Displaying and describing categorical data
- 2. The three rules of data analysis won’t be difficult to remember: 1. Make a picture—things may be revealed that are not obvious in the raw data. These will be things to think about. 2. Make a picture—important features of and patterns in the data will show up. You may also see things that you did not expect. 3. Make a picture—the best way to tell others about your data is with a well-chosen picture. The Three Rules of Data Analysis
- 3. We can “pile” the data by counting the number of data values in each category of interest. We can organize these counts into a frequency table, which records the totals and the category names. Frequency Tables
- 4. A relative frequency table is similar, but gives the percentages (instead of counts) for each category. Cumulative Frequency – calculates the sum of all relative frequencies for that particular category and all previous categories Relative Frequency Tables
- 5. Both types of tables show how cases are distributed across the categories. They describe the distribution of a categorical variable because they name the possible categories and tell how frequently each occurs. To calculate the relative frequency: Divide the count by the total number to cases Multiply by 100 to express as a percentage To calculate the cumulative relative frequency: Take the current category’s relative frequency and add it all previous relative frequencies Creating Frequency Tables
- 6. You might think that a good way to show the Titanic data is with this display. Is it? What’s Wrong With This Picture?
- 7. The ship display makes it look like most of the people on the Titanic were crew members, with a few passengers along for the ride. When we look at each ship, we see the area taken up by the ship, instead of the length of the ship. The ship display violates the area principle: The area occupied by a part of the graph should correspond to the magnitude of the value it represents. The Area Principle
- 8. A bar chart displays the distribution of a categorical variable, showing the counts for each category next to each other for easy comparison. A bar chart stays true to the area principle. Thus, a better display for the ship data is: Bar charts have spaces between the categories, while histograms do not. Bar Charts
- 9. A relative frequency bar chart displays the relative proportion of counts for each category. A relative frequency bar chart also stays true to the area principle. Replacing counts with percentages in the ship data: Bar Charts (cont.)
- 10. A relative frequency bar chart displays the relative proportion of counts for each category. A relative frequency bar chart also stays true to the area principle. Replacing counts with percentages in the ship data: Bar Charts (cont.)