Describing & Displaying Categorical Data

3 Rules of Data Analysis

1. Make a picture: a display of the data will reveal things that aren’t likely to be seen in a table of numbers and helps one THINK clearly about the patterns and relationships that might be hiding in the data

2. Make a picture: A well-designed display will SHOW the important features and pattern in the data. A picture will also show the unexpected things: the extraordinary (possibly wrong) data values or unexpected patterns

3. Make a picture: the best way to TELL others about data is with a well constructed picture

Making a picture will help someone…

THINK, SHOW, and TELL everything needed about a set of data

Reasons for making graphs

1. To understand data better

2. To show others what they have learned and what the want others to understand

Graphs need to be..

clear, correct, easy to understand, and HONEST

Good Graphs have..

• A title

• Clearly labeled axes

• A scale that’s appropriate for the data

• Appropriate colors or symbols with a key

Area Principle

A fundamental principle that states that the area occupied by a part of a graph should correspond to the magnitude of the value it represents

Frequency tables

The best and easiest way to summarize categorical variables; This table lists how many cases belong to each category (no overlap) (traditional =counts) (relative = %)

Bar Charts

Probably one of the most common and recognizable way to represent categorical data. its heights of its bars represent the frequency of the variable

Pie Charts

breaks the whole group into sections of a circle. Each “slice” is proportional to the fraction of a whole in each category

Contingency Tables

display counts and sometimes %s of individuals falling into names categories on 2 or more variables. Also categorizes the individuals on all variables at once to reveal possible patterns in one variable that may be contingent on the category of another

Marginal distribution

when the totals are in the margins

Conditional Distribution

shows the data is spread over ONE of the variables

Segmented bar chart

when one STACK the bars on top of each other with the benefits being that the differences become more obvious, the bars will always add up to 100%, and are great for comparing conditional distributions

Independent

When the distribution of one variable is the same for all categories of another in a contingency table. This means that there’s no association (relationship) between the variables

What Can go Wrong?

• Violating the Area Principle

• Not having an accurate visual representation of the data

• Confusing similar sounding %s

• Not looking at variables separately

• Not having enough individuals

• Overstating case

• Simpson’s paradox