Summarizing Categorical Data

STAT 20: Introduction to Probability and Statistics

Agenda

• Announcements
• Reading Questions
• Break
• Worksheet: Summarizing Categorical Data
• Appendix: Practice

Announcements

• My office hours will be Fridays from 9-11am in Evans Hall 340
• Group tutoring starts will be Thursdays from 5-7pm in Evans Hall 340

Reading Questions

• Please put your laptops under your desk and your phones away.
• Write your name, ID, and bubble in Version “A” on your answer sheet.
• You may work only with those at your table!

Which of the following is TRUE regarding a contingency table?

• A. It has the levels of one categorical variable along the top of the columns and the levels of a second categorical variable down the left side of the rows.

• B. It has the units of observation down the rows and the names of the variables recorded on each observation along the top of the columns.

• C. It has the levels of one numerical variable along the top of the columns and the levels of a second numerical variable down the left side of the rows.

• D. None of the above are true.

00:35

What proportion of those students in the marching band were juniors?

• A. 2/60
• B. 2/5
• C. 2/24
• D. 24/60

01:00

An example of a conditional proportion.

Which group is the largest among these voters?

• A. Independents with no degree
• B. Democrats with no degree
• C. Republicans with a degree
• D. We cannot tell with this plot.

The General Social Survey is a widely used sources of data on the attitudes, behaviors, and attributes of Americans. This plot shows the relationship between the political affiliation and college degree status of 500 participants.

Cannot tell which group is the largest since this plot as been normalized so that the proportions within each party sum to 1. The unnormalized plot on the following slide is one that allows us to answer this questions.

The unnormalized bar chart of counts preserves original counts and thus is good at comparing joint proportions. The normalized bar count shows condition proportions and thus is good for showing associations between variables.

00:30

You are running code that uses an external library. How many often do you need to load the library?

• A. Every time you run the piece of code in question.
• B. Once per .qmd document.
• C. Once every time you start an R session.
• D. None of these answers are correct.

00:30

How do you add a new layer to a ggplot visualization?

• A. With the ,.
• B. With the +.
• C. With the ;.
• D. Just start a new line.

00:30

Break

05:00

Now we can see which group is largest!

Worksheet: Summarizing Categorical Data

20:00

End of Lecture

Appendix: Practice!

Concept Questions

• The next few subquestions are based on the same table.

The table below displays data from a survey on a class of students.

What proportion of the class was in the marching band?

00:30

An example of a marginal proportion.

What proportion were sophomores not in the marching band?

00:30

An example of a joint proportion.

What were the dimensions of the raw data from which this table was constructed?

00:30

How would you characterize the association between these two variables?

00:30

CQ 3

What does this plot show? Important note: it looks like a leading “1” was cropped from the numbers along the y axis.

This is a confusing stacked bar chart! (unfortunately I wasn’t able to track down the source.)

The height of each total bar appears to be the energy supply from renewables worldwide in each of these years. The proportion on top, however, appears to be that number divided by the global total energy supply, which changes every year. The fact that those proportions are decreasing left to right as the bar heights are increasing suggests that renewables are increasing every year (the numerator) but the total energy supply (the denominator) is increasing at a faster rate.

01:00