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Displaying and Describing Categorical Data

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Displaying and Describing Categorical Data

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  1. Each year, The Princeton Review conducts surveys of high school students who are applying to college and of parents of college applicants. The report “2009 College Hopes & Worries Survey Findings” included a summary of how 12,715 high school students responded to the question “Ideally how far from home would you like the college you attend to be?” Also included was a summary of how 3,007 parents of students applying to college responded to the question “How far from home would you like the college your child attends to be?” • Identify the W’s of the survey.

  2. Displaying and Describing Categorical Data Chapter 3

  3. Before we begin • Data Analysis – organizing, displaying, summarizing, and asking further questions

  4. Three Rules of Data Analysis • Make a picture • Make a picture • Make a picture

  5. Think, Show, Tell • Think -- a picture is the easiest way for you to see patterns and relationships that may be hiding in the data • Show – an appropriately selected picture will show important features of the data, including extraordinary values or possible errors • Tell -- a picture is worth a thousand words

  6. Categorical Data • A categorical (or qualitative) variable names categories and answers questions about how cases fall into those categories. (e.g., sex, race, ethnicity) • The data are counts or percentages of individual cases in categories

  7. The W’s • Who: High school students applying to college, parents of college applicants • What: preference for distance from college to home (miles) • Why: not specified • Where: not specified • When: 2009 • How: survey

  8. The Results

  9. Frequency vs. Relative Frequency • Frequency -- the number of time that a category appears in the data set • Relative frequency =

  10. Bar ChartsFrequency vs. Relative Frequency

  11. Bar Charts • When to use: Number of variables: 1 Data type: categorical Purpose: displaying data distribution Leave space between each category!!!

  12. Comparative Bar Charts

  13. Comparative Bar Charts • When to use: Number of variables: 1 variable for two or more groups Data type: categorical Purpose: comparing two or more data distributions Relative frequency must be the vertical axis!!!

  14. Pie ChartsFrequency vs. Relative Frequency

  15. Contingency Table(a.k.a. Two-way Table) • A table that shows the frequency distribution across two variables

  16. Contingency Table(a.k.a. Two-way Table) • A table that shows the frequency distribution across two variables

  17. Marginal Distribution

  18. Questions • What percent of all students want to go to college less than 250 miles from home? • What percent parents want their children to go to college more than 1000 miles from home? • What percent of people who want college to be more than 1000 miles away from home are parents?

  19. Conditional Distribution • The distribution of a particular variable that satisfies a given condition

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