Chapter 3
Contingency Tables
Much of what we’ll do this semester can be condensed to a simple idea:
examining whether a response variable depends on one or more explanatory
variables, and if so, how. The procedures we’ll use will depend on whether
the variables involved are categorical or quantitative, as follows:
Explanatory Variable(s)
Response Variable
Methods
Categorical
Categorical
Contingency Tables
Categorical
Quantitative
ANOVA
Quantitative
Quantitative
Regression
Quantitative
Categorical
(not discussed)
We’ll start by looking at what to do when both the explanatory and
response variables are categorical. This chapter corresponds to Chapter 11
of the textbook.
3.1
Basics of Contingency Tables
First we’ll review the basic way we present data when both the explanatory
and response variables are categorical. You may have seen part or all of this
section before in your firstsemester statistics course.
◯
Displaying Data with Tables
When both the explanatory and response variables are categorical, each sub
ject can be classified into a particular combination of the variable values. We
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3.1 Basics of Contingency Tables
29
typically represent this using a table, called a
contingency table
or two
way table, with the explanatory variable values as rows and the response
variable values as columns. Each combination of explanatory and response
variable values constitutes a group of subjects, represented by a
cell
in the
table.
Note: This is always the setup we will use for contingency tables in this
course. You might also sometimes see contingency tables presented the
opposite way, with the explanatory variable values as columns and the
response variable values as rows. It would be okay to do things that
way instead, but everything we’re going to say in this chapter about
“rows” and “columns” would need to be reversed.
Example
3.1
:
We want to see if voters’ choices in the 2006 election for
governor of Florida (Charlie Crist, Jim Davis, or “other”) depended on their
level of education (no college, some college, or college degree). If we think
about the two variables together, there are nine different combinations, which
we can represent visually with a table:
Vote
Education
Crist
Davis
Other
No College
●
●
●
Some College
●
●
●
College Degree
●
●
●
Each individual in the population can be classified into one of these nine
groups, or cells in the table.
Populations and Samples
Usually we’re interested in the entire population.
We would like to know
the values of both variables for every member of the population, so we could
classify every individual subject. Instead, we typically have data only for a
sample. We can count how many subjects in the sample fall into each group
and fill in the cells of the contingency table with these
observed counts
from our sample.
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 Spring '08
 TA
 Normal Distribution, Variance, Probability theory, Statistical hypothesis testing, Pearson's chisquare test

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