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Chapter 15: Nonparametric Statistics

2. Learning Objectives. Nonparametric Statistical MethodsWilcoxon TestThe Wilcoxon Rank SumUsing the Wilcoxon Test with a Quantitative ResponseNonparametric Estimation Comparing Groups. 3. Learning Objective 1: Nonparametric Statistical Methods. Nonparametric methods are especially useful:When

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Chapter 15: Nonparametric Statistics

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    1. 1 Chapter 15: Nonparametric Statistics Section 15.1 How Can We Compare Two Groups by Ranking?

    2. 2 Learning Objectives Nonparametric Statistical Methods Wilcoxon Test The Wilcoxon Rank Sum Using the Wilcoxon Test with a Quantitative Response Nonparametric Estimation Comparing Groups

    3. 3 Learning Objective 1: Nonparametric Statistical Methods Nonparametric methods are especially useful: When the data are ranks for the subjects, rather than quantitative measurements. When it’s inappropriate to assume normality.

    4. 4 Learning Objective 1: Example: How to Get A Better Tan Experiment: A student wanted to compare ways of getting a tan without exposure to the sun. She decided to investigate which of two treatments would give a better tan: An “instant bronze sunless tanner” lotion A tanning studio

    5. 5 Subjects: Five female students participated in the experiment. Three of the students were randomly selected to use the tanning lotion. The other two students used the tanning studio. Learning Objective 1: Example: How to Get A Better Tan

    6. 6 Results: The girls’ tans were ranked from 1 to 5, with 1 representing the best tan. Possible Outcomes: Consider all possible rankings of the girls’ tans. A table of possibilities is displayed on the next page. Learning Objective 1: Example: How to Get A Better Tan

    7. 7 Learning Objective 1: Example: How to Get A Better Tan

    8. 8 For each possible outcome, a mean rank is calculated for the ‘lotion’ group and for the ‘studio’ group. The difference in the mean ranks is then calculated for each outcome. Learning Objective 1: Example: How to Get A Better Tan

    9. 9 For this experiment, the samples were independent random samples – the responses for the girls using the tanning lotion were independent of the responses for the girls using the tanning studio. Learning Objective 1: Example: How to Get A Better Tan

    10. 10 Suppose that the two treatments have identical effects. A girl’s tan would be the same regardless of which treatment she uses. Then, each of the ten possible outcomes is equally likely. So, each outcome has probability of 1/10. Learning Objective 1: Example: How to Get A Better Tan

    11. 11 Using the ten possible outcomes, we can construct a sampling distribution for the difference between the sample mean ranks. The distribution is displayed on the next page. Learning Objective 1: Example: How to Get A Better Tan

    12. 12 Learning Objective 1: Example: How to Get A Better Tan

    13. 13 Graph of the Sampling Distribution: Learning Objective 1: Example: How to Get A Better Tan

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