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SIDEBAR: REPLICATION: THE GOOD, THE BAD AND THE “PENALTY”.—cont'd
You will get output that does not include any measure of interaction and tests each of the two
factors in the correct way under this no-interaction assumption.
In the within-subject design in Chapter 7, we needed to do this to obtain the S-N-K analysis;
after all, in that within-subjects design, there was no replication - as we noted, for each combination
of person and task, there was, and can be, only one data point.
8.6 SUMMARY
In this chapter, we have introduced the studying of the impact of two factors on
the dependent measure/dependent variable. This necessitated the introduction of the
very important idea of interaction effects . These are joint effects that may impact
the dependent measure (in our core example, Sophistication Rating) in a way that
is not additive and may play a key role in explaining how different factors impact
the dependent measure. The two factors, individually, are not necessarily the only
important forces at work.
8.7 EXERCISE
1. Consider the situation where you have three age groups and four designs, and
wish to test whether (1) the true average sophistication rating is the same for
each design, (2) the true average sophistication rating is the same for each age
group, and (3) the two factors have (nonzero) interaction. You have independent
samples, as each person evaluates only one of the four designs (and each person
obviously belongs to only one age group). There are two people (replicates) for
each age/design combination, thus having 3*4*2 = 24 data values. Data for the
sophistication ratings for each design are in data iles in SPSS (ile name: Chapter
8..Exercise 1.data). The output in SPSS is in a ile (ile name: Chapter 8..Exercise
1.output). All iles are on a Web site indicated in the preface to the text.
Perform an ANOVA to test whether the (true) average sophistication ratings
are equal or not for the four designs, equal or not for the three age groups, and
whether there is an age*design interaction effect.
A Word ile (ile name: Chapter 8.Exercise 1.discussion) is also provided,
which discusses the results.
 
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