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means equally tall and thin/short and fat curves) for all values of X. For this to be
exactly true, it is often a bit dubious.
However, these two assumptions are referred to as “robust.” Essentially, this
means that if the two assumptions are “moderately violated,” it does not materially
affect the results of the analysis. In the world of user experience data, it is unlikely
that any assumption violations are suficiently large to affect the results materially.
There are ways to test these assumptions, but they are well beyond the scope of this
chapter.
The third assumption, called “independence,” is that the data points are inde-
pendent. This is a more critical assumption (because it is not robust), but is usually
the easiest to avoid violating. If each respondent provides one row of data and there
is no connection between the respondents/data points, the assumption is generally
satisied fully.
Overall, the majority of people who perform correlation and regression analyses
do not worry much about these assumptions, and in the vast majority of cases, there
is no problem with concluding an accurate interpretation of the results. Still, if the
results arrived at seem to very much belie common sense, perhaps somebody familiar
with these assumptions should be called upon for consultation.
9.9
EXERCISE
1.
Consider the Excel data in the ile “Chapter 9.Exercise 1,” which has 402 data
points on Y (column A) and X (column B).
a.
Run a correlation analysis. Is the correlation signiicant at
α
=0
.
05? What
percent of the variability in Y is explained by the linear relationship with X?
b.
Run a regression analysis. What is the least-squares line? What do you pre-
dict Y to be when X = 4?
c.
Repeat parts (a) and (b) using SPSS and the data in the ile named “Chapter
9..Exercise 1.data.” The output is in a ile named “Chapter 9..Exercise
1.output.”
The answers are in a Word ile named, “Chapter 9.Exercise 1.ANSWERS.”
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