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Nonparametric Statistics

Nonparametric Statistics

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Nonparametric Statistics

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

  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. 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. The Sign Test • We wish to compare two populations. • Populations are not independent

  5. Sign Test Method

  6. Sign Test Method

  7. Sign Test Method

  8. Rank-Sum Test • Data values from the two populations are not paired. • Normal assumptions are not satisfied, or are at least questionable.

  9. Rank-Sum Test

  10. Rank-Sum Test

  11. Rank-Sum Test

  12. Rank-Sum Test

  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. Spearman Rank Correlation Coefficient

  15. Spearman Rank Correlation Properties

  16. Spearman Rank Correlation Properties

  17. Test for Spearman Correlation

  18. Test for Spearman Correlation

  19. Spearman Correlation Test

  20. Spearman Correlation Test

  21. Spearman Correlation Test

  22. Runs Test for Randomness • Definitions:

  23. Runs Test for Randomness Hypotheses

  24. Conducting the Test

  25. Constructing a Runs Test

  26. Constructing a Runs Test

  27. Constructing a Runs Test

  28. Constructing a Runs Test