1 / 23

Statistics

This chapter explores methods for making inferences about population proportions and differences between proportions using categorical data. It covers one-way and two-way analyses, chi-square hypothesis tests, and multinomial experiments.

jguzman
Download Presentation

Statistics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Statistics 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 McClave, Statistics, 11th ed. Chapter 13: Categorical Data Analysis

  3. Where We’re Going • 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 McClave, Statistics, 11th ed. Chapter 13: Categorical Data Analysis

  4. 13.1: Categorical Data and the Multinomial Experiment • Properties of the Multinomial Experiment • The experiment consists of n identical trials. • There are k possible outcomes (called classes, categories or cells) to each trial. • The probabilities of the k outcomes, denoted by p1, p2, …, pk, where p1+ p2+ … + pk = 1, remain the same from trial to trial. • The trials are independent. • The random variables of interest are the cell counts n1, n2, …, nk of the number of observations that fall into each of the k categories. McClave, Statistics, 11th ed. Chapter 13: Categorical Data Analysis

  5. 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

  6. 13.2: Testing Categorical Probabilities: One-Way Table Candidate 1 is the choice of 61 voters. Candidate 2 is the choice of 53 voters. Candidate 3 is the choice of 36 voters. n =150 McClave, Statistics, 11th ed. Chapter 13: Categorical Data Analysis

  7. 13.2: Testing Categorical Probabilities: One-Way Table Reject the null hypothesis McClave, Statistics, 11th ed. Chapter 13: Categorical Data Analysis

  8. 13.2: Testing Categorical Probabilities: One-Way Table Test of a Hypothesis about Multinomial Probabilities: One-Way Table H0: p1= p1,0, p2= p2,0, … , pk= pk,0 where p1,0, p2,0, …, pk,0 represent the hypothesized values of the multinomial probabilities Ha: At least one of the multinomial probabilities does not equal its hypothesized value where Ei = np1,0, is the expected cell count given the null hypothesis. McClave, Statistics, 11th ed. Chapter 13: Categorical Data Analysis

  9. 13.2: Testing Categorical Probabilities: One-Way Table Conditions Required for a Valid 2 Test: One-Way Table • A multinomial experiment has been conducted. • The sample size n will be large enough so that, for every cell, the expected cell count E(ni) will be equal to 5 or more. McClave, Statistics, 11th ed. Chapter 13: Categorical Data Analysis

  10. 13.2: Testing Categorical Probabilities: One-Way Table Example 13.2: Distribution of Opinions About Marijuana Possession Before Television Series has Aired Table 13.2: Distribution of Opinions About Marijuana Possession After Television Series has Aired McClave, Statistics, 11th ed. Chapter 13: Categorical Data Analysis

  11. 13.2: Testing Categorical Probabilities: One-Way Table McClave, Statistics, 11th ed. Chapter 13: Categorical Data Analysis

  12. 13.2: Testing Categorical Probabilities: One-Way Table Expected Distribution of 500 Opinions About Marijuana Possession After Television Series has Aired McClave, Statistics, 11th ed. Chapter 13: Categorical Data Analysis

  13. 13.2: Testing Categorical Probabilities: One-Way Table Expected Distribution of 500 Opinions About Marijuana Possession After Television Series has Aired McClave, Statistics, 11th ed. Chapter 13: Categorical Data Analysis

  14. 13.2: Testing Categorical Probabilities: One-Way Table Expected Distribution of 500 Opinions About Marijuana Possession After Television Series has Aired Reject the null hypothesis McClave, Statistics, 11th ed. Chapter 13: Categorical Data Analysis

  15. 13.2: Testing Categorical Probabilities: One-Way Table • Inferences can be made on any single proportion as well: • 95% confidence interval on the proportion of citizens in the viewing area with no opinion is McClave, Statistics, 11th ed. Chapter 13: Categorical Data Analysis

  16. 13.3: Testing Categorical Probabilities: Two-Way Table • Chi-square analysis can also be used to investigate studies based on qualitative factors. • Does having one characteristic make it more/less likely to exhibit another characteristic? McClave, Statistics, 11th ed. Chapter 13: Categorical Data Analysis

  17. 13.3: Testing Categorical Probabilities: Two-Way Table The columns are divided according to the subcategories for one qualitative variable and the rows for the other qualitative variable. McClave, Statistics, 11th ed. Chapter 13: Categorical Data Analysis

  18. 13.3: Testing Categorical Probabilities: Two-Way Table McClave, Statistics, 11th ed. Chapter 13: Categorical Data Analysis

  19. 13.3: Testing Categorical Probabilities: Two-Way Table • The results of a survey regarding marital status and religious affiliation are reported below (Example 13.3 in the text). Religious Affiliation Marital Status H0: Marital status and religious affiliation are independent Ha: Marital status and religious affiliation are dependent McClave, Statistics, 11th ed. Chapter 13: Categorical Data Analysis

  20. 13.3: Testing Categorical Probabilities: Two-Way Table • The expected frequencies (see Figure 13.4) are included below: Religious Affiliation Marital Status The chi-square value computed with SAS is 7.1355, with p-value = .1289. Even at the  = .10 level, we cannot reject the null hypothesis. McClave, Statistics, 11th ed. Chapter 13: Categorical Data Analysis

  21. 13.3: Testing Categorical Probabilities: Two-Way Table McClave, Statistics, 11th ed. Chapter 13: Categorical Data Analysis

  22. 13.4: A Word of Caution About Chi-Square Tests McClave, Statistics, 11th ed. Chapter 13: Categorical Data Analysis

  23. 13.4: A Word of Caution About Chi-Square Tests Be sure McClave, Statistics, 11th ed. Chapter 13: Categorical Data Analysis

More Related