Chapter 8
Nonparametric Methods
The methods you’ve seen before for dealing with a quantitative response
variable have always assumed that the response variable has a normal
distribution. In this chapter we’ll learn about methods that make almost no
distributional assumptions. We call these nonparametric methods.
The name “nonparametric” comes from the fact that traditional statisti
cal methods assume that the response variable has some distribution (typi
cally normal) and then try to say something about the parameters (like the
mean or standard deviation) that describe that distribution. Nonparametric
methods work an entirely different way.
The first section of this chapter will introduce a nonparametric hypoth
esis test that corresponds to a traditional hypothesis test that you learned
about in your previous course, while the second section discusses some
more general ideas about all nonparametric methods. There are plenty of
more complicated nonparametric methods out there for dealing with all
sorts of different situations.
This chapter is merely intended to give you
the general idea of how nonparametric methods work.
8.1
MannWhitney
U
Test
In your first statistics course, you learned about a
t
test for whether the
subjects in two independent groups have the same population mean for some
response variable (Section 10.2 of our textbook). One of the assumptions of
that test was that the data came from an approximately normal population
distribution.
The MannWhitney
U
test is a nonparametric method for
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8.1 MannWhitney
U
Test
159
analyzing the same type of data, but it doesn’t make any assumption about
normality. This means that a traditional
t
test is unreliable when the data
comes from a highly nonnormal distribution or contains outliers, while the
Mann Whitney
U
test will still work well in these situations.
Note:
This test is also called the Wilcoxon ranksum test.
I don’t
want to call it that, because I don’t want us to get it confused with
the Wilcoxon signedranks test, which is something entirely different
that the textbook also talks about in another section.
To further
complicate matters, our textbook calls the MannWhitney
U
test just
the Wilcoxon test and it describes the test using a slightly different
test statistic from the one we’ll use here.
It doesn’t really matter,
because the two versions of the test yield exactly the same pvalue
and thus the same results.
Basic Setup
We record the value of some response variable for subjects in two different
groups, which we then rank from smallest to largest among the values
from the two groups combined. (Alternatively, our data may have consisted
simply of ranks to begin with.)
Remember that we’re testing whether or not there’s a difference between
the groups. Let’s think about what we think we might see.
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 Summer '08
 TA
 Statistics, Statistical hypothesis testing, Nonparametric statistics, mannwhitney u test

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