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

SECTION 14.3 | More about the Two-Factor ANOVA 467
2. In a two-factor ANOVA, which of the following is not computed directly but rather
is found by subtraction?
a. SS between treatments
b. SS A
c. SS B
d. SS A×B
3. A two-factor, independent-measures research study is evaluated using an analysis
of variance. The F-ratio for factor A has df = 1, 40 and the F-ratio for factor B has
df = 3, 40. Based on this information, what are the df values for the F-ratio for the
A × B interaction?
a. df = 2, 40
b. df = 3, 40
c. df = 4, 40
d. df = 7, 40
ANSWERS
1. D, 2. D, 3. B
14.3 More about the Two-Factor ANOVA
LEARNING OBJECTIVES
7. Explain how simple main effects can be used to analyze and describe the details of
main effects and interactions.
8. Explain how adding a participant variable as a second factor can reduce variability
caused by individual differences.
■ Testing Simple Main Effects
The existence of a significant interaction indicates that the effect (mean difference) for
one factor depends on the levels of the second factor. When the data are presented in a
matrix showing treatment means, a significant interaction indicates that the mean differences
within one column (or row) show a different pattern than the mean differences within
another column (or row). In this case, a researcher may want to perform a separate analysis
for each of the individual columns (or rows). In effect, the researcher is separating the twofactor
experiment into a series of separate single-factor experiments. The process of testing
the significance of mean differences within one column (or one row) of a two-factor design
is called testing simple main effects.
To demonstrate this process, we once again use the data from the paper vs. computer
screen study (Example 14.2), which are summarized in Figure 14.4.
EXAMPLE 14.4
For this demonstration we test for significant mean differences within each row of the
two-factor data matrix. That is, we test for significant mean differences between paper vs.
screen for the self-regulated condition, and then repeat the test for the fixed-time condition.
In terms of the two-factor notational system, we test the simple main effect of factor B for
each level of factor A.
For the Self-Regulated Condition Because we are restricting the data to the first
row of the data matrix, the data effectively have been reduced to a single-factor study