1. CHAPTER 14: Nonparametric Methods to accompany Introduction to Business Statistics seventh edition, by Ronald M. Weiers Presentation by Priscilla Chaffe-Stengel Donald N. Stengel © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted on a publicly accessible website, in whole or in part.

2. Chapter 14 - Learning Objectives Differentiate between nonparametric and parametric hypothesis tests. Determine when a nonparametric test should be used instead of its parametric counterpart. Appropriately apply each of the nonparametric methods introduced. © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or post to a publicly accessible website, in whole or in part.

3. Chapter 14 Key Terms Nonparametric tests Wilcoxon signed rank test:  One sample  Paired samples Wilcoxon rank sum test, two independent samples Kruskal-Wallis Test, three or more independent samples Friedman test, randomized block design Sign Test, paired samples Runs test for randomness Kolmogorov-Smirnov test for normality Spearman coefficient of rank correlation © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or post to a publicly accessible website, in whole or in part.

4. Nonparametric Tests Advantages:  Fewer assumptions about the population  Shape  Variance  Valid for small samples  Defined over a range of variables, nominal and ordinal scales included  Calculations simple Disadvantages:  Sample data used less efficiently  Power of nonparametric analysis lower  Places greater reliance on statistical tables if computer statistical package or spreadsheet not being used © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or post to a publicly accessible website, in whole or in part.

5. Wilcoxon Signed Rank Test, One Sample Requirements:  Variable - Continuous data  Scale - Interval or ratio scale of measurement The Research Question (H a ): Test the value of a single population median, m { , >, <} m 0 Critical Value/Decision Rule: W, Wilcoxon signed rank test © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or post to a publicly accessible website, in whole or in part.

6. An Example Problem 14.8: According to the director of a county tourist bureau, there is a median of 10 hours of sunshine per day during the summer months. For a random sample of 20 days during the past three summers, the number of hours of sunshine has been recorded below. Use the 0.05 level in evaluating the director’s claim. 8 9 810 9 7 7 9 7 7 9 811 9 10 7 811 812 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or post to a publicly accessible website, in whole or in part.

7. Problem 14.8, continued hrs. d i |d i | 8–229–11 9–118–22 8–2211 + 11 10 009–11 9–1110 00 7–337–33 7–338–22 9–1111 + 11 7–338–22 7–3312+22 There are: 7 with rank 1 1, 2, 3, 4, 5, 6, 7 average rank = 4 6 with rank 2 8, 9, 10, 11, 12, 13 average rank = 10.5 5 with rank 3 14, 15, 16, 17, 18 average rank = 16 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or post to a publicly accessible website, in whole or in part.

8. Problem 14.8, continued hrs. d i |d i | Rank R+ R– 8–2210.5-10.59–114-4 9–114-48–2210.5-10.5 8–2210.5-10.511+1144- 10 00---9–114-4 9–114-410 00--- 7–3316-167–3316-16 7–3316-168–2210.5-10.5 9–114-411+1144- 7–3316-168–2210.5-10.5 7–3316-1612+2210.510.5- So,  R+ = 18.5,  R– = 152.5 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or post to a publicly accessible website, in whole or in part.

9. Problem 14.8, continued I. H 0 : m = 10 hours H 1 : m  10 hours II. Rejection Region:  = 0.05, n = 18 data values not equal to the hypothesized median of 10 If  R+ 130, reject H 0. III. Test Statistics:  R+ = 18.5  R– = 152.5 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or post to a publicly accessible website, in whole or in part.

10. Problem 14.8, concluded IV. Conclusion: Since the test statistic of  R+ = 18.5 falls below the critical value of W = 41, we reject H 0 with at least 95% confidence. V. Implications: There is enough evidence to dispute the director’s claim that this county has a median of 10 hours of sunshine per day during the summer months. © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or post to a publicly accessible website, in whole or in part.

11. Wilcoxon Signed Rank Test for Comparing Paired Samples Requirements:  Variable - Continuous data  Scale - Interval or ratio scale of measurement The Research Question (H 1 ): Test the difference in two population medians, paired samples, m d { , >, <} 0 Critical Value/Decision Rule: W, Wilcoxon rank sum test © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or post to a publicly accessible website, in whole or in part.

12. Wilcoxon Rank Sum Test for Comparing Two Independent Samples Requirements:  Variable - Continuous data  Scale – At least ordinal scale of measurement The Research Question (H 1 ): Test the difference in two population medians from two independent samples, m 1 { , >, <} m 2 Critical Value/Decision Rule: W, Wilcoxon rank sum test © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or post to a publicly accessible website, in whole or in part.

13. Kruskal-Wallis Test, Comparing More Than Two Independent Samples Requirements:  Scale - Ordinal, interval or ratio scale  Independent samples from populations with identical distributions The Research Question (H 1 ): At least one of the medians differs from the others. © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or post to a publicly accessible website, in whole or in part.