial designs?

Main effects
Interactions

What is a main effect?

The overall effect of a single variable/factor
-The effect of one variable, ignoring the other variables

Can have as many main effects as there are factors

How can you identify main effects when looking at means?

Compute row and column means that combine data for al cells at one level of a variable

What is an interaction?

When the effect of one factor depends on the level of another factor

How can you identify interactions when looking at means?

Calculate differences with rows and columns
Always do the same group first
See whether the differences differ

How can you identify main effects with graphs?

One line is higher than the other line
or one side of the graph is always higher than the other side (i.e. a steep slope)

How can you identify interactions with graphs?

The lines aren't parallel

How do you know if it is significant?

When looking at the spss analysis, if 'sig' (p-value) is less that 0.05 then it is significant.

What does F(1,36) = 9.86, p<0.05 mean?

F: test used
1: df for source (from output)
36: df total (bottom of output)
9.86: F for that source in output

How do you report results?

Report conclusion (reject or not) for each poss. effect. Only write up stats for significant effects.

A factorial ANOVA revealed no significant effect of either gender or exercise type. However, these two factors did significantly interact to predict weight loss, F(1,36) = 9.86, p<0.05

Then describe interaction (look at graphs -or means- and describe); only interpret significant effects

The nature of the interaction suggested that exercise type did not matter for males but did matter for females. High impact exercise resulted in more weight loss than low impact exercise among female participants.