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Chapter 3- Contingency Tables

# Chapter 3- Contingency Tables - STA 3024 Introduction to...

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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 chi-squared 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 age-by-education 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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Chapter 3- Contingency Tables - STA 3024 Introduction to...

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