Tabular and Graphical Representations of Data

8/24/11

Representing Categorical Data

• In a data table, it is not always possible to see what is truly happening with the data.

• When you break down a categorical variable and count the total number of cases that fit into each category, you can use that to create a frequency table.

• If you divide each of the values by the total count, you have a relative frequency table.

Representing Categorical Data

• Bar charts or bar graphs is a simple representation that converts the frequency tables into a visual representation.

• Pie charts turn relative frequency tables into a visual representation as well, but instead of using height to represent larger frequencies, it uses area.

Contingency Tables• If we want to look at more than one variable at a

time, we can create a contigency table. Example: The following compares survival on the Titanic with the method of travel. – The variable survival has two categories and the variable

Class has four categories. – Obviously, totals for both must be the same.

Class

Sur-vival

First Second Third Crew Total

Alive 203 118 178 212 711

Dead 122 167 528 673 1490

Total 325 285 706 885 2201

Conditional Distribution

• By limiting the scope to individual rows or columns of the contingency table, you can create conditional distributions.– The condition referred to is the characteristic

of the categorical variable.

• In elbow groups, define the conditional distributions for the characteristics “Alive” and “Dead”

Continued group work: Segmented bar chart.

• A segmented bar chart represents 100% of data by stacking bars instead of placing them next to each other. The added benefit is that we can make eyeball comparisons and very frequently we can make good decisions based on a visual comparison.

This is a segmented bar chart. What conclusions can be made by examining it?

In your elbow groups, create two side-by-side segmented bar charts for the conditional distributions of Alive and Dead.