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Ch 3 Notes - Contingency Tables

# Ch 3 Notes - Contingency Tables - Chapter 3 Contingency...

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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 first-semester 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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