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Unformatted text preview: Chapter 4 Nonparametric Methods For the rest of the semester, we’ll be discussing different ways to analyze data with a quantitative response variable. The methods you’ve seen before for dealing with a quantitative response variable have always assumed that the response variable has a normal distribution. We’ll make that same assump- tion for some methods we’ll learn about in later chapters, but 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. 4.1 Mann-Whitney 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 4.1 Mann-Whitney U Test 53 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 Mann-Whitney U test is a nonparametric method for an- alyzing 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 non-normal 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 rank-sum test. I don’t want to call it that, because I don’t want us to get it confused with the Wilcoxon signed-ranks test, which is something entirely different that the textbook also talks about in another section. To further complicate matters, our textbook calls the Mann-Whitney 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 p-value 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...
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This note was uploaded on 02/04/2011 for the course SDS 3482 taught by Professor Thompson during the Spring '09 term at University of Florida.
- Spring '09