Topic 4: Exploring Categorical Data

1. Topic 4: Exploring Categorical Data

2. Frequency tables and bar plots

3. Data matrix for emails Rows 1, 2, 3, and 3921 of a data matrix are displayed below. It contains data collected on 3,921 emails that were received.

4. Data matrix for emails Rows 1, 2, 3, and 3921 of a data matrix are displayed below. It contains data collected on 3,921 emails that were received. Categorical variables

5. Frequency Table • A table that summarizes data for a single categorical variable is called a frequency table. • A frequency table can display raw counts, proportions, or both. • Examples for the variable number are below. raw count

6. Frequency Table • A table that summarizes data for a single categorical variable is called a frequency table. • A frequency table can display raw counts, proportions, or both. • Examples for the variable number are below. raw count proportion

7. Frequency Table • A table that summarizes data for a single categorical variable is called a frequency table. • A frequency table can display raw counts, proportions, or both. • Examples for the variable number are below. raw count both proportion

8. Bar plot A bar plot is a graphical representation of a frequency table. raw count proportion

9. The order of the bars There is often a natural ordering for the bars, such as by class year in the example below.

10. Changing the order of the bars When the bars are ordered from highest count to lowest count, it is sometimes called a Pareto chart.

11. Bar plot vs. pie chart Pie charts are another way to graphically represent a frequency table. They are well known, but generally not as useful as bar plots.

12. Categorical data pairs: contingency tables, side-by-side bar plots, segmented bar plots, and mosaic plots

13. Recall the data matrix for emails Rows 1, 2, 3, and 3921 of a data matrix are displayed below. It contains data collected on 3,921 emails that were received. Categorical variables

14. Pairing two categorical variables Rows 1, 2, 3, and 3921 of a data matrix are displayed below. It contains data collected on 3,921 emails that were received.

15. Contingency Table • A table that summarizes data for two categorical variables is called a contingency table.

16. Row and column proportions Row proportions are computed using row totals, and column proportions using column totals.

17. Segmented bar plot vs. side-by-side bar plot

18. Segmented bar plot: count vs. proportion

19. Mosaic Plot

20. Mosaic Plot

21. Simpson’s Paradox

22. Example: long-term study on smoking A survey of 1,314 women in the United Kingdom during 1972-1974 asked each woman whether she was a smoker. Twenty years later, a follow-up survey observed whether each woman was dead or still alive. Below is a summary of the results.

23. Example: long-term study on smoking A survey of 1,314 women in the United Kingdom during 1972-1974 asked each woman whether she was a smoker. Twenty years later, a follow-up survey observed whether each woman was dead or still alive. Below is a summary of the results.

24. Example: long-term study on smoking A survey of 1,314 women in the United Kingdom during 1972-1974 asked each woman whether she was a smoker. Twenty years later, a follow-up survey observed whether each woman was dead or still alive. Below is a summary of the results.