# ch13 - blu03683_ch13.qxd 10/05/2005 06:24 PM Page 659 13...

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Objectives After completing this chapter, you should be able to 1 State the advantages and disadvantages of nonparametric methods. 2 Test hypotheses, using the sign test. 3 Test hypotheses, using the Wilcoxon rank sum test. 4 Test hypotheses, using the signed-rank test. 5 Test hypotheses, using the Kruskal-Wallis test. 6 Compute the Spearman rank correlation coefFcient. 7 Test hypotheses, using the runs test. Outline 13–1 Introduction 13–2 Advantages and Disadvantages of Nonparametric Methods 13–3 The Sign Test 13–4 The Wilcoxon Rank Sum Test 13–5 The Wilcoxon Signed-Rank Test 13–6 The Kruskal-Wallis Test 13–7 The Spearman Rank Correlation Coefficient and the Runs Test 13–8 Summary 13–1 13 Nonparametric Statistics CHAPTER

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660 Chapter 13 Nonparametric Statistics 13–2 Statistics Today Too Much or Too Little? Suppose a manufacturer of ketchup wishes to check the bottling machines to see if they are functioning properly. That is, are they dispensing the right amount of ketchup per bottle? A 40-ounce bottle is currently used. Because of the natural variation in the manufacturing process, the amount of ketchup in a bottle will not always be exactly 40 ounces. Some bot- tles will contain less than 40 ounces, and others will contain more than 40 ounces. To see if the variation is due to chance or to a malfunction in the manufacturing process, a runs test can be used. The runs test is a nonparametric statistical technique. See Statistics Today—Revisited. This chapter explains such techniques, which can be used to help the manufacturer determine the answer to the question. 13–1 Introduction Statistical tests, such as the z , t , and F tests, are called parametric tests. Parametric tests are statistical tests for population parameters such as means, variances, and proportions that involve assumptions about the populations from which the samples were selected. One assumption is that these populations are normally distributed. But what if the popu- lation in a particular hypothesis-testing situation is not normally distributed? Statisticians have developed a branch of statistics known as nonparametric statistics or distribution- free statistics to use when the population from which the samples are selected is not
normally distributed. Nonparametric statistics can also be used to test hypotheses that do not involve specifc population parameters, such as m , s ,or p. For example, a sportswriter may wish to know whether there is a relationship between the rankings o± two judges on the diving abilities o± 10 Olympic swimmers. In another situation, a sociologist may wish to determine whether men and women enroll at random ±or a specifc drug rehabilitation program. The statistical tests used in these situ- ations are nonparametric or distribution-±ree tests. The term nonparametric is used ±or both situations.

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## This note was uploaded on 11/25/2011 for the course MATH 063 taught by Professor Soshiani during the Spring '09 term at San Jose City College.

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ch13 - blu03683_ch13.qxd 10/05/2005 06:24 PM Page 659 13...

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