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.
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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
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The Sign Test
• We wish to compare two populations.
– Populations are not independent
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Sign Test Method
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Sign Test Method
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Sign Test Method
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Rank-Sum Test
• Data values from the two populations are not
paired.
• Normal assumptions are not satisfied, or are at
least questionable.
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Rank-Sum Test
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Rank-Sum Test
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Rank-Sum Test
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Rank-Sum Test
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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.
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Spearman Rank Correlation Coefficient
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Spearman Rank Correlation Properties
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Spearman Rank Correlation Properties
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Test for Spearman Correlation
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Test for Spearman Correlation
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Spearman Correlation Test
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Spearman Correlation Test
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Spearman Correlation Test
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Runs Test for Randomness
• Definitions:
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Runs Test for Randomness Hypotheses
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Conducting the Test
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Constructing a Runs Test
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Constructing a Runs Test
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Constructing a Runs Test
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Constructing a Runs Test
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