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Lecture Statistical techniques in business and economics (14/e): Chapter 18 - Lind, Marchal, Wathen

Chapter 18 - Nonparametric methods: analysis of ranked data. When you have completed this chapter, you will be able to: Conduct the sign test for dependent samples using the binomial and standard normal distributions as the test statistics, conduct a test of hypothesis for dependent samples using the Wilcoxon signed-rank test, conduct and interpret the Wilcoxon rank-sum test for independent samples,. | Nonparametric Methods: Analysis of Ranked Data Chapter 18 GOALS Conduct the sign test for dependent samples using the binomial and standard normal distributions as the test statistics. Conduct a test of hypothesis for dependent samples using the Wilcoxon signed-rank test. Conduct and interpret the Wilcoxon rank-sum test for independent samples. Conduct and interpret the Kruskal-Wallis test for several independent samples. Compute and interpret Spearman’s coefficient of rank correlation. Conduct a test of hypothesis to determine whether the correlation among the ranks in the population is different from zero. The Sign Test The Sign Test is based on the sign of a difference between two related observations. Assumption regarding the shape of the population of differences is NOT necessary. The binomial distribution is the test statistic for small samples and the standard normal (z) for large samples. The test requires dependent (related) samples. Procedure to conduct the test: . | Nonparametric Methods: Analysis of Ranked Data Chapter 18 GOALS Conduct the sign test for dependent samples using the binomial and standard normal distributions as the test statistics. Conduct a test of hypothesis for dependent samples using the Wilcoxon signed-rank test. Conduct and interpret the Wilcoxon rank-sum test for independent samples. Conduct and interpret the Kruskal-Wallis test for several independent samples. Compute and interpret Spearman’s coefficient of rank correlation. Conduct a test of hypothesis to determine whether the correlation among the ranks in the population is different from zero. The Sign Test The Sign Test is based on the sign of a difference between two related observations. Assumption regarding the shape of the population of differences is NOT necessary. The binomial distribution is the test statistic for small samples and the standard normal (z) for large samples. The test requires dependent (related) samples. Procedure to conduct the test: Determine the sign (+ or -) of the difference between pairs. Determine the number of usable pairs. Compare the number of positive (or negative) differences to the critical value. n is the number of usable pairs (without ties), X is the number of pluses or minuses, and the binomial probability π = .5 EXAMPLE The director of information systems at Samuelson Chemicals recommended that an in-plant training program be instituted for managers. The objective is to improve the knowledge of database usage in accounting, procurement, production, and so on. A sample of 15 managers was selected at random. A panel of database experts determined the general level of competence of each manager with respect to using the database. Their competence and understanding were rated as being either outstanding, excellent, good, fair, or poor. After the three-month training program, the same panel of information systems experts rated each manager again. The two ratings (before and after) are shown along with the