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Lecture Business statistics in practice (7/e): Chapter 18 - Bowerman, O'Connell, Murphree

Chapter 18 - Nonparametric methods. After mastering the material in this chapter, you will be able to: Use the sign test to test a hypothesis about a population median, compare the locations of two distributions using a rank sum test for independent samples, compare the locations of two distributions using a signed ranks test for paired samples,. | Nonparametric Methods Chapter 18 Copyright © 2014 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin Nonparametric Methods 18.1 The Sign Test: A Hypothesis Test about the Median 18.2 The Wilcoxon Rank Sum Test 18.3 The Wilcoxon Signed Ranks Test 18.4 Comparing Several Populations Using the Kruskal-Wallis H Test 18.5 Spearman’s Rank Correlation Coefficient 18- 18.1 Sign Test: A Hypothesis Test about the Median Define S = the number of sample measurements (less/greater) than M0 x to be a binomial random variable with p = 0.5 We can reject H0: Md = M0 at the level of significance (probability of Type I error equal to ) by using the appropriate p-value LO18-1: Use the sign test to test a hypothesis about a population median. 18- Sign Test: A Hypothesis Test about the Median Continued Alternative Test Statistic p-Value Ha: Md > Mo S=number of measurements greater than Mo The probability that x is greater than or equal to S Ha: Md Nonparametric Methods 18.1 The Sign Test: A Hypothesis Test about the Median 18.2 The Wilcoxon Rank Sum Test 18.3 The Wilcoxon Signed Ranks Test 18.4 Comparing Several Populations Using the Kruskal-Wallis H Test 18.5 Spearman’s Rank Correlation Coefficient 18- 18.1 Sign Test: A Hypothesis Test about the Median Define S = the number of sample measurements (less/greater) than M0 x to be a binomial random variable with p = 0.5 We can reject H0: Md = M0 at the level of significance (probability of Type I error equal to ) by using the appropriate p-value LO18-1: Use the sign test to test a hypothesis about a population median. 18- Sign Test: A Hypothesis Test about the Median Continued Alternative Test Statistic p-Value Ha: Md > Mo S=number of measurements greater than Mo The probability that x is greater than or equal to S Ha: Md 18- 18.2 The Wilcoxon Rank Sum Test Given two independent samples of sizes n1 and n2 from populations 1 and 2 with distributions D1 and D2 Rank the (n1+ n2) observations from smallest to largest (average ranks for ties) T1 = sum of ranks, sample 1 T2 = sum of ranks, sample 2 T = T1 if n1 n2 and T = T2 if n1> n2 We can reject H0: D1 and D2 are identical probability distributions at the level of significance if and only if the test statistic T satisfies the appropriate rejection condition LO18-2: Compare the locations of two distributions using a rank sum test for independent samples. 18- The Wilcoxon Rank Sum Test Continued Alternative Reject H0 if Ha: D1 is shifted right of D2 T ≥ Tu if n1 ≤ n2 T ≤ Tu if n1 > n2 Ha: D1 is shifted left of D2 T ≤ TL if n1 ≤ n2 T ≥ .