STA 3024 Introduction to Statistics 2
Chapter 3: Contingency Tables
The next three chapters will investigate the association between variables. There are two
types of variables (categorical and quantitative) which implies 4 general types of associations
that we could investigate.
However, we shall only consider 3 of them.
The table below
outline the direction we are heading
Table 1: Methods to Investigate the Association between Variables
Explanatory Variable(s)
Response Variable
Method
Chapter 3
Categorical
Categorical
Contingency Tables
Chapter 4
Categorical
Quantitative
Analysis of Variance (ANOVA)
Chapter 5 and 6
Quantitative
Quantitative
Regression Analysis
Quantitative
Categorical
(not discussed)
This chapter looks at the case where both explanatory and response variable are categor
ical. We will learn how to test if the two variables are independent by using the chisquared
test. If they are dependent (have some kind of association), then we’ll learn how to describe
the strength and pattern of that association.
This chapter corresponds to Chapter 11 of our textbook.
1
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PART I  REVIEW AND REMARKS
A
contingency table
is a display for two categorical variables. A contingency table
shows how many subjects are at each combination of categories of two categorical variables.
Contingecy tables are especially important because they are often used to analyze survey
results. For example, we might ask subjects one question in which they identify their gen
der (male/female), and we might ask another question in which they describe the frequency
of their use of TV remote controls (often/sometimes/never). The methods of this section
can then be used to determine whether the use of TV remote controls is independent of
gender. (We probably already know the answer to that one.) Applications of this type are
very numerous, so the methods presented in this chapter are among those most often used.
We certaintly have seen a contigency table from section 3.1 of our chapter 1. But I do
see your exciment to see another example so here we go.
Example Age and Education:
Table 2 presents Census Bureau data for the year 2000
on the level of education reached by Americans of different ages.
Many people under 25
years of age have not completed their education, so they are left out of the table.
Both
variables, age and education, are grouped into categories. This is a contigency table because
it describes two categorical variables. Education is the row variable because each row in
the table describes people with one level of education. Age is the column variable because
each column describes one age group. The entries in the table are the counts of persons in
each agebyeducation class. Although both age and education in this table are categorical
variables, both have a natural order from least to most.
The order of the rows and the
columns in Table 2 reflects the order of the categories.
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 Spring '08
 TA
 Statistics, Normal Distribution, Probability theory, Chisquare distribution, Pearson's chisquare test, Categorical distribution

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