Chapter 6 Sections 1-2

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How can we best grasp the information contained in Table 6.1? First, look at the distribution of each variable separately. The distribution of a categorical variable says how often each outcome occurred. The “Total” column at the right of the table contains the totals for each of the rows. These row totals give the distribution of sex and education level in the entire group of 1012 adults: 195 were women with no college education, 303 were women with a college education, and so on. If the row and column totals are missing, the first thing to do in studying a two–way table is to calculate them. The distributions of sex and education alone and preferred lifestyle alone are called marginal distributions marginal distributions because they appear at the right and bottom margins of the two–way table. Percents are often more informative than counts. We can display the marginal distribution of sex and education in percents by dividing each row total by the table total and converting to a percent.

6.1 Video Gaming and Grades. The popularity of computer, video, online, and virtual reality games has raised concerns about their ability to negatively affect youth. The data in this exercise are based on a recent survey of 14- to 18-year-olds in Connecticut high schools. Here are the grade distributions of boys who have and have not played video games: (a)How many people does this table describe? How many of these have played video games? (b)Give the marginal distribution of the grades. What percent of the boys represented in the table received a grade of C or lower?

6.2 Ages of College Students. Here is a two–way table of U.S. Census Bureau data describing the age and sex of all American students enrolled in college. The table entries are counts in thousands of students (a)How many college undergraduates are there? (b)Find the marginal distribution of age group. What percent of undergraduates are in the 18- to 24-year-old college age group?

Let’s say we want to compare the preferred lifestyles of women and men with different levels of education. To do this, compare percents for each sex and education category. To study the preferred lifestyles of women who have not been to college, we look only at the “Women no college” row in Table 6.1. To find the percent of women with no college who prefer a job outside the home, divide the count of such women by the total number of women with no college (the row total)

6.3 Video Gaming and Grades. Exercise 6.1 gives data on the grade distribution of boys who have and have not played video games. To see the relationship between grades and game-playing experience, find the conditional distributions of grades (the response variable) for players and nonplayers. What do you conclude?

6.4 Ages of College Students. Exercise 6.2 gives U.S. Census Bureau data describing the age and sex of all American students enrolled in college. We suspect that the percent of women is higher among students in the 25- to 34-year-old age group than in the 18- to 24-year-old age group. Do the data support this suspicion?

6.5 Marginal Distributions Aren’t the Whole Story. Here are the row and column totals for a two–way table with two rows and two columns: Make up two different sets of counts a, b, c, and d for the body of the table that give these same totals. This shows that the relationship between two variables cannot be obtained from the two individual distributions of the variables.