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Unformatted text preview: Chapter 4 Nonparametric Methods For the rest of the semester, well be discussing different ways to analyze data with a quantitative response variable. The methods youve seen before for dealing with a quantitative response variable have always assumed that the response variable has a normal distribution. Well make that same assump- tion for some methods well learn about in later chapters, but in this chapter well 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. After we discuss some general ideas in the first section of this chapter, the following two section s will cover two different nonparametric hypothesis Were short on time, so well have to skip the second procedure, which would have been Section 4.3. testing procedures, each of which corresponds to a traditional hypothesis test that you learned about in your previous course: The Mann-Whitney U test is a nonparametric version of the two- sample t test in Section 10.2 of the textbook. The Wilcoxon signed-ranks test is a nonparametric version of the matched pairs t test in Section 10.4 of the textbook. I dont really expect you to remember anything about these t tests. There are plenty of more complicated nonparametric methods out there for dealing with all sorts of different situations. This chapter is merely in- tended to give you the general idea of how nonparametric methods work. 4.1 Comparison to Traditional Methods 50 4.1 Comparison to Traditional Methods In many situations, we have the choice of whether to use a traditional method or a nonparametric method. Lets first discuss what we should consider when making that choice. Motivation for Nonparametric Methods As well see later, nonparametric methods typically work by ranking all the response variable values and then looking at the ranks of the observations rather than the actual values. This causes nonparametric methods to work better than traditional methods in certain situations. Non-Normality and Small Samples Many procedures that assume a normal distribution for the response variable can still work reasonably well if the true distribution is somewhat different from normal, as long as the sample size is fairly large. However, these pro- cedures can work poorly if either of the following is true: The response variable distribution is somewhat different from normal, but the sample size is small....
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This note was uploaded on 02/08/2011 for the course STA 3024 taught by Professor Ta during the Spring '08 term at University of Florida.
- Spring '08