Statistics for the Behavioral Sciences by Frederick J. Gravetter, Larry B. Wallnau ISBN 10: 1305504917 ISBN 13: 9781305504912

SUMMARY 473
SUMMARY
1. A research study with two independent variables is
called a two-factor design. Such a design can be diagramed
as a matrix with the levels of one factor defining
the rows and the levels of the other factor defining
the columns. Each cell in the matrix corresponds to a
specific combination of the two factors.
2. Traditionally, the two factors are identified as factor
A and factor B. The purpose of the ANOVA is to
determine whether there are any significant mean
differences among the treatment conditions or cells in
the experimental matrix. These treatment effects are
classified as follows:
a. The A-effect: Overall mean differences among the
levels of factor A.
b. The B-effect: Overall mean differences among the
levels of factor B.
c. The A × B interaction: Extra mean differences that
are not accounted for by the main effects.
3. The two-factor ANOVA produces three F-ratios: one
for factor A, one for factor B, and one for the A × B
interaction. Each F-ratio has the same basic structure:
F 5 MS seither A or B or A 3 Bd
treatment effect
MS within treatments
The formulas for the SS, df, and MS values for the twofactor
ANOVA are presented in Figure 14.5.
4. A significant interaction means that the effect of one
factor depends on the levels of the second factor. In
this case, evaluating the simple main effects for the
factor can provide a complete description of the effect
of that factor including its interaction with the second
factor.
5. Large individual differences within treatment often
can be reduced by using a participant variable, such as
age or gender, as an additional factor.
FIGURE 14.5
The ANOVA for an independentmeasures
two-factor design.
Total
SS 5 SX 2 2
df 5 N 21
G 2
N
Between treatments
T 2
G 2
SS 5 S 2
n N
df 5 (number of cells) 2 1
Within treatments
SS 5 S
df 5 S
SS each cell
df each cell
Factor A (rows)
SS 5 S
n
T 2
ROW
ROW
G 2
Factor B (columns)
T 2
COL
2 SS 5 S
N
n 2
COL
G 2
N
df 5 (levels of A) 21
df 5(levels of B ) 2 1
Interaction
SS is found by
subtraction
df is found by
subtraction
MS factor
SS for the factor
5 MS within 5
df for the factor
SS within treatments
df within treatments