Chapter 7 Nonparametric Statistics 7 1 Introduction Parametric

Chapter 7 Nonparametric Statistics

7. 1 - Introduction • Parametric tests – Have a requirement about the distribution of the population • Nonparametric tests – Have no such requirement

7. 2 – The Sign Test •

The Sign Test •

Example 7. 2. 1 The first row of the table below shows the number of children’s books in 11 randomly selected homes with children in a town. Use the data to test the claim that the median number of books in homes with children in this town is greater than 12.

Example 7. 2. 1 •

7. 3 – The Wilcoxon Signed-Rank Test •

Test Statistic •

The Wilcoxon Signed-Rank Test •

The Wilcoxon Signed-Rank Test •

Example •

7. 4 – The Wilcoxon Rank-Sum Test There are two commonly used techniques for throwing a shot put: glide and rotational. The first and third rows of the table below give the maximum distances (in m) of 12 different athletes using the glide method and 13 athletes using the rotational method at international competitions (data collected by David Meyer, 2010). Use this data to test the claim that there is not a significant difference between these two methods.

The Wilcoxon Rank-Sum Test •

Theorem 7. 4. 1 •

The Wilcoxon Rank-Sum Test •

The Wilcoxon Rank-Sum Test •

Example •

7. 5 – The Runs Test for Randomness Purpose: To test the claim that a set of data with two types of values is arranged randomly Definition 7. 5. 1 A run is a sequence of data of the same type preceded and followed by data of a different type or by no data at all

Example 7. 5. 1 •

Theorem 7. 5. 1 •

Theorem 7. 5. 1 •

The Runs Test for Randomness •

Example 7. 5. 1 •

Example 7. 5. 1 Conclusion – Do not reject H 0 – It appears that the songs are randomly chosen