Although there is nothing to prevent someone from examining simple interaction
effects in the absence of a significant higher-order interaction, cases for which this would
make any logical sense are rare. If, however, the experimenter has a particular reason for
looking at, for example, the ABinteraction at each level of C, he is perfectly free to do so.
On the other hand, if a higher-order interaction is significant, the experimenter should cast
a wary eye on all lower-order effects and consider testing the important simple effects.
However, to steal a line from Winer (1971, p. 442), “Statistical elegance does not necessar-
ily imply scientifically meaningful inferences.” Common sense is at least as important as
statistical manipulations.
13.13 A Computer Example
The following example illustrates the analysis of a three-way factorial design with unequal
numbers of participants in the different cells. It is roughly based on a study by Seligman,
Nolen-Hoeksema, Thornton, and Thornton (1990), although the data are contrived and one
of the independent variables (Event) is fictitious. The main conclusions of the example are
in line with the results reported. Note that we will not discuss how SPSS handles unequal
sample sizes in this example until we come to Chapter 15.
The study involved collegiate swimming teams. At a team practice, all participants
were asked to swim their best event as fast as possible, but in each case the time that was
reported was falsified to indicate poorer than expected performance. Thus each swimmer
was disappointed at receiving a poor result. Half an hour later, each swimmer was asked to
perform the same event, and their times were again recorded. The authors predicted that on
the second trial more pessimistic swimmers would do worse than on their first trial,
whereas optimists would do better.
Participants were classified by their explanatory Style (optimism versus pessimism),
Sex, and the preferred Event. The dependent variable was the ratio of , so a
value greater than 1.00 means that the swimmer did better on the second trial. The data and
results are given in Table 13.17. The results were obtained using SPSS. In examining the
results remember that SPSS prints several lines out output that we rarely care about, and
they can just be ignored.
Time 1 >Time 2
Section 13.13 A Computer Example 453
Table 13.16 (continued)
=2235.33 2 1290.67 2 758.33=186.33
SSAB atC 2 =SSCells BC at C 22 SSA at C 22 SSB at C 2
= 43 [(20.00 2 21.667)^2 1 Á 1 (15.00 2 21.667)^2 ]=2235.33
SSCells AB at C 2 =na(Xij 22 X..3)^2
= 43 2[(15.00 2 21.667)^2 1 Á 1 (28.75 2 21.667)^2 ]=758.33
SSB at C 2 =naa(X.j 22 X..2)^2
= 43 3[(29.00 2 21.667)^21 (14.33 2 21.667)^2 ]=1290.67
SSA at C 2 =nba(Xi.2 2 X..2)^2
