# Factorial ANOVA - PowerPoint by vymIR8ke

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```									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.
 Testingmode 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 between-subjects
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      Choose the Sidak post hoc
you have a between subjects factor.   test.
Plots

axis, Gender for Separate Lines.
2. Click Add Button, then Continue
Buttton.
Method 1 for Simple
UNIANOVA VO2 BY Gender Gatorade                    Effects
/METHOD=SSTYPE(3)
/INTERCEPT=INCLUDE
/EMMEANS=TABLES(OVERALL)
/PRINT=OPOWER ETASQ HOMOGENEITY DESCRIPTIVE
/CRITERIA=ALPHA(.05)

Enter the first interaction term in the Compare ( ).
Then switch the order.

Click Paste, then Window to view Syntax
Window
Method 2 for Simple Effects

MANOVA
VO2 BY Gender(0 1) Gatorade(1 3)
/print CELLINFO SIGNIF( Univ MULTIV AVERF HF GG).
Output: Descriptives
See page 405 of Field for an additional
test to check for homogeneity of
variance.

Check homogeneity of variance if
you have a between subjects factor.
The null hypothesis is that the
groups have equal variance. In this
case you retain the null. You don’t
want this to be significant, if it is
significant you are violating an
assumption of ANVOA: homogeneity
of variance.

The groups have equal variance, Levine’s
test F(5,42) = 1.53, p = .20
ANOVA Results

No main effect for Gender F(1,42) = 2.032, p = .161.
Sig. main effect for Gatorade F(2,42) = 20.065, p = .000
Sig. interaction between Gender and Gatorade dose F(2,42)
= 11.911, p = .000
Gender * Gatorade F(2,42) = 11.91, p = .000

None                66.88 ± 10.33      60.62 ± 4.96      63.75 ± 8.47
2 pints             66.87 ± 12.52      62.50 ± 6.55      64.69 ± 9.91
4 pints             35.63 ± 10.84      57.50 ± 7.07     46.56 ± 14.34
Gender Mean         56.46 ± 18.50      60.21 ± 6.34     58.33 ± 13.81

Gender F(1,42) = 2.032, p = .161              Gatorade F(2,42) = 20.065, p=.000

This slide indicates which means are being compared by each F ratio.
Post hoc for Gender Main Effect

Gender F(1,42) = 2.032, p = .161
Post hoc for Gatorade Main Effects

4 pints was significantly different from
none and 2 pints.
Simple Effects Testing 2 Steps
Compare gender at each level of
Are males diff from females for                    Male          Female
none?                                None      66.88 ± 10.33   60.62 ± 4.96
2 pints   66.87 ± 12.52   62.50 ± 6.55
Are males diff from females for 2
pints?                               4 pints   35.63 ± 10.84   57.50 ± 7.07

Are males diff from females for 4
pints?

Compare the dose of gatorade for
each level of gender. For males is
there a difference between none, 2                Male           Female
pints, 4 pints?
None      66.88 ± 10.33   60.62 ± 4.96
For females is there a difference    2 pints   66.87 ± 12.52   62.50 ± 6.55
between none, 2 pints, 4 pints?      4 pints   35.63 ± 10.84   57.50 ± 7.07
Difference in Gender at each Gatorade Level

Males are significantly
different from females for 4
each Gender Level

For males, 4 pints is significantly
different from none and 2 pints.
Homework
Analyze the Task 1 the book, see page 455.

Do a Sidak post hoc test instead of the planned contrast
suggested in the book.

Use simple effects testing for a significant interaction.

Use the Sample Methods and Results section as a guide to
write a methods and results section for your homework.

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