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 469
Note that this F-ratio has the same df values (1, 16) as the test for factor B main effects
(paper vs. screen) in the original ANOVA. Therefore, the critical value for the F-ratio is
the same as that in the original ANOVA. With df = 1, 16 the critical value is 4.49. In this
case, our F-ratio far exceeds the critical value, so we conclude that there is a significant
difference between the two modes of presentation, paper and screen, when study time is
self-regulated.
For the Fixed-Time Condition The test for the fixed-time condition follows the same
process. The data for this condition are as follows:
For these data,
Paper
Fixed-time condition
Computer
Screen
n = 5 n = 5 N = 10
M = 8 M = 9 G = 85
T = 40 T = 45
SS between treatments
5S T 2
n 2 G 2
N
5 402
5 1 452
5 2 852
10
5 320 1 405 2 722.5
5 2.5
Again, we are comparing only two treatments, so df = 1 and,
MS between treatments
5 2.5
1 5 2.5
Using MS within treatments
= 3 from the original two-factor analysis, the F-ratio for the fixedtime
condition is
F 5 MS between treatments
MS within treatments
5 2.5
3 5 0.833
As before, this F-ratio has df = 1, 16 and is compared with the critical value F = 4.49.
This time the F-ratio is not the critical region and we conclude that there is no significant
difference between paper and computer when study time is self-regulated.
■
As a final note, we should point out that the evaluation of simple main effects is used to
account for the interaction as well as the overall main effect for one factor. In Example 14.2,
the significant interaction indicates that the difference between paper vs. computer screen
(factor B) depends on how time is controlled (factor A). The evaluation of the simple main
effects demonstrates this dependency. Specifically, the mode of presentation has no significant
effect on performance when study time is fixed, but does have a significant effect
when time is self-controlled. Thus, the analysis of simple main effects provides a detailed
evaluation of the effects of one factor including its interaction with a second factor.
The fact that the simple main effects for one factor encompass both the interaction and
the overall main effect of the factor can be seen if you consider the SS values. For this
demonstration,