Chapter 10.4（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 10.4 Analysis of Variance . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Section 10.4 Objectives How to use one-way analysis of variance to test claims involving three or more means An introduction to two-way analysis of variance . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. One-Way ANOVA One-way analysis of variance It is a hypothesis-testing technique that is used to compare the means of three or more populations. Analysis of variance is usually abbreviated as ANOVA. . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. 5 Larson/Farber 4th ed Chapter 10 For a one-way ANOVA test, the null and alternative hypotheses are always similar to these statements. H0: μ1 = μ2 = μ3 =…= μk (all population means are equal) Ha: At least one of the means is different from the others. One-Way ANOVA 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. One-Way ANOVA Before performing a one-way ANOVA test, you must check that these conditions are satisfied. Each sample must be randomly selected from a normal, or approximately normal, population. The samples must be independent of each other. Each population must have the same variance. . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. One-Way ANOVA The test statistic for a one-way ANOVA test is the ratio of two variances. Test statistic = Mean square between, is denoted by MSB - The variance between samples measures the differences related to the treatment given to each sample. Mean square within, is denoted by MSW. - The variance within samples measures the differences related to entries within the same sample and is usually due to sampling error. . 1 Copyright 2019, 2015,