694 CHAPTER 13 Nonparametric Tests 3.Nonparametric Tests a. Which of the following terms is sometimes used instead of “nonparametric test”: normality test; abnormality test; distribution-free test; last testament; test of patience? b. Why is the answer to part (a) better than “nonparametric test”? 4.Dropped Object The table below describes the behavior of an object dropped near the surface of the Earth. The time is in seconds, and the distance traveled is in meters. Find the rank correlation coefficient, then form a conclusion based on its value. Time 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Distance 0.049 0.196 0.441 0.784 1.225 1.764 2.401 3.136 3.969 5.Dropped Object For paired sample data such as those given in Exercise 4, identify at least one advantage of using the appropriate nonparametric test over the parametric test. 6.Sign Test Identify three different configurations of data that can be analyzed using the sign test. 7.Runs Test Assume that we use the runs test of randomness above and below the mean for the annual gross revenue of Amazon.com, Inc. each year for the past 25 years. If the number of runs is G = 2, what do we know about Amazon.com? 8.Sign Test and Wilcoxon Signed-Ranks Test Paired data consist of pulse rates before and after a training program. What is a major advantage of the Wilcoxon signed-ranks test over the sign test when analyzing data consisting of matched pairs of the before>after differences? 9.Wilcoxon Tests What is the difference between the Wilcoxon signed-ranks test and the Wilcoxon rank-sum test? 10.Kruskal-Wallis Test What parametric test can also be conducted instead of the Kruskal-Wallis test? What is an advantage of using the Kruskal-Wallis test instead of the parametric test? Review Exercises Using Nonparametric Tests. In Exercises 1–10, use a 0.05 significance level with the indicated test. If no particular test is specified, use the appropriate nonparametric test from this chapter. 1.The Freshman 15 The “Freshman 15” refers to the belief that college students gain 15 lb (or 6.8 kg) during their freshman year. Listed below are weights (kg) of randomly selected male college freshmen (from Data Set 13 “Freshman 15” in Appendix B). The weights were measured in September and later in April. Use the sign test to test the claim that for the population of freshman male college students there is not a significant difference between the weights in September and the weights in the following April. What do you conclude about the Freshman 15 belief? September 67 68 87 81 60 70 68 68 80 April 67 68 88 82 61 71 69 69 82 2. Wilcoxon Signed-Ranks Test Repeat the preceding exercise using the Wilcoxon signedranks test. 3.Rank Correlation Use the paired sample data from Exercise 1 and analyze the data using the rank correlation coefficient. What does the result tell us about the belief that college students gain 15 lb (or 6.8 kg) during their freshman year?
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