Comparing more than two means: one factor ANOVA with a withinsubject design - Improving the User Experience through Practical Data Analytics - page 163

CHAPTER

7

Comparing more than
two means: one factor
ANOVA with a within-
subject design

7.1 INTRODUCTION
As we suggested in Chapter 6, there are probably many times when you are presented
with several alternatives and asked which is “best.” We also noted that, of course,
the word, “best,” needs to be clariied, as obviously, “best” can be the highest—for
example, satisfaction with a design; other times, “best” might be the smallest—for
example, time to complete a task. As a matter of fact, while we hate to be repetitive,
we note again that this kind of comparison test may be one of the most common types
of jobs you're assigned as a researcher.
Chapter 2 considered comparing two means, with independent samples—for
example, the mean satisfaction rating given for two Web designs. We had what we
referred to as “independent samples,” which meant that different people provided
ratings for each design. We discussed reasons why we might not want to have the
same person evaluating both designs. In Chapter 3, we considered the same issue of
comparing two means, but with the same person evaluating both designs. We referred
to that as “paired data.” In both cases, we performed a t-test (but different ones!!) to
test the hypotheses:

H0: μ1=μ2

H1: μ1≠μ2 .

A key to Chapters 2 and 3 was that there were, indeed, only two designs (or tasks,
or, to be general, “columns”) whose means were being compared.
In Chapter 6, we generalized the problem addressed in Chapter 2 to the case of
having the means of more than two designs, or tasks, or, anything else. We retained
the key condition of Chapter 2 of having independent samples—different people