Chapter_13

# Chapter_13 - Statistics Chapter 13 Categorical Data...

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Chapter 13: Categorical Data Analysis Statistics

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McClave, Statistics, 11th ed. Chapter 13: Categorical Data Analysis 2 Where We’ve Been Presented methods for making inferences about the population proportion associated with a two-level qualitative variable (i.e., a binomial variable) Presented methods for making inferences about the difference between two binomial proportions
Where We’re Going McClave, Statistics, 11th ed. Chapter 13: Categorical Data Analysis 3 Discuss qualitative (categorical) data with more than two outcomes Present a chi-square hypothesis test for comparing the category proportions associated with a single qualitative variable – called a one-way analysis Present a chi-square hypothesis test relating two qualitative variables – called a two-way analysis

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13.1: Categorical Data and the Multinomial Experiment Properties of the Multinomial Experiment 1. The experiment consists of n identical trials. 2. There are k possible outcomes (called classes , categories or cells ) to each trial. 3. The probabilities of the k outcomes, denoted by p 1 , p 2 , …, p k , where p 1 + p 2 + … + p k = 1, remain the same from trial to trial. 4. The trials are independent. 5. The random variables of interest are the cell counts n 1 , n 2 , …, n k of the number of observations that fall into each of the k categories. McClave, Statistics, 11th ed. Chapter 13: Categorical Data Analysis 4
13.2: Testing Categorical Probabilities: One-Way Table Suppose three candidates are running for office, and 150 voters are asked their preferences. Candidate 1 is the choice of 61 voters. Candidate 2 is the choice of 53 voters. Candidate 3 is the choice of 36 voters. Do these data suggest the population may prefer one candidate over the others? McClave, Statistics, 11th ed. Chapter 13: Categorical Data Analysis 5

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13.2: Testing Categorical Probabilities: One-Way Table Candidate 1 is the choice of 61 voters.
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