Database Reference
In-Depth Information
CHAPTER
8
Comparing more than
two means: two factor
ANOVA with independent
samples; the important role of
interaction
8.1 INTRODUCTION
Chapter 6 introduced simple analysis of variance (ANOVA), where there is one fac-
tor or treatment variable, and more than two levels of this factor. In the example used
in Chapter 6, the one factor was the age of the person rating the sophistication of a
design, and the dependent variable was the sophistication rating (on a 1-5 Likert
scale). There were ive age groups, or ive levels of the factor.
Now suppose we wish to determine if the sophistication rating varies not only
with the age of the respondent, but also with the gender of the respondent. Now we
have two factors. How should we proceed?
Two-factor ANOVA to the rescue.
SIDEBAR: THE DANGER OF SEQUENTIAL TESTING
Hopefully, you've planned your study well enough so you've collected the data for all the factors
you want to consider in your posttest analysis. But invariably, there will be times where you don't
collect the data on all the factors that may have an impact on your dependent variable.
For example, you launch a survey that attempts to quantify inequality of pay between males and
females for the same job. In the demographic section of your career survey you, of course, collect
data on gender; you then test whether there is a difference in pay between the genders. However,
you did not collect data on highest level of education completed. After the results are in, it dawns on
you that level of education would possibly be a useful factor, since it can also affect pay; if the two
genders have a large difference in highest educational level completed, this could be the key factor
in explaining any discrepancy in pay between males and females.
What to do? Well, we could conduct another survey. This time, we would collect data on the fac-
tor: highest level of education completed, as well as pay, and test whether this factor affects pay.
Continued
 
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