Chapter 10.2（课件）- 《统计学基础（英文版）》同步教学（人民大学版）

Chapter Chi-Square Tests and the F-Distribution 10 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. 1 Larson/Farber 6th ed Chapter 1 Chapter Outline 10.1 Goodness-of-Fit Test 10.2 Independence 10.3 Comparing Two Variances 10.4 Analysis of Variance . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Section 10.2 Independence . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Section 10.2 Objectives How to use a contingency table to find expected frequencies How to use a chi-square distribution to test whether two variables are independent . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Contingency Tables r × c contingency table Shows the observed frequencies for two variables. The observed frequencies are arranged in r rows and c columns. The intersection of a row and a column is called a cell. . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Contingency Tables Example: The contingency table shows the results of a random sample of 2197 adults classified by their favorite way to eat ice cream and gender. (Adapted from Harris Poll) . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Finding the Expected Frequency for Contingency Table Cells Assuming the two variables are independent, you can use the contingency table to find the expected frequency for each cell. The expected frequency for a cell Er,c in a contingency table is . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Finding the Expected Frequency for Contingency Table Cells When you find the sum of each row and column in a contingency table, you are calculating the marginal frequencies. A marginal frequency is the frequency that an entire category of one of the variables occurs. The observed frequencies in the interior of a contingency table are called joint frequencies. . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Example: Finding Expected Frequencies Find the expected frequency for each cell in the contingency table. Assume that the variables, favo