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## Nonparametric Statistics

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**Chapter 12**Nonparametric Statistics Understandable Statistics Ninth Edition By Brase and Brase Prepared by Yixun Shi Bloomsburg University of Pennsylvania**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.**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**The Sign Test**• We wish to compare two populations. • Populations are not independent**Rank-Sum Test**• Data values from the two populations are not paired. • Normal assumptions are not satisfied, or are at least questionable.**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.**Runs Test for Randomness**• Definitions: