1. Nonparametric Statistics Chapter 12 Understandable Statistics Ninth Edition By Brase and Brase Prepared by Yixun Shi Bloomsburg University of Pennsylvania

2. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.12 | 2 Nonparametric Situations At times, we will not know anything about the distributions of the populations from which we are sampling. Recall that all of our inference techniques thus far have assumed either a normal or binomial distribution from the populations of interest.

3. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.12 | 3 Nonparametric Tests Advantages: –Easy to apply –Quite general in nature Disadvantages: –Wastes information –Accept the null hypothesis more often than with other tests –Less sensitive

4. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.12 | 4 The Sign Test We wish to compare two populations. –Populations are not independent

5. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.12 | 5 Sign Test Method

6. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.12 | 6 Sign Test Method

7. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.12 | 7 Sign Test Method

8. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.12 | 8 Rank-Sum Test Data values from the two populations are not paired. Normal assumptions are not satisfied, or are at least questionable.

9. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.12 | 9 Rank-Sum Test

10. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.12 | 10 Rank-Sum Test

11. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.12 | 11 Rank-Sum Test

12. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.12 | 12 Rank-Sum Test

13. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.12 | 13 Spearman Rank Correlation Suppose we have a sample of size n of paired data points (x, y). The data points, (x, y), must be ranked variables. The Spearman Rank Correlation will tell us if the data pairs have a monotone increasing or a monotone decreasing relationship.

14. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.12 | 14 Spearman Rank Correlation Coefficient

15. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.12 | 15 Spearman Rank Correlation Properties

16. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.12 | 16 Spearman Rank Correlation Properties

17. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.12 | 17 Test for Spearman Correlation

18. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.12 | 18 Test for Spearman Correlation

19. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.12 | 19 Spearman Correlation Test

20. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.12 | 20 Spearman Correlation Test

21. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.12 | 21 Spearman Correlation Test

22. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.12 | 22 Runs Test for Randomness Definitions:

23. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.12 | 23 Runs Test for Randomness Hypotheses

24. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.12 | 24 Conducting the Test

25. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.12 | 25 Constructing a Runs Test

26. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.12 | 26 Constructing a Runs Test

27. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.12 | 27 Constructing a Runs Test

28. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.12 | 28 Constructing a Runs Test