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

SECTION 14.2 | An Example of the Two-Factor ANOVA and Effect Size 465
Similarly, the η 2 formulas for factor B and for the interaction are as follows:
for factor B, h 2 5
SS B
SS B
5
(14.18)
SS total
2 SS A
2 SS A3B
SS B
1 SS within treatments
for A 3 B, h 2 5
SS A3B
SS A3B
5
(14.19)
SS total
2 SS A
2 SS B
SS A3B
1 SS within treatments
Because each of the η 2 equations computes a percentage that is not based on the total
variability of the scores, the results are often called partial eta squares. For the data in
Example 14.2, the equations produce the following values:
h 2 for factor A stimes controld 5 11.25
11.25 1 48 5 0.190
h 2 for factor B spresentation moded 5 11.25
11.25 1 48 5 0.190
h 2 for the A 3 B interaction 5 31.25
31.25 1 48 5 0.394
IN THE LITERATURE
Reporting the Results of a Two-Factor ANOVA
The APA format for reporting the results of a two-factor ANOVA follows the same
basic guidelines as the single-factor report. First, the means and standard deviations are
reported. Because a two-factor design typically involves several treatment conditions,
these descriptive statistics often are presented in a table or a graph. Next, the results of all
three hypothesis tests (F-ratios) are reported. The results for the study in Example 14.2
could be reported as follows:
The means and standard deviations for all treatment conditions are shown in Table 1.
The two-factor analysis of variance showed no significant main effect for time control,
F(1, 16) = 3.75, p > .05, η 2 = 0.190 or for presentation mode, F(1, 16) = 3.75, p > .05,
η 2 = 0.190. However, the interaction between factors was significant, F(1, 16) = 10.41,
p < .01, η 2 = 0.394.
TABLE 1
Mean quiz score for each treatment condition
Paper
Presentation Mode
Computer Screen
Time Control
Self-regulated
Fixed
M = 9.00 M = 5.00
SD = 1.58 SD = 1.73
M = 8.00 M = 9.00
SD = 1.87 SD = 1.73