Bell Ringer The State Education Department requires local school districts to keep these records on all students: age, race or ethnicity, days absent, current grade level, standardized test scores in reading and math, and any disabilities or educational needs. Identify the Who, What, When, Where, Why, and How (if possible) List each variable and decide if each is quantitative or categorical.

Describing and Displaying Categorical Data Chapter 3 part 2 Describing and Displaying Categorical Data

Contingency Tables A contingency table allows us to look at two categorical variables together.

Each frequency distribution is called a marginal distribution of its respective variable. The marginal distribution of Survival is:

Each frequency distribution is called a marginal distribution of its respective variable. The marginal distribution of Class is:

Each cell of the table gives the count for a combination of values of the two values. For example, the second cell in the crew column tells us that 673 crew members died when the Titanic sunk.

Conditional Distributions A conditional distribution shows the distribution of one variable for just the individuals who satisfy some condition on another variable. The following is the conditional distribution of ticket Class, conditional on having survived:

Conditional Distributions The following is the conditional distribution of ticket Class, conditional on having died:

Write a statement about the pie chart display of the conditional distributions. The conditional distributions tell us that there is a difference in class for those who survived and those who didn’t.

We see that the distribution of Class for the survivors is different from that of the nonsurvivors. This leads us to believe that Class and Survival are associated, that they are not independent. In other words… it seems as though survival was at least partially dependent on Class, and therefore the variables are not independent.

Example #1: Students in an Intro Stats course were asked to describe their politics as Liberal, Moderate, or Conservative. Here are the results: Liberal Moderate Conservative Total Female 35 36 6 77 Male 50 44 21 115 85 80 27 192 What percent of the class is male? What percent of the class considers themselves to be Conservative? What percent of the males in the class considers themselves to be Conservative? What percent of all students in the class are males who consider themselves to be Conservative?

Example #2: Students in an Intro Stats course were asked to describe their politics as Liberal, Moderate, or Conservative. Here are the results: Liberal Moderate Conservative Total Female 35 36 6 77 Male 50 44 21 115 85 80 27 192 Find the conditional distributions of political views for the females. Find the conditional distributions of political views for the males. Make a graphical display that compares the two distributions. Do the variables Politics and Gender appear to be independent? Explain.

Today’s Assignment: Chapter 3 Exercises: pg. 40 #19, 28, 30