Aim: How do we analyze data with a two-way table? HW: Read chapter 2.5 page 142-148 Complete last slide Aim: How do we analyze data with a two-way table?

Studying Relationships between 2 variables Always ask whether each variable is quantitative or categorical 2 quantitative variables, we use a scatterplot to examine the relationship and fit a line to the data if the relationship is approximately linear If 1 variable is qauntitative and the other categorical, we can use boxplot, frequencies histogram, bar graphs, stemplot or pie charts (chapter 1)

Categorical Data Variables such as gender, race, and occupation Categorical variables are also created by grouping values of a quantitative variable into classes Use the counts (frequency) or percents (relative frequency) of individuals that fall into various categories Example: frequency of drinking

What is the two-way table? The key idea in studying relationships between two variables is that both variables must be measured on the same individual or case When both variables are categorical, the raw data are summarized in a two-way table that gives counts of observations for each combination of values of the two categorical variables

Example of two-way table Alcohol abuse has been described by college presidents as the number one problem on campus and it is an important cause of death in young adults. How common is it? A survey of 17,096 students in U.S. four-year colleges collected information on drinking behavior and alcohol-related problems. The researchers defined “frequent binge drinking” as having five or more drinks in a row three or more times in the past two weeks.

Example of two-way table Here is the two-way table classifying students by gender and whether or not they are frequent binge drinkers: Two variables: frequent binge drinking and gender

Setting Up Two-Way Table Row Variable (dependent variable): each horizontal row in the table describes the drinking behavior Column Variable (independent variable): each vertical column describes one gender group Cell: combination of the two groups Because there are only 2 rows and 2 columns, this table is called a 2 x 2 table

Describing relationships between categorical data Need to compute different types of percents; therefore, the two-way table needs a total column Table shows you total number of men, woman, participants and total number of each grouping variable

Joint Distribution Joint Distributions: the collection of these proportions of the two categorical variables To find proportions between two categorical variables you must divide the proportion you are looking at and the total Example: The proportion of males who are frequent binge drinkers is found by simply dividing 1630 by sample size 17,096 equally 0.095  estimate that 9.5% of college students are male frequent binge drinkers

Joint Distribution

Marginal Distribution Marginal Distribution: used when examining the distribution of a single variable in a two-way table

Marginal Distribution: for this example We have two variables in this example, so there is to marginal distributions to calculate Marginal Distribution of GENDER: found by dividing the total amount of males (7180) and females (9916) by the total sample size (17,096).

Marginal Distribution: for this example For marginal distribution, percents are usually preferred Marginal Distribution of BINGE DRINKING: divide the total yes (3314) and the total no (13,782) by the sample size (17,096)

Homework: Full-time and part-time college students. The Census Bureau provides estimates of numbers of people in the United States classified in various ways. Let's look at college students. The following table gives us data to examine the relation between age and full-time or part-time status. The numbers in the table are expressed as thousands of U.S. college students. a) What is the U.S. Census Bureau estimate of the number of full-time college students aged 15 to 19? (b) Give the joint distribution of age and status for this table. (c) What is the marginal distribution of age? Display the results graphically. (d) What is the marginal distribution of status? Display the results graphically.