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Analyzing Categorical Data: Individuals, Variables, and Distributions

This text explores the analysis of categorical data, including how to display, calculate, and interpret distributions using bar graphs and two-way tables. It also discusses the importance of avoiding deceptive graphs and properly labeling axes.

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Analyzing Categorical Data: Individuals, Variables, and Distributions

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  1. Do Now • From the following table, determine… • The individuals • The variables and whether they are categorical • Describe the characteristics of Chris G. Previous 4 CD Purchasers on a Music Website

  2. CHAPTER 1Exploring Data 1.1Analyzing Categorical Data

  3. Analyzing Categorical Data • DISPLAY categorical data with a bar graph • IDENTIFY what makes some graphs of categorical data deceptive • CALCULATE and DISPLAY the marginal distribution of a categorical variable from a two-way table • CALCULATE and DISPLAY the conditional distribution of a categorical variable for a particular value of the other categorical variable in a two-way table • DESCRIBE the association between two categorical variables

  4. Categorical Variables Categorical variables place individuals into one of several groups or categories. Variable Values Count Percent

  5. Displaying Categorical Data Frequency tables can be difficult to read. Sometimes is is easier to analyze a distribution by displaying it with a bar graph or pie chart.

  6. Graphs: Good and Bad Bar graphs compare several quantities by comparing the heights of bars that represent those quantities. Our eyes, however, react to the area of the bars as well as to their height. • When you draw a bar graph, make the bars equally wide. It is tempting to replace the bars with pictures for greater eye appeal. • Don’t do it! • There are two important lessons to keep in mind: • beware the pictograph, and • watch those scales.

  7. What’s Wrong With This Picture? • You might think that a good way to show the Titanic data is with this display:

  8. The Area Principle • The ship display makes it look like most of the people on the Titanic were crew members, with a few passengers along for the ride. • When we look at each ship, we see the area taken up by the ship, instead of the length of the ship. • The ship display violates the area principle: • The area occupied by a part of the graph should correspond to the magnitude of the value it represents.

  9. Bar Charts • A bar chart displays the distribution of a categorical variable, showing the counts for each category next to each other for easy comparison. • A bar chart stays true to the area principle. • Thus, a better display for the ship data is:

  10. Bar Charts (cont.) • A relative frequencybar chart displays the relative proportion of counts for each category. • A relative frequency bar chart also stays true to the area principle. • Replacing counts with percentages in the ship data:

  11. Truncating the y-axis Differences in years are greatly exaggerated

  12. Properties of “Good” Graphs Keep it caled axes abeled axes nits itle

  13. Properties of “Good” Graphs What’s wrong with the following graph? Larson/Farber 4th ed. 13

  14. Properties of “Good” Graphs What’s wrong with the following graph? Larson/Farber 4th ed. 14

  15. Properties of “Good” Graphs What’s wrong with the following graph? Larson/Farber 4th ed. 15

  16. Properties of “Good” Graphs What’s wrong with the following graph? Larson/Farber 4th ed. 16

  17. Properties of “Good” Graphs What’s wrong with the following graph? Source: www.excelcharts.com Larson/Farber 4th ed. 17

  18. Properties of “Good” Graphs What’s wrong with the following graph? Source: www.wheels.org Larson/Farber 4th ed. 18

  19. Properties of “Good” Graphs What’s wrong with the following graph? Larson/Farber 4th ed. 19

  20. Two-Way Tables and Marginal Distributions When a dataset involves two categorical variables, we begin by examining the counts or percents in various categories for one of the variables. A two-way table describes two categorical variables, organizing counts according to a row variable and a column variable. What are the variables described by this two-way table? How many young adults were surveyed?

  21. Two-Way Tables and Marginal Distributions The marginal distribution of one of the categorical variables in a two-way table of counts is the distribution of values of that variable among all individuals described by the table. Note: Percents are often more informative than counts, especially when comparing groups of different sizes. • How to examine a marginal distribution: • Use the data in the table to calculate the marginal distribution (in percents) of the row or column totals. • Make a graph to display the marginal distribution.

  22. Two-Way Tables and Marginal Distributions Examine the marginal distribution of chance of getting rich.

  23. Relationships Between Categorical Variables A conditional distribution of a variable describes the values of that variable among individuals who have a specific value of another variable. • How to examine or compare conditional distributions: • Select the row(s) or column(s) of interest. • Use the data in the table to calculate the conditional distribution (in percents) of the row(s) or column(s). • Make a graph to display the conditional distribution. • Use a side-by-side bar graph or segmented bar graph to compare distributions.

  24. Relationships Between Categorical Variables Calculate the conditional distribution of opinion among males. Examine the relationship between gender and opinion.

  25. Relationships Between Categorical Variables Can we say there is an association between gender and opinion in the population of young adults? Making this determination requires formal inference, which will have to wait a few chapters. Caution! Even a strong association between two categorical variables can be influenced by other variables lurking in the background.

  26. Data Analysis: Making Sense of Data • DISPLAY categorical data with a bar graph • IDENTIFY what makes some graphs of categorical data deceptive • CALCULATE and DISPLAY the marginal distribution of a categorical variable from a two-way table • CALCULATE and DISPLAY the conditional distribution of a categorical variable for a particular value of the other categorical variable in a two-way table • DESCRIBE the association between two categorical variables

  27. Homework • Turn in Syllabus – due tomorrow, THURSDAY 8/15 • Sign up for Remind101 – instructions are in the syllabus • Pg. 21 - #13, 14, 15, 17, 18 – due tomorrow

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