Workshop Statistics: Discovery with Data, Fourth Edition

TOPIC 25

Inference for Two-Way Tables

One of the questions on the General Social Survey asks Americans how often they read the newspaper. Has the distribution of responses changed over the decades? Do the distributions differ for people with different political viewpoints? In this topic, you will investigate these issues and others that can be analyzed with the same statistical technique.

Overview

You will continue to study techniques for analyzing categorical variables in this topic. In Topic 21, you learned inference techniques for comparing two groups on a binary categorical response. In this topic, you will learn a technique that is more general in two respects: First, this technique lets you compare results across more than two groups. Second, the response variable can have more than two categories. The technique you will learn is a chi-square test for two-way tables. You first studied such tables in Topic 6 with descriptive methods such as segmented bar graphs and conditional proportions; now you will study an inferential method for generalizing to a larger population or drawing cause-and-effect conclusions. You will find this type of chi-square test has much in common with, though it also differs from, a chi-square goodness-of-fit test. Again, you will see the importance of considering how the data were collected before determining the scope of conclusions that can be drawn.

Preliminaries

1. How often do you read a newspaper? What about your parents? (Activity 25-1)
2. Would ...