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

464 CHAPTER 14 | Two-Factor Analysis of Variance (Independent Measures)
TABLE 14.6
A summary table for the
two-factor ANOVA for the
data from Example 14.2.
Source SS df MS F
Between treatments 53.75 3
Factor A (time control) 11.25 1 11.25 F(1, 16) = 3.75
Factor B (paper/screen) 11.25 1 11.25 F(1, 16) = 3.75
A × B 31.25 1 31.25 F(1, 16) = 10.42
Within treatments 48 16 3
Total 101.75 19
The following example is an opportunity to test your understanding of the calculations
required for a two-factor ANOVA.
EXAMPLE 14.3
The following data summarize the results from a two-factor independent-measures
experiment:
Factor B
B 1
B 2
B 3
Factor A
A 1 T = 0 T = 10 T = 20
n = 10 n = 10 n = 10
SS = 30 SS = 40 SS = 50
A 2
T = 40 T = 30 T = 20
n = 10 n = 10 n = 10
SS = 60 SS = 50 SS = 40
Calculate the total for each level of factor A and compute SS for factor A, then calculate the
totals for factor B, and compute SS for this factor. You should find that the totals for factor
A are 30 and 90, and SS A
= 60. All three totals for factor B are equal to 40. Because they
are all the same, there is no variability, and SS B
= 0.
■
■ Measuring Effect Size for the Two-Factor ANOVA
The general technique for measuring effect size with an ANOVA is to compute a value for η 2 ,
the percentage of variance that is explained by the treatment effects. For a two-factor
ANOVA, we compute three separate values for eta squared: one measuring how much of
the variance is explained by the main effect for factor A, one for factor B, and a third for the
interaction. As we did with the repeated-measures ANOVA (p. 427) we remove any variability
that can be explained by other sources before we calculate the percentage for each of
the three specific treatment effects. Thus, for example, before we compute the η 2 for factor
A, we remove the variability that is explained by factor B and the variability explained by
the interaction. The resulting equation is
for factor A, h 2 5
SS A
SS total
2 SS B
2 SS A3B
(14.16)
Note that the denominator of Equation 14.15 consists of the variability that is explained
by factor A and the other unexplained variability. Thus, an equivalent version of the
equation is,
for factor A, h 2 5
SS A
SS A
1 SS within treatments
(14.17)