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

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

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.

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

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

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

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

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

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.

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

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

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

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

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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