Relationship Between Two Categorical Variables

A variable that takes on values which can be divided into groups or categories.

• Two-way Table

• Residuals

• Categorical variable

A way of organizing data from two categorical variables in order to investigate the association between them.

• Causal relationship

• Relative Frequency Table

• Two-way Table

Created by dividing the value in each cell in a two-way table by the total number of responses in the entire table, or the total responses in a row or column

• Categorical variable

• Relative Frequency Table

• Residuals

Does there appear to be an association between the class of vehicle and its drive train?

• Yes. All classes of vehicles have similar proportions of drive trains.

• No. All classes of vehicles have similar proportions of drive trains.

• Yes. All classes of vehicles have differing proportions of drive trains.

• No. All classes of vehicles have differing proportions of drive trains.

How many sophomores like burritos and pizza?

• 6

• 5

• 11

• 50

100 men and 40 women are surveyed about their preferences. Is there an association between gender and past-time preferences?

• No. Men and women prefer the same activities at roughly the same rate.

• Yes. Men and women prefer the same activities at roughly the same rate.

• No. Men and women prefer the same activities at different rates.

• Yes. Men and women prefer the same activities at different rates.

Which statement is true based on the segmented bar graph above?

• The number of kids with cell phones is about the same for ages 13-15 and 16-18

• About 75% of kids with cell phones are ages 13-15

• About 75% of kids age 13-15 have a cell phone

• 320 kids were involved in this survey

Does there appear to be an association between gender and favorite sport?

• Yes, the segments all look about the same for the groups.

• No, the segments all look about the same for the groups.

• Yes, there appears to be a higher percentage of females who prefer baseball and a higher percentage of males prefer football.

• Yes, there appears to be about the same percentage of both males and females who prefer basketball.

The Pew Research Center asked a random sample of 2024 adult cell-phone owners from the United States their age and which type of cell phone they own: iPhone, Android, or other (including non-smart phones). Use the information in the two-way table to make a segmented bar chart to show the relationship between age and type of cell phone.

Which of the following is the segmented bar chart?

• 
• 
• 
• You can't make a segmented bar chart for these variables!

A version of a two-way table in which the value in each cell is divided by the total number of responses in the entire table or by the total number of responses in a row or a column.

Answer explanation

A relative frequency table is a version of a two-way table in which the value in each cell is divided by the total number of responses in the entire table or by the total number of responses in a row or a column. The table illustrates the first type for the relationship between the condition of a textbook and its price for 120 of the books at a college bookstore.