Factorial ANOVA

Chapter 12

Research Designs
 Between

– Between (2 between subjects factors)
 Mixed Design (1 between, 1 within subjects factor)
 Within – Within (2 within subjects factors)
 The purpose of this experiment was to determine the effects of testing mode (treadmill, bike) and gender (male, female) on maximum VO2.
Testing

mode is a within subjects factor with 2 levels
Gender is a between subjects factor with 2 levels
Maximum VO2 is the dependent variable.

A 3 x 2 Design
 The

designs are sometimes identified by the number of factors and the levels of each factor.
 The purpose of this experiment was to determine the effects of intensity (low, med, high) and gender (male, female) on strength development. All subjects experience all three intensities.  A 3 x 2 factorial ANOVA was used to determine the effects of intensity (low, med, high) and gender (male, female) on strength development.
 Gender is a between subjects factor, intensity is a within subjects factor.

Interaction?
 Interaction

is the combined effects of the factors on the dependent variable.
 Two factors interact when the differences between the means on one factor depend upon the level of the other factor.
 If training programs affect men and women differently then training programs interact with gender.
 If training programs affect men and women the same they do not interact.

No Interactions (Parallel Slopes)

The red lines represent the average scores for
BOTH A1 &
A2 at each level of B.
The red lines are graphing
B Main
Effects.

No Interaction
Red line is the
Average A1 mean (averaged across all levels of B).
Blue line is the average A2 mean. Main effect for
A compares the red and blue mean values. Significant Interaction
Groups A1 and A2 are
NOT
EQUALLY affected by the levels of
B.

Strong Interaction
Groups A1 and A2 are NOT EQUALLY affected by the levels of B.
A1 goes DOWN
A2 goes UP
Draw in the means for A1 and A2?
Draw in means for
B1, B2, B3.

Significant Interaction
Groups A1 and A2 are NOT
EQUALLY
affected by the levels of B.
Draw in the means for A1 and
A2.
Draw in means for
B1, B2, B3.

Factorial ANOVA Assumptions






Between-Between designs have the same assumptions as One-way ANOVA.
 Dependent Variable is interval or ratio.
 The variables are normally distributed
 The groups have equal variances (for betweensubjects factors)
 The groups are randomly assigned.
Between-Within are similar to Repeated measures
ANOVA, but now sphericity must be applied to the pooled data (across groups) & the individual group, this is referred to as multisample sphericity or circularity. Sphericity :requires equal differences between within subjects means. In other words the changes between each time point must be equal.

A Between-Between Factorial ANOVA
 The

purpose of this experiment was to determine the effects of practice (1, 3, 5 days/wk) and experience (athlete, non-athlete) on throwing accuracy.
 9 athletes & 9 non-athletes were randomly assigned to the practice groups (1, 3, 5 days/wk).  A 3 x 2 Factorial ANOVA with two between subjects factors practice (1, 3, 5 days/wk) and experience (athlete, non-athlete) was used to test the effects of practice and experience on throwing accuracy.

ANOVA Terminology
 The

purpose of this experiment was to compare the effects of Gender (M,F) and the dose of
Gatorade (none, 2 pints, 4 pints) on VO2.
Subjects were randomly assigned to Gatorade groups.  The independent variables Gatorade and Gender are FACTORS.
 The Gatorade has 3 LEVELS (none, 2 pints, 4 pints) , Gender has 2 LEVELS
 The dependent variable in this experiment is VO2
 This a 2 x 3 ANOVA with two between subjects factors. The Effects of Gender & Gatorade on VO2

Create a categorical variable for all
Between-Subjects Factors.
Gender (0 – Male, 1 – Female)
Gatorade (1 – None, 2 – 2 pints, 3 –
4 pints.

Enter Dependent Variable and Factors

Options Button

Check homogeneity of variance if you have a