The summary table for the analysis of variance is presented in Table 13.14c. From this
we can see that the three main effects and the A 3 Cinteraction are significant. None of
the other interactions is significant.^7Simple Effects
Since we have a significant interaction, the main effects of Aand Cshould be interpreted
with caution, if at all. To this end, the AC interaction has been plotted in Figure 13.4. When
plotted, the data show that for the inexperienced driver, night conditions produce consider-
ably more steering corrections than do day conditions, whereas for the experienced driver
the difference in the number of corrections made under the two conditions is relatively
slight. Although the data might give us some confidence in reporting a significant effect for
A(the difference between experienced and inexperienced drivers), they should leave us a
bit suspicious about differences due to variable C. At a quick glance, it would appear that
there is a significant Ceffect for the inexperienced drivers, but possibly not for the experi-
enced drivers. To examine this question more closely, we must consider the simple effects
of Cunder and separately. This analysis is presented in Table 13.15, from which we
can see that there is a significant effect between day and night condition, not only for the
inexperienced drivers, but also for the experienced drivers. (Note that we can again check
the accuracy of our calculations; the simple effects should sum to .)
From this hypothetical experiment, we would conclude that there are significant differ-
ences among the three types of roadway, and between experienced and inexperienced driv-
ers. We would also conclude that there is a significant difference between day and night
conditions, for both experienced and inexperienced drivers.SSC 1 SSAC
A 1 A 2
450 Chapter 13 Factorial Analysis of Variance
(^7) You will notice that this analysis of variance included seven Fvalues and thus seven hypothesis tests. With so
many hypothesis tests, the familywise error rate would be quite high. Most people ignore the problem and simply
test each Fat a per-comparison error rate of a5.05. However, if you are concerned about error rates, it would
be appropriate to employ the equivalent of either the Bonferroni or multistage Bonferroni tprocedure. This is
generally practical only when you have the probability associated with each F, and can compare this probability
against the probability required by the Bonferroni (or multistage Bonferroni) procedure. An interesting example
of this kind of approach is found in Rosenthal and Rubin (1984). I suspect that most people will continue to
evaluate each Fon its own, and not worry about familywise error rates.
5
Day Night
Variable C
10
15
A 1
(Inexperienced)
A 2
(Experienced)
Mean Number Corrections
20
25
30
Figure 13.4 ACinteraction for data in Table 13.14