# FACTORIAL ANOVA

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```					FACTORIAL ANOVA
Overview of Factorial ANOVA
 Factorial Designs
 Types of Effects
 Assumptions
 Analyzing the Variance
 Regression Equation
 Fixed and Random Effects
FACTORIAL DESIGNS

 All combinations of levels of two or
more independent variables (factors) are
measured
Types of Factorials
Between subjects (independent)
Within subjects (related)
Mixed
Between Subjects
A
1              2
Subjects Subjects
1   1-10     21-30
B
Subjects       Subjects
2   11-20          31-40
Within Subjects
A
1              2
Subjects Subjects
1   1-40     1-40
B
Subjects       Subjects
2   1-40           1-40
Mixed (A Between, B Within)
A
1              2
Subjects Subjects
1   1-20     21-40
B
Subjects       Subjects
2   1-20           21-40
TYPES OF EFFECTS
 A main effect is the overall effect of
each IV by itself, averaging over the
levels of any other IVs
 An interaction occurs when the effects of
one factor change depending on the level
of another factor
Simple Effects
 An interaction can be understood as a
difference in simple effects
A simple effect is the effect of one factor
on only one level of another factor
If the simple effects differ, there is an
interaction
70
60
50
d.v.   40               B2
30
20               B1
10
0
1       2
A
70
60               B2
50
d.v.   40               B1
30
20
10
0
1       2
A
70           B2
60
50
d.v.   40
30               B1
20
10
0
1       2
A
70
60
B2
50
d.v.   40
30
20           B1
10
0
1       2
A
ASSUMPTIONS
 Interval/ratio data
 Normal distribution or N at least 30
 Independent observations
 Homogeneity of variance
 Proportional or equal cell sizes
ANALYZING THE VARIANCE

Total Variance = Model + Residual
Model Variance is further divided into:
 Factor A
 Factor B
 A x B interaction
Comparing Variance
F-test for each main effect and for the
interaction
Each F-test compares variance for the
effect to Residual variance
REGRESSION EQUATION

Y = b0  b1A i + b 2 Bi + b 3ABi + ei

bo is mean of base group
b1 is the main effect of factor A
b2 is the main effect of factor B
b3 is the A x B interaction
FIXED VS. RANDOM EFFECTS

Fixed Factor: only the levels of interest
are selected for the factor, and there is no
intent to generalize to other levels
Random Factor: the levels are selected at
random from the possible levels, and
there is an intent to generalize to other
levels
APA Format Example
The two-way between subjects ANOVA
showed a significant main effect of customer
type, F(1,1482) = 5.04, p = .025, partial h2 =
.00, a non-significant main effect of industry
type, F(2,1482) = 0.70, p = .497, partial h2 =
.00, and a significant interaction, F(2,1482) =
3.12, p = .044, partial h2 = .00.

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 views: 3 posted: 2/10/2012 language: pages: 24